CN111938641B - Optimized self-adaptive extended Kalman filtering bioelectrical impedance imaging method - Google Patents

Optimized self-adaptive extended Kalman filtering bioelectrical impedance imaging method Download PDF

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CN111938641B
CN111938641B CN202010817473.6A CN202010817473A CN111938641B CN 111938641 B CN111938641 B CN 111938641B CN 202010817473 A CN202010817473 A CN 202010817473A CN 111938641 B CN111938641 B CN 111938641B
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CN111938641A (en
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赵明康
郑天予
张帅
张雪莹
李颖
王宏斌
徐桂芝
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Hebei University of Technology
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Abstract

The invention discloses an optimized self-adaptive expansion Kalman filtering bioelectrical impedance imaging method, which relates to measuring the impedance of a certain part of a body, and rebuilding the impedance image of the lower limb of the human body by using the optimized self-adaptive expansion Kalman filtering bioelectrical impedance imaging method, and comprises the steps of establishing a mathematical model of the lower limb of the human body based on prior information of a real structure; solving a positive problem; solving an inverse problem by using an optimized self-adaptive extended Kalman filtering algorithm; and outputting the electrical impedance reconstruction image of the lower limb of the human body. According to the invention, the optimized self-adaptive correction coefficient is introduced in the reconstruction process to improve the weight occupied by observed quantity, the Kalman gain matrix is adjusted online, the stability of the Kalman algorithm in electrical impedance imaging is improved, and the defects that the existing disclosed bioelectrical impedance imaging technology has low noise resistance, cannot simultaneously have high accuracy of reconstructed images and small calculated quantity are overcome, and the existing Kalman filtering algorithm applied to reconstructed images has the defect that the algorithm accuracy may lose the original performance and filter divergence.

Description

一种优化自适应扩展卡尔曼滤波生物电阻抗成像方法An optimized adaptive extended Kalman filter bioelectrical impedance tomography method

技术领域Technical Field

本发明的技术方案涉及测量身体某个部位的电阻抗,具体地说是一种优化自适应扩展卡尔曼滤波生物电阻抗成像方法。The technical solution of the present invention relates to measuring the electrical impedance of a certain part of the body, specifically an optimized adaptive extended Kalman filter bioelectrical impedance imaging method.

背景技术Background Art

电阻抗成像技术(Electrical Impedance Tomography,EIT)是一种低成本、非侵入性的成像技术,通过放置在物体表面上的接触电极注入适当的电流模式来获得表面上的电势,从而测量具有高时间分辨率的表面电势值来估计物体横截面内部的电特性,例如电导率分布。电阻抗成像技术已用于工业,地球物理以及其他工程和应用科学领域。在地球物理学中,被用于定位地下矿藏资源分布。在石油开采中,已被用于监测注入流体流入地球的流量。生物电阻抗成像技术(Biological Electrical Impedance Imaging Tomography,BEIIT)中则是在人体皮肤上给予激励电流获得响应电压,由电流值和电压值产生图像表示人体的内部电导率分布的技术。在医学上,生物电阻抗成像技术已用于监测重症监护病房机械通气患者的吸入空气分布,也有文献报道了生物电阻抗成像技术被应用于胃排空、脑功能监测、乳房成像和肺功能评估。虽然到目前为止,电阻抗成像技术尚未在医疗机构中替代正电子发射断层扫描、计算机断层扫描一类方法,但由于它是一种无损伤、非侵入性、响应迅速且成本较低的成像技术,与使用有害辐射的其他医学成像技术相比,它不会引起任何副作用,因此具有潜在的临床应用价值。Electrical impedance tomography (EIT) is a low-cost, non-invasive imaging technology that obtains the potential on the surface by injecting appropriate current patterns through contact electrodes placed on the surface of the object, thereby measuring the surface potential value with high time resolution to estimate the electrical properties inside the cross-section of the object, such as the conductivity distribution. Electrical impedance tomography has been used in industry, geophysics, and other engineering and applied science fields. In geophysics, it is used to locate the distribution of underground mineral resources. In oil production, it has been used to monitor the flow of injected fluids into the earth. In bioelectrical impedance tomography (BEIIT), an excitation current is given to the human skin to obtain a response voltage, and an image is generated from the current value and voltage value to represent the internal conductivity distribution of the human body. In medicine, bioelectrical impedance tomography has been used to monitor the distribution of inhaled air in mechanically ventilated patients in intensive care units. There are also literature reports that bioelectrical impedance tomography has been applied to gastric emptying, brain function monitoring, breast imaging, and lung function assessment. Although electrical impedance tomography has not yet replaced methods such as positron emission tomography and computed tomography in medical institutions, it has potential clinical application value because it is a non-destructive, non-invasive, responsive and low-cost imaging technology. Compared with other medical imaging technologies that use harmful radiation, it does not cause any side effects.

然而,与使用其他辐射医学成像技的技术相比,现有生物电阻抗成像技术存在的逆问题是高度病态的。这是因为,其一,欠定性,电极数目有限电流流经路径有限,解的未知量远大于条件数,两者不匹配,所以解不是唯一的;其二,非线性,场域内的电位本身就是电导率分布的函数,通过表面电压测量值求解电导率是非线性问题;其三,不稳定性,边界电位对场域内部电导率变化不敏感,逆问题求解实质上是求微商,测量边界电压值微小变化会导致内部电导率巨大变化,使得求解过程不稳定。从上述分析可知,解电阻抗成像技术逆问题存在严重的不适定性。选择有效的算法可提高重构计算的稳定性和计算精度,达到生物电阻抗成像的图像具有高分辨率、成像时间短的目的。人体从地球重力环境到失重或超重环境,会导致体液发生转移,体液分为细胞外液和细胞内液。当细胞外液、细胞内液转移时,人体各组织的电导率也会发生变化,使用电阻抗成像技术生成人体不同部位的横截面图像,能够实现对长期在轨飞行的航天员健康状态进行连续监测和定期评估,针对这一场景,选用动态成像方式。动态成像方式具体分为经典算法和新型图像重建算法,例如神经网络、遗传算法。经典算法分为非迭代法和迭代法,有:线性反投影算法、Newton-Raphsom算法、Landweber算法、共轭梯度算法、截断奇异值分解算法,还有基于不同正则化法改进的算法。但是,这些算法无法同时解决伪影、分辨率低、抗干扰能力低、对目标要求高、连续成像的问题,如人体下肢、电导率变化时大时小、结构紧凑、如何获取连续失真小的生物电阻抗成像技术图像来反映真实腿部电导率分布从而为体液研究提供有价值的信息成为当前亟待解决的问题。However, compared with other radiation medical imaging technologies, the inverse problem of existing bioimpedance imaging technology is highly ill-posed. This is because, first, it is underdetermined. The number of electrodes is limited and the current flow path is limited. The unknown quantity of the solution is much larger than the condition number. The two do not match, so the solution is not unique. Second, it is nonlinear. The potential in the field is itself a function of the conductivity distribution. Solving the conductivity through the surface voltage measurement value is a nonlinear problem. Third, it is instability. The boundary potential is insensitive to the change of conductivity inside the field. Solving the inverse problem is essentially to find the derivative. A small change in the measured boundary voltage value will cause a huge change in the internal conductivity, making the solution process unstable. From the above analysis, it can be seen that there is a serious ill-posedness in solving the inverse problem of electrical impedance imaging technology. Selecting an effective algorithm can improve the stability and calculation accuracy of the reconstruction calculation, so as to achieve the purpose of high resolution and short imaging time of bioimpedance imaging images. When the human body moves from the earth's gravity environment to a weightless or overweight environment, body fluids will be transferred. Body fluids are divided into extracellular fluid and intracellular fluid. When the extracellular fluid and intracellular fluid are transferred, the conductivity of various tissues in the human body will also change. The use of electrical impedance imaging technology to generate cross-sectional images of different parts of the human body can realize continuous monitoring and regular evaluation of the health status of astronauts flying in orbit for a long time. For this scenario, dynamic imaging is selected. Dynamic imaging methods are specifically divided into classical algorithms and new image reconstruction algorithms, such as neural networks and genetic algorithms. Classical algorithms are divided into non-iterative methods and iterative methods, including: linear back projection algorithm, Newton-Raphsom algorithm, Landweber algorithm, conjugate gradient algorithm, truncated singular value decomposition algorithm, and algorithms improved based on different regularization methods. However, these algorithms cannot simultaneously solve the problems of artifacts, low resolution, low anti-interference ability, high target requirements, and continuous imaging. For example, the lower limbs of the human body, the conductivity changes from time to time, the structure is compact, and how to obtain continuous low-distortion bioelectrical impedance imaging technology images to reflect the real leg conductivity distribution and provide valuable information for body fluid research has become a problem that needs to be solved urgently.

现有公开的生物电阻抗成像技术有:CN106037650A公开了一种混合变差生物电阻抗成像方法,该方法将吉洪诺夫正则化与总变差正则化占不同权重来确定混合变差算法的目标函数,应用优化的L曲线自适应调节正则化参数,由最速下降法进行逆问题求解并进行胸腔电阻抗图像重建,上述现有技术方案存在实验模型过于理想化,而且目标单一、电导率分布均匀,抗噪能力低的缺陷;CN103462605A公开了一种生物电阻抗成像方法,正问题计算中采用非均匀剖分,逆问题采用标准粒子群法获得接近真实值的电阻抗分布值,并将其作为正则化高斯-牛顿算法的初始值,再通过正则化高斯-牛顿算法进行重建图像,该技术方案存在无法同时拥有重建图像精度高和计算量小的缺陷;The currently disclosed bioimpedance imaging technologies include: CN106037650A discloses a mixed variation bioimpedance imaging method, which determines the objective function of the mixed variation algorithm by assigning different weights to Tikhonov regularization and total variation regularization, and uses the optimized L curve to adaptively adjust the regularization parameter, solves the inverse problem by the steepest descent method, and reconstructs the chest impedance image. The above-mentioned prior art solutions have the defects of over-idealization of the experimental model, single target, uniform conductivity distribution, and low noise resistance; CN103462605A discloses a bioimpedance imaging method, which adopts non-uniform partitioning in the forward problem calculation, adopts the standard particle swarm method in the inverse problem to obtain the impedance distribution value close to the true value, and uses it as the initial value of the regularized Gauss-Newton algorithm, and then reconstructs the image by the regularized Gauss-Newton algorithm. The technical solution has the defect that it cannot simultaneously have high reconstructed image accuracy and small calculation amount;

卡尔曼滤波(Kalman Filtering,KF)算法是通过当前时刻的前一时刻的预测值和当前时刻的测量值的协方差递归运算的一种基于数值最优估计的新型图像重建算法,更新求解过程中,滤波卡尔曼增益权重可以随不同的时刻而改变自己的值,并且只保留前一时刻的协方差值,因此其运行速度快求解精确度高。但卡尔曼滤波算法的性能取决于系统数学模型的准确性和噪声统计特性的完整性。然而,在实际应用中是无法建立精确、一模一样的数学模型的,其噪声特性很难被恰当地描述,也不具备对噪声统计变化的自适应力,从而导致卡尔曼滤波算法不稳定精度下降甚至发散,最为关键的是只针对线性系统。针对解决非线性问题,提出了扩展卡尔曼滤波(Extended Kalman Filtering,EKF)算法,这也是在非线性系统中使用的最广泛的方法。扩展卡尔曼滤波算法利用泰勒级数展开对非线性系统进行局部线性化,扩大了卡尔曼滤波方程的适用范围。扩展卡尔曼滤波算法保留了许多与卡尔曼滤波相关的计算效率优势。由于扩展卡尔曼滤波算法对非线性函数进行低阶泰勒级数展开,将高阶部分截去,导致精度在应用时并不能满足系统要求。The Kalman Filtering (KF) algorithm is a new image reconstruction algorithm based on numerical optimal estimation, which recursively calculates the covariance of the predicted value at the previous moment and the measured value at the current moment. During the updating and solving process, the filter Kalman gain weight can change its value at different moments, and only retains the covariance value at the previous moment, so it runs fast and has high solving accuracy. However, the performance of the Kalman filter algorithm depends on the accuracy of the system mathematical model and the integrity of the noise statistical characteristics. However, in practical applications, it is impossible to establish an accurate and identical mathematical model, its noise characteristics are difficult to be properly described, and it does not have the ability to adapt to the changes in noise statistics, which leads to the instability of the Kalman filter algorithm, the decrease in accuracy and even divergence. The most critical thing is that it is only for linear systems. In order to solve nonlinear problems, the Extended Kalman Filtering (EKF) algorithm is proposed, which is also the most widely used method in nonlinear systems. The Extended Kalman Filtering algorithm uses Taylor series expansion to locally linearize the nonlinear system, expanding the scope of application of the Kalman filter equation. The extended Kalman filter algorithm retains many of the computational efficiency advantages associated with the Kalman filter. However, since the extended Kalman filter algorithm performs a low-order Taylor series expansion on the nonlinear function and cuts off the high-order part, the accuracy does not meet the system requirements when applied.

现有公开的卡尔曼滤波算法应用的技术有:CN101499173B公开了一种PET成像中卡尔曼滤波图像重建方法,通过PET正电子发射断层扫描仪得到原始投影线的正弦图,然后建立状态空间体系,通过基于状态空间的卡尔曼滤波法得出放射性活度分布以重建图像,该技术方案存在运算量大、重建速度慢的缺陷;CN106097285B公开了一种基于自适应扩展卡尔曼滤波的ECT图像重建方法,该方案存在当系统模型,系统输入有偏差或实际数据突变时,无法在线实时修正卡尔曼增益,导致该算法精度可能会丧失原有性能的缺陷;1998年Vauhkonen等人将卡尔曼滤波算法引入到电阻抗层析成像中;2010年薛永文等发表的论文《修正的扩展卡曼滤波器在EIT中的应用》,文中对Flavio Celso Trigo等在论文《Electrical Impedance tomography Using The ExtebdedKalman Filter》中给出的扩展卡尔曼方程组进行了修正,上述技术方案存在随着测量次数增加图像相对误差越来越大且出现失真,表现为算法的预测值与实际值之间的绝对值的差值会逐渐增大,即滤波器发散的缺陷。The existing technologies for applying Kalman filter algorithms are as follows: CN101499173B discloses a Kalman filter image reconstruction method in PET imaging, wherein a sinusoidal diagram of the original projection line is obtained by a PET positron emission tomography scanner, and then a state space system is established, and the radioactivity distribution is obtained by a Kalman filter method based on the state space to reconstruct the image. This technical solution has the defects of large amount of calculation and slow reconstruction speed; CN106097285B discloses an ECT image reconstruction method based on an adaptive extended Kalman filter, which has the defect that when the system model and system input are biased or the actual data suddenly changes, the Kalman gain cannot be corrected online in real time, resulting in the algorithm accuracy may lose the original performance; Vauhkonen et al. introduced the Kalman filter algorithm into electrical impedance tomography in 1998; Xue Yongwen et al. published a paper entitled "Application of Modified Extended Kalman Filter in EIT" in 2010, which reviewed the paper entitled "Electrical Impedance tomography Using The Extebded Kalman Filter" by Flavio Celso Trigo et al. The extended Kalman equations given in "Filter" have been corrected. The above technical solution has the defect that the relative error of the image becomes larger and larger and distortion occurs as the number of measurements increases, which is manifested as the absolute value difference between the predicted value of the algorithm and the actual value gradually increases, that is, the defect of filter divergence.

总之,现有公开的生物电阻抗成像技术存在抗噪能力低,无法同时拥有重建图像精度高和计算量小的缺陷,现有公开的卡尔曼滤波算法应用于重建图像中尚存在算法精度可能会丧失原有性能和滤波器发散的缺陷。In summary, the existing publicly available bioelectrical impedance imaging technology has the defects of low noise resistance and inability to simultaneously have high image reconstruction accuracy and low computational complexity. The existing publicly available Kalman filtering algorithm applied to image reconstruction still has the defects of possible loss of original performance of the algorithm accuracy and filter divergence.

发明内容Summary of the invention

本发明所要解决的技术问题是:提供一种优化自适应扩展卡尔曼滤波生物电阻抗成像方法,用优化自适应扩展卡尔曼滤波生物电阻抗成像方法进行人体下肢电阻抗图像的重建,包括建立基于真实结构先验信息的人体下肢数学模型;求解正问题;用优化自适应扩展卡尔曼滤波算法求解逆问题;人体下肢电阻抗重建图像的输出。本发明在重建过程中引入优化自适应修正系数提高观测量所占权重,在线调整卡尔曼增益矩阵,提高了卡尔曼算法在电阻抗成像中的稳定性,克服了现有公开的生物电阻抗成像技术存在抗噪能力低,无法同时拥有重建图像精度高和计算量小的缺陷,现有公开的卡尔曼滤波算法应用于重建图像中尚存在算法精度可能会丧失原有性能和滤波器发散的缺陷。The technical problem to be solved by the present invention is: to provide an optimized adaptive extended Kalman filter bioelectrical impedance imaging method, and to reconstruct the electrical impedance image of the lower limbs of the human body by using the optimized adaptive extended Kalman filter bioelectrical impedance imaging method, including establishing a mathematical model of the lower limbs of the human body based on real structural prior information; solving the direct problem; solving the inverse problem by using the optimized adaptive extended Kalman filter algorithm; and outputting the electrical impedance reconstruction image of the lower limbs of the human body. The present invention introduces an optimized adaptive correction coefficient in the reconstruction process to increase the weight of the observed quantity, and adjusts the Kalman gain matrix online, thereby improving the stability of the Kalman algorithm in electrical impedance imaging, overcoming the defects of the existing disclosed bioelectrical impedance imaging technology, such as low noise resistance, and the inability to simultaneously have high reconstructed image accuracy and small calculation amount. The existing disclosed Kalman filter algorithm is applied to the reconstructed image, and there are still defects that the algorithm accuracy may lose the original performance and the filter diverges.

本发明解决该技术问题所采用的技术方案是:一种优化自适应扩展卡尔曼滤波生物电阻抗成像方法,具体步骤如下:The technical solution adopted by the present invention to solve the technical problem is: an optimized adaptive extended Kalman filter bioelectrical impedance imaging method, the specific steps are as follows:

A.设置进行优化自适应扩展卡尔曼滤波电阻抗成像所用的装置:A. Set up the device used for optimizing adaptive extended Kalman filter electrical impedance imaging:

进行优化自适应扩展卡尔曼滤波电阻抗成像所用装置采用模块化设计,是串联与并联混合式的结构,其构成包括计算机模块、通信模块、总控与处理模块、电压/电流恒流输出模块、激励通道选通模块、测量通道选通模块、电极阵列和信号调制模块;计算机模块用来控制总控与处理模块和自适应扩展卡尔曼滤波成像算法的程序运行,总控与处理模块通过通信模块接收来自计算机模块的指令并通过数据总线、地址总线和控制总线实现对电阻抗成像装置系统的控制与协调各模块之间的工作,实时精准完成对硬件系统各模块的控制并通过通信模块及时反馈给计算机模块信息以做出相应调整,电压/电流转换恒流输出模块用于产生正弦电压信号,再经过隔离、滤波、电压增益电路、电压/电流转换恒流源电路,将电压转换成电流,总控与处理模块通过通信模块控制该模块电压信号的频率、幅值和相位,实施对激励信号频率、幅值和相位的调整,激励通道选通模块接收来自总控与处理模块的指令采用低导通电阻的模拟多路来选择和切换电极阵列中的注入模式,将电流信号通过相应的电极注入被测对象,建立敏感区域,测量通道选通模块接收来自总控与处理模块的指令选择和切换电极阵列的测量模式,将提取到的被测对象电压信号送到信号调制模块,信号调制模块通过仪表放大电路、滤波电路、解调电路、可变增益放大电路、低通滤波器和A/D转换电路,对测量通道选通模块输入过来的电压信号处理成数字信号,通过总控与处理模块与通信模块实时将数字电压信号传入计算机模块,计算机将采集的电压数据和电流数据通过自适应扩展卡尔曼滤波算法进行图像重建成像;The device used for optimizing the adaptive extended Kalman filter electrical impedance imaging adopts a modular design and is a hybrid structure of series and parallel connections. It consists of a computer module, a communication module, a master control and processing module, a voltage/current constant current output module, an excitation channel gating module, a measurement channel gating module, an electrode array and a signal modulation module; the computer module is used to control the program operation of the master control and processing module and the adaptive extended Kalman filter imaging algorithm, the master control and processing module receives instructions from the computer module through the communication module and controls the electrical impedance imaging device system and coordinates the work between the modules through the data bus, address bus and control bus, and accurately controls the modules of the hardware system in real time and feeds back information to the computer module in time through the communication module to make corresponding adjustments, the voltage/current conversion constant current output module is used to generate a sinusoidal voltage signal, and then converts the voltage into current through isolation, filtering, voltage gain circuit, and voltage/current conversion constant current source circuit, the master control and processing module The processing module controls the frequency, amplitude and phase of the voltage signal of the module through the communication module, and adjusts the frequency, amplitude and phase of the excitation signal. The excitation channel gating module receives instructions from the master control and processing module and uses low on-resistance analog multi-channel to select and switch the injection mode in the electrode array, injects the current signal into the object under test through the corresponding electrode, and establishes a sensitive area. The measurement channel gating module receives instructions from the master control and processing module to select and switch the measurement mode of the electrode array, and sends the extracted voltage signal of the object under test to the signal modulation module. The signal modulation module processes the voltage signal input from the measurement channel gating module into a digital signal through an instrument amplifier circuit, a filter circuit, a demodulation circuit, a variable gain amplifier circuit, a low-pass filter and an A/D conversion circuit, and transmits the digital voltage signal to the computer module in real time through the master control and processing module and the communication module. The computer reconstructs the collected voltage data and current data through an adaptive extended Kalman filter algorithm.

B.用优化自适应扩展卡尔曼滤波生物电阻抗成像方法进行人体下肢电阻抗图像的重建,其技术方案如下:B. The optimized adaptive extended Kalman filter bioimpedance imaging method is used to reconstruct the electrical impedance image of the human lower limbs. The technical scheme is as follows:

第一步,建立基于真实结构先验信息的人体下肢数学模型;The first step is to establish a mathematical model of the human lower limbs based on real structural prior information;

第二步,求解正问题;The second step is to solve the positive problem;

第三步,用优化自适应扩展卡尔曼滤波算法求解逆问题;The third step is to solve the inverse problem using the optimized adaptive extended Kalman filter algorithm;

第四步,人体下肢电阻抗重建图像的输出:Step 4: Output of the human lower limb electrical impedance reconstruction image:

由上述A所述设置进行卡尔曼滤波生物电阻抗成像所用的装置来输出B所述的用自适应扩展卡尔曼滤波生物电阻抗成像方法进行人体下肢电阻抗图像的重建得到的胸腔电阻抗图像,具体实施过程如下:The apparatus for Kalman filter bioelectrical impedance imaging described in A is used to output the chest electrical impedance image obtained by reconstructing the electrical impedance image of the human lower limbs using the adaptive extended Kalman filter bioelectrical impedance imaging method described in B. The specific implementation process is as follows:

在计算机模块写入激励人体腿部电流的幅值和频率,将激励信号通过电极阵列施加至人体腿部即被测对象表面,通过电极测量腿部电压信号并传入计算机,通过调用优化自适应扩展卡尔曼滤波算法程序成像;总控与处理模块为本发明所以装置的核心,由通信模块发出与接收来自计算机模块的控制指令,实现对上述A所述装置的硬件系统的全局控制和协调运行工作;电压/电流恒流输出模块用于将产生1kHz-1MHz范围内可调的正弦波信号,转换成幅值在0.1mA-5mA范围内可调节的电流信号,通过激励通道选通模块,实现激励电极的开与关,使激励信号按照设定的方式流入相应的电极,注入被测对象;通过控制测量通道选通模块实现测量电极的开与关,使测量电极中相应电极提取被测对象电压信号,便将信号送入信号调制模块;再由信号调理模块内部的仪表放大电路、滤波电路、解调电路、可变增益放大电路、低通滤波器和A/D转换电路对测量通道选通模块输入过来的电压信号处理成数字信号;然后再将数字电压信号由通信模块传入计算机模块,将数字电压信号转换为模拟电压信号,通过优化自适应扩展卡尔曼滤波算法程序实现腿部电阻抗图像重建,最后通过计算机输出人体下肢电阻抗重建图像;The amplitude and frequency of the current that stimulates the human leg are written into the computer module, and the excitation signal is applied to the human leg, i.e., the surface of the object to be measured, through the electrode array. The voltage signal of the leg is measured through the electrode and transmitted to the computer, and imaging is performed by calling the optimized adaptive extended Kalman filter algorithm program; the general control and processing module is the core of all devices of the present invention, and the communication module sends and receives control instructions from the computer module to realize the global control and coordinated operation of the hardware system of the device described in A above; the voltage/current constant current output module is used to convert the adjustable sine wave signal in the range of 1kHz-1MHz into an adjustable current signal in the range of 0.1mA-5mA, and realize the opening and closing of the excitation electrode through the excitation channel selection module, so that the excitation The excitation signal flows into the corresponding electrode in a set manner and is injected into the object to be measured; the measuring electrode is turned on and off by controlling the measuring channel gating module, so that the corresponding electrode in the measuring electrode extracts the voltage signal of the object to be measured, and then the signal is sent to the signal modulation module; the voltage signal input from the measuring channel gating module is processed into a digital signal by the instrument amplifier circuit, filter circuit, demodulation circuit, variable gain amplifier circuit, low-pass filter and A/D conversion circuit inside the signal conditioning module; the digital voltage signal is then transmitted to the computer module from the communication module, the digital voltage signal is converted into an analog voltage signal, and the leg electrical impedance image reconstruction is realized by optimizing the adaptive extended Kalman filter algorithm program, and finally the human lower limb electrical impedance reconstruction image is output through the computer;

至此,完成用优化自适应扩展卡尔曼滤波生物电阻抗成像方法进行人体下肢电阻抗图像的重建,得到人体下肢电阻抗图像。At this point, the reconstruction of the human lower limb electrical impedance image using the optimized adaptive extended Kalman filter bioimpedance imaging method is completed, and the human lower limb electrical impedance image is obtained.

上述一种优化自适应扩展卡尔曼滤波生物电阻抗成像方法,所述第一步建立基于真实结构先验信息的人体下肢数学模型的具体方法如下:In the above-mentioned optimized adaptive extended Kalman filter bioelectrical impedance imaging method, the specific method of the first step of establishing a mathematical model of the human lower limb based on real structural prior information is as follows:

(1.1)腿部CT图像预处理:(1.1) Leg CT image preprocessing:

采用改进Perona&Malik模型基于偏微分方程的图像方法消除边缘噪声以提高轮廓线提取精度,具体操作如下:The improved Perona&Malik model is used to eliminate edge noise based on partial differential equations to improve the accuracy of contour extraction. The specific operations are as follows:

设x0(a,b)为腿部的CT灰度图像,引入时间变量t∈[0,T],改进的Perona&Malik偏微分方程为如下公式(1)所示,Assume x 0 (a, b) is the CT grayscale image of the leg, introduce the time variable t∈[0,T], and the improved Perona&Malik partial differential equation is shown in the following formula (1):

公式(1)中,Gτ为高斯平滑模板,τ为高斯核的尺度,为图像梯度模,c为扩散系数用于控制扩散速度;In formula (1), G τ is the Gaussian smoothing template, τ is the scale of the Gaussian kernel, is the image gradient modulus, c is the diffusion coefficient used to control the diffusion speed;

由此完成腿部CT图像预处理;Thus, the leg CT image preprocessing is completed;

(1.2)获得腿部及内部各组织的边缘图像:(1.2) Obtain edge images of the legs and internal tissues:

采用腐蚀、膨胀的图像处理的阈值分割算法,首先对上述步骤(1.1)腿部CT图像预处理后的图像进行二值化处理,然后去除检查床提取腿部轮廓,再利用去除检查床的图像减去腿部轮廓图像,即得到腿部轮廓图像,同样操作,得到肌肉轮廓图像、脂肪轮廓图像和骨头轮廓图像,最后通过对腿部轮廓、肌肉轮廓、脂肪轮廓和骨头轮廓的融合,获得腿部及内部各组织的边缘图像;The threshold segmentation algorithm of the image processing of corrosion and expansion is adopted. First, the image of the leg CT image preprocessed in the above step (1.1) is binarized, and then the leg contour is extracted by removing the examination bed. Then, the leg contour image is subtracted from the image without the examination bed to obtain the leg contour image. The muscle contour image, fat contour image and bone contour image are obtained by the same operation. Finally, the edge image of the leg and its internal tissues is obtained by fusing the leg contour, muscle contour, fat contour and bone contour.

(1.3)提取腿部及内部各组织的边缘图像的轮廓线坐标:(1.3) Extract the contour coordinates of the edge image of the leg and internal tissues:

对上述步骤(1.2)获得的腿部及内部各组织的边缘图像采用基于二值图像的轮廓提取算法提取腿部及内部各组织的边缘图像的轮廓线坐标,具体操作方法如下:The edge image of the leg and its internal tissues obtained in the above step (1.2) is used to extract the contour line coordinates of the edge image of the leg and its internal tissues using a contour extraction algorithm based on a binary image. The specific operation method is as follows:

设y(c,d)为上述步骤(1.2)获得的腿部及内部各组织的边缘图像的像素点,Y(c,d)为应用二值化规则处理后获得的腿部及内部各组织的边缘图像的像素点,用如下所示公式(2)判断当前像素是否为腿部、肌肉、脂肪和骨头轮廓边界像素,Let y(c, d) be the pixel point of the edge image of the leg and its internal tissues obtained in the above step (1.2), and Y(c, d) be the pixel point of the edge image of the leg and its internal tissues obtained after applying the binarization rule. Use the following formula (2) to determine whether the current pixel is a leg, muscle, fat, or bone contour boundary pixel.

公式(2)中,当Y(c,d)=0时,当前像素不是轮廓边界像素点,不保留,当Y(c,d)=1时,当前像素是轮廓边界像素点,该当前像素点保留,应用此规则对上述步骤(1.2)得到的图像的每个像素进行处理,保留在图像中的像素为轮廓线坐标,由此完成了腿部及内部各组织的边缘图像的轮廓线坐标的提取;In formula (2), when Y(c, d) = 0, the current pixel is not a contour boundary pixel and is not retained. When Y(c, d) = 1, the current pixel is a contour boundary pixel and is retained. This rule is applied to process each pixel of the image obtained in step (1.2) above. The pixels retained in the image are the contour line coordinates, thereby completing the extraction of the contour line coordinates of the edge image of the leg and internal tissues.

(1.4)构建人体下肢仿真数学模型:(1.4) Constructing a mathematical model of human lower limb simulation:

基于上述步骤(1.3)中获得的腿部及内部各组织的边缘图像的轮廓线坐标,运用有限元仿真软件建立人体下肢仿真数学模型;Based on the contour line coordinates of the edge images of the legs and internal tissues obtained in the above step (1.3), a finite element simulation software is used to establish a simulation mathematical model of the human lower limbs;

至此,完成建立基于真实结构先验信息的人体下肢数学模型。At this point, the mathematical model of the human lower limbs based on real structural prior information has been completed.

上述一种优化自适应扩展卡尔曼滤波生物电阻抗成像方法,所述第二步求解正问题的具体方法如下:In the above-mentioned optimized adaptive extended Kalman filter bioelectrical impedance imaging method, the specific method of solving the positive problem in the second step is as follows:

(2.1)定义人体下肢数学模型的物理特性;(2.1) Define the physical characteristics of the mathematical model of the human lower limbs;

(2.2)对人体下肢数学模型离散化处理;(2.2) Discretization of the mathematical model of the human lower limbs;

(2.3)施加边界条件;(2.3) Apply boundary conditions;

(2.4)计算边界电压值;(2.4) Calculate the boundary voltage value;

由此完成求解正问题。This completes the solution to the positive problem.

上述一种优化自适应扩展卡尔曼滤波生物电阻抗成像方法,所述第三步用优化自适应扩展卡尔曼滤波算法求解逆问题的具体方法如下:In the above-mentioned optimized adaptive extended Kalman filter bioelectrical impedance imaging method, the specific method of using the optimized adaptive extended Kalman filter algorithm to solve the inverse problem in the third step is as follows:

(3.1)建立状态方程和观测方程:(3.1) Establish the state equation and observation equation:

(3.1.1)建立状态方程:(3.1.1) Establish the state equation:

所建立的状态方程如下公式(3)所示,The established state equation is shown in the following formula (3):

σk=Ak-1σk-1k-1 (3),σ k =A k-1 σ k-1k-1 (3),

公式(3)中,σk为k时刻阻抗值,σk-1为k-1时刻阻抗值,Ak-1∈Rm×m,m为有限元模型剖分后单元的个数,采用随机游走模式,则Ak-1=Im,Im为单位矩阵,ωk-1为k-1时刻的系统噪声,该系统噪声设置为白噪声序列,其满足如下公式(4),In formula (3), σ k is the impedance value at time k, σ k-1 is the impedance value at time k-1, A k-1 ∈R m×m , m is the number of units after the finite element model is segmented, and the random walk mode is adopted, then A k-1 =I m , I m is the unit matrix, ω k-1 is the system noise at time k-1, and the system noise is set as a white noise sequence, which satisfies the following formula (4),

E(ωk-1)=0,E(ωk-1ωk-1 T)=Qk-1 (4),E(ω k-1 )=0,E(ω k-1 ω k-1 T )=Q k-1 (4),

公式(4)中,E为数学期望符号,Qk-1为k-1时刻ωk-1的协方差矩阵;In formula (4), E is the mathematical expectation symbol, Q k-1 is the covariance matrix of ω k-1 at time k-1;

(3.1.2)建立观测方程:(3.1.2) Establish the observation equation:

(3.1.2.1)建立非线性方程:(3.1.2.1) Establish the nonlinear equation:

所建立的非线性方程如下公式(5)所示,The established nonlinear equation is shown in the following formula (5):

uk=Ukk)+νk (5),u k =U kk )+ν k (5),

公式(5)中,uk为边界电压测量向量,Ukk)为边界电压测量值与阻抗值之间的非线性关系,vk为k时刻观测噪声,vk与ωk-1不相关,设置为白噪声序列,其满足如下公式(6),In formula (5), uk is the boundary voltage measurement vector, Uk ( σk ) is the nonlinear relationship between the boundary voltage measurement value and the impedance value, vk is the observation noise at time k, vk is uncorrelated with ωk-1 and is set as a white noise sequence, which satisfies the following formula (6):

E(νk)=0,E(νkνk T)=Rk,E(ωkνk T)=0 (6),E(ν k )=0,E(ν k ν k T )=R k ,E(ω k ν k T )=0 (6),

公式(6)中,Rk为k时刻vk的协方差矩阵;In formula (6), R k is the covariance matrix of v k at time k;

(3.1.2.2)对(3.2.2.1)中的非线性方程进行一阶泰勒级数展开:(3.1.2.2) Perform a first-order Taylor series expansion on the nonlinear equation in (3.2.2.1):

如下公式(7)为对上述步骤(3.2.2.1)中的非线性方程进行的一阶泰勒级数展开,The following formula (7) is the first-order Taylor series expansion of the nonlinear equation in the above step (3.2.2.1),

uk=Uk0)+Jk0)·(σk0)+νk (7),u k =U k0 )+J k0 )·(σ k0 )+ν k (7),

公式(7)中,Jk0)为雅可比矩阵,其计算公式为如下公式(8)所示,In formula (7), J k0 ) is the Jacobian matrix, and its calculation formula is shown in the following formula (8):

(3.1.2.3)建立观测方程:(3.1.2.3) Establish the observation equation:

进而建立观测方程如下公式(9)所示,Then the observation equation is established as shown in the following formula (9):

zk=Jσkk (9),z k =Jσ kk (9),

公式(9)中,zk为边界电压测量值,J为灵敏度矩阵,σk为阻抗值;In formula (9), z k is the boundary voltage measurement value, J is the sensitivity matrix, and σ k is the impedance value;

(3.2)设置初始值σ0(3.2) Set the initial value σ 0 :

所设置的初始值σ0为如下公式(10)所示,The initial value σ 0 is set as shown in the following formula (10):

σ0=0,C0=∞ (10),σ 0 =0,C 0 =∞ (10),

公式(10)中,C0为误差协方差矩阵初始值;In formula (10), C 0 is the initial value of the error covariance matrix;

(3.3)由k-1时刻得到k时刻的目标状态预测方程:(3.3) The target state prediction equation at time k is obtained from time k-1:

由k-1时刻得到k时刻的目标状态预测方程如下公式(11)所示,The target state prediction equation at time k is obtained from time k-1 as shown in the following formula (11):

公式(11)中,为σk的先验估计,即预测值;In formula (11), is the prior estimate of σ k , i.e. the predicted value;

(3.4)计算k时刻误差协方差矩阵的先验估计 (3.4) Calculate the prior estimate of the error covariance matrix at time k

由如下公式(12)计算k时刻误差协方差矩阵的先验估计 The prior estimate of the error covariance matrix at time k is calculated by the following formula (12):

公式(12)中,γk为自适应修正系数,其计算方法如下公式(13)所示,In formula (12), γ k is the adaptive correction coefficient, and its calculation method is shown in the following formula (13):

公式(13)中,trace为迹符号,为新息序列的协方差矩阵,其的计算方法如下公式(14)所示,In formula (13), trace is the trace symbol, is the covariance matrix of the new information sequence, and its calculation method is shown in the following formula (14):

公式(14)中,ξk为新息序列,其计算方法如下公式(15)所示,In formula (14), ξ k is the new information sequence, and its calculation method is shown in the following formula (15):

公式(15)中,zk为边界电压测量值,为zk的预测值;In formula (15), zk is the measured value of the boundary voltage, is the predicted value of z k ;

γk取值范围如下公式(16)所示,The value range of γ k is shown in the following formula (16):

(3.5)计算扩展卡尔曼增益矩阵:(3.5) Calculate the extended Kalman gain matrix:

由如下公式(17)计算扩展卡尔曼增益矩阵KkThe extended Kalman gain matrix K k is calculated by the following formula (17):

公式(17)中,Kk为卡尔曼增益矩阵;In formula (17), K k is the Kalman gain matrix;

(3.6)计算k时刻误差协方差矩阵:(3.6) Calculate the error covariance matrix at time k:

由如下k时刻的状态更新方程即公式(18)来计算k时刻的阻抗值σkThe impedance value σ k at time k is calculated by the following state update equation at time k, that is, formula (18):

(3.7)计算k时刻误差协方差矩阵Ck(3.7) Calculate the error covariance matrix C k at time k:

公式(19)中,I为单位矩阵;In formula (19), I is the unit matrix;

(3.8)判断是否继续递推预测,当确定为“是”时,回转至上述步骤(3.3),当确定为“否”时,则跳转至下面的第四步;(3.8) Determine whether to continue recursive prediction. If it is determined to be "yes", go back to the above step (3.3). If it is determined to be "no", jump to the fourth step below;

由此完成用优化自适应扩展卡尔曼滤波算法求解逆问题。This completes the solution of the inverse problem using the optimized adaptive extended Kalman filter algorithm.

上述一种优化自适应扩展卡尔曼滤波生物电阻抗成像方法,其中,进行生物电阻抗成像所用装置是通过公知途径获得的,所涉及的操作方法,所述改进Perona&Malik模型基于偏微分方程的图像方法是本技术领域中所公知的。The above-mentioned optimized adaptive extended Kalman filter bioelectrical impedance imaging method, wherein the device used for bioelectrical impedance imaging is obtained through a well-known way, and the operation method involved, and the improved Perona&Malik model based on partial differential equations are well known in the technical field.

本发明的有益效果是:与现有技术相比,本发明方法具有如下实质性的特点和显著进步:The beneficial effects of the present invention are: compared with the prior art, the method of the present invention has the following substantial characteristics and significant improvements:

(1)CN106037650A一种混合变差生物电阻抗成像方法是本申请人早先申请的发明专利,实践证明,该早先申请的发明专利存在实验模型过于理想化,而且目标单一、电导率分布均匀,抗噪能力低的缺陷。为了克服CN106037650A技术存在的缺陷,本发明的发明人团队基于真实人体下肢先验信息进行数学模型的构建,对于目标多、电导率分布不均匀的成像效果好,算法在重建过程中稳定性好且引入自适应修正系数调整预测值所占比重,提高新测量数据比重,有效精确地跟踪目标区域的动态变化趋势及计算其具体状态,提高了图像重建分辨率,既能保证算法精度又具有实时性,当数据成阶梯式变化时,图像重建算法能实时快速稳定收敛。在CN106037650A的基础上获得现在的本发明要求保护的技术方案不是本领域技术人员轻而易举就能得到的。(1) CN106037650A, a hybrid variation bioelectrical impedance imaging method, is an invention patent previously applied for by the applicant. Practice has proved that the invention patent previously applied for has the defects of over-idealization of the experimental model, single target, uniform conductivity distribution, and low noise resistance. In order to overcome the defects of the CN106037650A technology, the inventor team of the present invention constructs a mathematical model based on the prior information of the lower limbs of the real human body. The imaging effect is good for multiple targets and uneven conductivity distribution. The algorithm has good stability during the reconstruction process and introduces an adaptive correction coefficient to adjust the proportion of the predicted value, increase the proportion of new measurement data, effectively and accurately track the dynamic change trend of the target area and calculate its specific state, improve the image reconstruction resolution, and ensure both algorithm accuracy and real-time performance. When the data changes in a step-by-step manner, the image reconstruction algorithm can converge quickly and stably in real time. It is not easy for a person skilled in the art to obtain the technical solution claimed by the present invention on the basis of CN106037650A.

(2)与CN103462605A一种生物电阻抗成像方法相比,本发明具有的突出的实质性特点和显著进步是利用新息协方差计算得到自适应修正系数,计算量小且计算过程简单。(2) Compared with the bioelectrical impedance imaging method of CN103462605A, the present invention has the outstanding substantial characteristics and significant progress of using the new information covariance calculation to obtain the adaptive correction coefficient, which has a small amount of calculation and a simple calculation process.

(3)与CN101499173B一种PET成像中卡尔曼滤波图像重建方法相比,本发明具有的突出的实质性特点和显著进步是利用新息协方差计算得到自适应修正系数,没有增加扩展卡尔曼滤波算法的复杂度。(3) Compared with the Kalman filter image reconstruction method in PET imaging in CN101499173B, the present invention has the outstanding substantive feature and significant improvement of using the new information covariance calculation to obtain the adaptive correction coefficient without increasing the complexity of the extended Kalman filter algorithm.

(4)与CN103312297A一种迭代扩展增量卡尔曼滤波方法相比,本发明具有的突出的实质性特点和显著进步是克服了难以获得先验信息的缺陷,能有效在线预测,不仅抑制了算法的发散不收敛,还提高了算法稳定性以及准确性。(4) Compared with the iterative extended incremental Kalman filtering method of CN103312297A, the outstanding substantive characteristics and significant progress of the present invention are that it overcomes the defect of difficulty in obtaining prior information and can effectively predict online, which not only suppresses the divergence and non-convergence of the algorithm, but also improves the stability and accuracy of the algorithm.

(5)2010年薛永文等发表的论文《修正的扩展卡曼滤波器在EIT中的应用》,文中对Flavio Celso Trigo等在论文《Electrical Impedance tomography Using The ExtebdedKalman Filter》中对给出的扩展卡尔曼方程组进行了修正,该论文提供的方案在一步成像中有所效果,不过当随着测量次数增加,图像相对误差越来越大且出现失真,表现为算法的预测值与实际值之间的绝对值逐渐增大。针对此问题,本发明引入优化自适应修正系数来削弱算法的记忆长度提高观测量所占权重,在线调整卡尔曼增益矩阵使得新息序列保持正交以提高卡尔曼算法在电阻抗成像中的稳定性。与论文《修正的扩展卡曼滤波器在EIT中的应用》中的公开的技术方案相比,本发明具有的突出的实质性特点和显著进步是通过引入优化自适应修正系数膨胀观测数据权重达到实时修正观测值在估计值中的作用,在状态突变时,比如肌肉部分与骨骼部分电阻率值相差悬殊,新息序列与误差协方差矩阵正相关,新息序列增大误差协方差矩阵增大所以自适应修正系数也会增大,重视新息序列在重建中的地位,降低陈旧数据的权重,并且自适应修正系数计算量小易实现具有实时性。(5) In 2010, Xue Yongwen et al. published a paper entitled "Application of Modified Extended Kalman Filter in EIT". In the paper, the extended Kalman equations given in the paper "Electrical Impedance tomography Using The ExtebdedKalman Filter" by Flavio Celso Trigo et al. were modified. The solution provided in the paper was effective in one-step imaging. However, as the number of measurements increased, the relative error of the image became larger and larger and distortion occurred, which was manifested as the absolute value between the predicted value and the actual value of the algorithm gradually increased. In response to this problem, the present invention introduces an optimized adaptive correction coefficient to weaken the memory length of the algorithm and increase the weight of the observed quantity. The Kalman gain matrix is adjusted online to keep the new information sequence orthogonal to improve the stability of the Kalman algorithm in electrical impedance tomography. Compared with the disclosed technical solutions in the paper "Application of Modified Extended Kalman Filter in EIT", the present invention has outstanding substantial characteristics and remarkable progress in that it achieves the role of real-time correction of observation values in estimated values by introducing optimized adaptive correction coefficients to inflate the weights of observed data. When the state suddenly changes, for example, the resistivity values of the muscle part and the bone part are very different, the new information sequence is positively correlated with the error covariance matrix. As the new information sequence increases, the error covariance matrix increases, so the adaptive correction coefficient will also increase. It attaches importance to the status of the new information sequence in reconstruction, reduces the weight of obsolete data, and the adaptive correction coefficient has a small amount of calculation, is easy to implement and has real-time performance.

(6)本发明提高了人体下肢图像重建的成像速度和图像分辨率,在重建过程中引入了自适应修正系数,计算量小,计算过程简单,适应性强,提高了算法的精确性和稳定性及实时性。(6) The present invention improves the imaging speed and image resolution of human lower limb image reconstruction, introduces an adaptive correction coefficient in the reconstruction process, has a small amount of calculation, a simple calculation process, strong adaptability, and improves the accuracy, stability and real-time performance of the algorithm.

(7)本发明方法应用的范围不局限于电阻抗成像领域,也可应用于岩土工程、资源和环境保护等领域中用于检测对象,本发明方法特别的适用于对电特性变化进行成像与检测的场合。(7) The application scope of the method of the present invention is not limited to the field of electrical impedance imaging, but can also be used in the fields of geotechnical engineering, resource and environmental protection for detecting objects. The method of the present invention is particularly suitable for imaging and detecting changes in electrical characteristics.

(8)本发明方法是将生物电阻抗成像方法与卡尔曼滤波方法进行组合,构成一项新的技术方案,通过建立基于真实结构先验信息的人体下肢数学模型,对模型进行用有限元法剖分离散分成小单元,施加边界条件计算边界电压值,将有限元数学模型用自适应扩展卡尔曼滤波算法求解逆问题并重建腿部图像,在重建过程中引入了优化的自适应修正系数提高观测量所占权重,在线调整卡尔曼增益矩阵,提高了卡尔曼算法在电阻抗成像中的稳定性,克服了现有公开的生物电阻抗成像技术存在抗噪能力低,无法同时拥有重建图像精度高和计算量小的缺陷,现有公开的卡尔曼滤波算法应用于重建图像中尚存在算法精度可能会丧失原有性能和滤波器发散的缺陷。(8) The method of the present invention combines the bioelectrical impedance imaging method with the Kalman filtering method to form a new technical solution. By establishing a mathematical model of the human lower limb based on real structural prior information, the model is discretized into small units using the finite element method, boundary conditions are applied to calculate the boundary voltage value, and the finite element mathematical model is used to solve the inverse problem and reconstruct the leg image using an adaptive extended Kalman filtering algorithm. In the reconstruction process, an optimized adaptive correction coefficient is introduced to increase the weight of the observed quantity, and the Kalman gain matrix is adjusted online to improve the stability of the Kalman algorithm in electrical impedance imaging. The defects of the existing disclosed bioelectrical impedance imaging technology, such as low noise resistance and inability to simultaneously have high reconstructed image accuracy and low calculation amount, are overcome. The existing disclosed Kalman filtering algorithm used in reconstructing images still has the defects that the algorithm accuracy may lose its original performance and the filter diverges.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

下面结合附图和实施例对本发明进一步说明。The present invention is further described below in conjunction with the accompanying drawings and embodiments.

图1是本发明方法中用优化自适应扩展卡尔曼滤波生物电阻抗成像方法进行人体下肢电阻抗图像的重建的流程示意图。FIG1 is a schematic diagram of a process of reconstructing an electrical impedance image of a human lower limb using an optimized adaptive extended Kalman filter bioelectrical impedance imaging method in the method of the present invention.

图2是图1中的“建立基于真实结构先验信息的人体下肢数学模型”的流程示意图。FIG. 2 is a flow chart of “establishing a mathematical model of human lower limbs based on real structural prior information” in FIG. 1 .

图3是图1中的“求解正问题”的流程示意图。FIG. 3 is a flow chart of “solving the positive problem” in FIG. 1 .

图4是图1中的“用优化自适应扩展卡尔曼滤波算法求解逆问题”的流程示意图。FIG. 4 is a flow chart of “using an optimized adaptive extended Kalman filter algorithm to solve the inverse problem” in FIG. 1 .

图5是本发明方法中进行卡尔曼滤波生物电阻抗成像所用装置的结构示意图。FIG. 5 is a schematic diagram of the structure of the device used for Kalman filter bioelectrical impedance imaging in the method of the present invention.

图6是本发明方法中输出的人体下肢电阻抗图像重建得到的电阻抗图像数学模型。FIG. 6 is a mathematical model of the electrical impedance image reconstructed from the electrical impedance image of the lower limbs of the human body output in the method of the present invention.

图中,1.计算机模块,2.通信模块,3.总控与处理模块,4.电压/电流恒流输出模块,5.激励通道选通模块,6.测量通道选通模块,7.电极阵列,8.信号调制模块,9.被测对象。In the figure, 1. computer module, 2. communication module, 3. general control and processing module, 4. voltage/current constant current output module, 5. excitation channel gating module, 6. measurement channel gating module, 7. electrode array, 8. signal modulation module, 9. measured object.

具体实施方式DETAILED DESCRIPTION

图1所示实施例表明,本发明方法中用优化自适应扩展卡尔曼滤波生物电阻抗成像方法进行人体下肢电阻抗图像的重建的流程:建立基于真实结构先验信息的人体下肢数学模型→求解正问题→用优化自适应扩展卡尔曼滤波算法求解逆问题→人体下肢电阻抗图像的输出。The embodiment shown in Figure 1 shows the process of reconstructing the electrical impedance image of the human lower limb using the optimized adaptive extended Kalman filter bioimpedance imaging method in the method of the present invention: establishing a mathematical model of the human lower limb based on real structural prior information → solving the forward problem → solving the inverse problem using the optimized adaptive extended Kalman filter algorithm → outputting the electrical impedance image of the human lower limb.

图2所示实施例表明,图1中的“建立基于真实结构先验信息的人体下肢数学模型”的流程是:腿部CT图像预处理→获得腿部及内部各组织的边缘图像→提取腿部及内部各组织的边缘图像的轮廓线坐标构→构建人体下肢仿真数学模型。The embodiment shown in Figure 2 indicates that the process of "establishing a mathematical model of the human lower limbs based on real structure prior information" in Figure 1 is: preprocessing of leg CT images → obtaining edge images of the legs and internal tissues → extracting contour coordinates of edge images of the legs and internal tissues → constructing a simulated mathematical model of the human lower limbs.

图3所示实施例表明,图1中的“求解正问题”的流程是:定义人体下肢数学模型的物理特性→对人体下肢数学模型离散化处理→施加边界条件→计算边界电压值。The embodiment shown in FIG3 shows that the process of “solving the positive problem” in FIG1 is: defining the physical characteristics of the mathematical model of the human lower limbs → discretizing the mathematical model of the human lower limbs → applying boundary conditions → calculating boundary voltage values.

图4所示实施例表明,图1中的“用优化自适应扩展卡尔曼滤波算法求解逆问题”的流程是:建立状态方程和观测方程→设置初始值σ0→由k-1时刻得到k时刻的目标状态预测方程→计算k时刻误差协方差矩阵的先验估计→计算扩展卡尔曼增益矩阵→计算k时刻误差协方差矩阵→计算k时刻误差协方差矩阵Ck→判断是否继续递推预测?当确定为“是”时,回转至上述步骤“由k-1时刻得到k时刻的目标状态预测方程”,当确定为“否”时,则跳转至下面的第四步:人体下肢电阻抗图像的输出。The embodiment shown in FIG4 shows that the process of “using the optimized adaptive extended Kalman filter algorithm to solve the inverse problem” in FIG1 is: establish the state equation and the observation equation → set the initial value σ 0 → obtain the target state prediction equation at time k from time k-1 → calculate the prior estimate of the error covariance matrix at time k → Calculate the extended Kalman gain matrix → Calculate the error covariance matrix at time k → Calculate the error covariance matrix C k at time k → Determine whether to continue recursive prediction? When it is determined to be "yes", return to the above step "obtain the target state prediction equation at time k from time k-1", and when it is determined to be "no", jump to the fourth step below: output of the electrical impedance image of the human lower limb.

图5所示实施例表明,本发明方法进行卡尔曼滤波生物电阻抗成像所用装置的结构是由计算机模块1、通信模块2、总控与处理模块3、电压/电流恒流输出模块4、激励通道选通模块5、测量通道选通模块6、电极阵列7、信号调制模块8和被测对象9构成;计算机算法模块1用来控制总控与处理模块3和优化自适应扩展卡尔曼滤波算法程序运行,总控与处理模块3通过数据总线、地址总线和控制总线完成实现对该生物电阻抗成像装置系统的控制与协调各模块之间的工作,实时精准完成对硬件系统各模块的控制并通过通信模块2及时反馈给计算机模块1相关信息以做出相应调整,电压/电流恒流输出模块4用于产生正弦电压信号,再经过隔离、滤波、电压增益电路和电压/电流转换恒流源电路,将电压转换成电流,激励通道选通模块5采用低导通电阻的多路模拟开关来选择和切换电极中的注入模式,将电流信号通过相应的电极注入被测对象9,测量通道选通模块6用于选择电极的测量模式,电极阵列7放置在被测对象9表面,以提取被测对象9表面感应的电压信号,传到信号调制模块8,信号调制模块8通过仪表放大电路、滤波电路、解调电路、可变增益放大电路、低通滤波器和转换电路,将电压信号处理成数字信号,通过总控与处理模块3与通信模块2实时将数字电压信号传入计算机模块1,计算机将采集的电压数据和电流数据通过优化自适应扩展卡尔曼滤波算法完成图像重建成像。The embodiment shown in FIG5 shows that the structure of the device used for Kalman filter bioelectrical impedance imaging by the method of the present invention is composed of a computer module 1, a communication module 2, a master control and processing module 3, a voltage/current constant current output module 4, an excitation channel gating module 5, a measurement channel gating module 6, an electrode array 7, a signal modulation module 8 and a measured object 9; the computer algorithm module 1 is used to control the master control and processing module 3 and optimize the operation of the adaptive extended Kalman filter algorithm program, the master control and processing module 3 completes the control of the bioelectrical impedance imaging device system and coordinates the work between the modules through the data bus, the address bus and the control bus, and accurately completes the control of the modules of the hardware system in real time and timely feeds back the relevant information to the computer module 1 through the communication module 2 to make corresponding adjustments, the voltage/current constant current output module 4 is used to generate a sinusoidal voltage signal, and then after isolation, The filtering, voltage gain circuit and voltage/current conversion constant current source circuit convert the voltage into current. The excitation channel selection module 5 adopts a multi-way analog switch with low on-resistance to select and switch the injection mode in the electrode, and injects the current signal into the object under test 9 through the corresponding electrode. The measurement channel selection module 6 is used to select the measurement mode of the electrode. The electrode array 7 is placed on the surface of the object under test 9 to extract the voltage signal induced on the surface of the object under test 9 and transmit it to the signal modulation module 8. The signal modulation module 8 processes the voltage signal into a digital signal through an instrument amplifier circuit, a filter circuit, a demodulation circuit, a variable gain amplifier circuit, a low-pass filter and a conversion circuit. The digital voltage signal is transmitted to the computer module 1 in real time through the general control and processing module 3 and the communication module 2. The computer uses the collected voltage data and current data to complete image reconstruction imaging through the optimized adaptive extended Kalman filter algorithm.

图6所示为本发明的优化自适应扩展卡尔曼滤波算法重建的腿部数学模型的图像,该图像表明本发明采用的优化自适应扩展卡尔曼滤波算法在重建过程中稳定性好且引入由新息协方差计算得到的优化自适应修正系数调整新息权重,减小陈旧测量数据权重,计算量比传统计算方法小,计算过程复杂度低,能适应较复杂的图像重建,当数据突变时,也能保证有效精确及时地预测变化趋势以及输出,提高了算法的精确性和稳定性及实时性从而达到提高图像重建的成像速度和图像分辨率的目的。Figure 6 shows an image of the mathematical model of the leg reconstructed by the optimized adaptive extended Kalman filter algorithm of the present invention. The image shows that the optimized adaptive extended Kalman filter algorithm adopted by the present invention has good stability in the reconstruction process and introduces the optimized adaptive correction coefficient obtained by calculating the new information covariance to adjust the new information weight, thereby reducing the weight of obsolete measurement data. The amount of calculation is smaller than that of traditional calculation methods, and the complexity of the calculation process is low. It can adapt to more complex image reconstruction, and when the data mutates, it can also ensure effective, accurate and timely prediction of change trends and outputs, thereby improving the accuracy, stability and real-time performance of the algorithm, thereby achieving the purpose of improving the imaging speed and image resolution of image reconstruction.

实施例Example

本实施例一种优化自适应扩展卡尔曼滤波生物电阻抗成像方法,具体步骤如下:This embodiment provides an optimized adaptive extended Kalman filter bioelectrical impedance imaging method, and the specific steps are as follows:

A.设置进行优化自适应扩展卡尔曼滤波电阻抗成像所用的装置:A. Set up the device used for optimizing adaptive extended Kalman filter electrical impedance imaging:

进行优化自适应扩展卡尔曼滤波电阻抗成像所用装置采用模块化设计,如图5所示,是串联与并联混合式的结构,其构成包括计算机模块、通信模块、总控与处理模块、电压/电流恒流输出模块、激励通道选通模块、测量通道选通模块、电极阵列和信号调制模块;计算机模块用来控制总控与处理模块和自适应扩展卡尔曼滤波成像算法的程序运行,总控与处理模块通过通信模块接收来自计算机模块的指令并通过数据总线、地址总线和控制总线实现对电阻抗成像装置系统的控制与协调各模块之间的工作,实时精准完成对硬件系统各模块的控制并通过通信模块及时反馈给计算机模块信息以做出相应调整,电压/电流转换恒流输出模块用于产生正弦电压信号,再经过隔离、滤波、电压增益电路、电压/电流转换恒流源电路,将电压转换成电流,总控与处理模块通过通信模块控制该模块电压信号的频率、幅值和相位,实施对激励信号频率、幅值和相位的调整,激励通道选通模块接收来自总控与处理模块的指令采用低导通电阻的模拟多路来选择和切换电极阵列中的注入模式,将电流信号通过相应的电极注入被测对象,建立敏感区域,测量通道选通模块接收来自总控与处理模块的指令选择和切换电极阵列的测量模式,将提取到的被测对象电压信号送到信号调制模块,信号调制模块通过仪表放大电路、滤波电路、解调电路、可变增益放大电路、低通滤波器和A/D转换电路,对测量通道选通模块输入过来的电压信号处理成数字信号,通过总控与处理模块与通信模块实时将数字电压信号传入计算机模块,计算机将采集的电压数据和电流数据通过自适应扩展卡尔曼滤波算法进行图像重建成像;The device used for optimizing the adaptive extended Kalman filter electrical impedance imaging adopts a modular design, as shown in Figure 5, which is a hybrid structure of series and parallel, and its composition includes a computer module, a communication module, a master control and processing module, a voltage/current constant current output module, an excitation channel gating module, a measurement channel gating module, an electrode array and a signal modulation module; the computer module is used to control the program operation of the master control and processing module and the adaptive extended Kalman filter imaging algorithm, the master control and processing module receives instructions from the computer module through the communication module, and controls the electrical impedance imaging device system and coordinates the work between the modules through the data bus, address bus and control bus, and accurately completes the control of each module of the hardware system in real time and feeds back information to the computer module in time through the communication module to make corresponding adjustments, the voltage/current conversion constant current output module is used to generate a sinusoidal voltage signal, and then converts the voltage into current through isolation, filtering, voltage gain circuit, and voltage/current conversion constant current source circuit. The control and processing module controls the frequency, amplitude and phase of the voltage signal of the module through the communication module, and adjusts the frequency, amplitude and phase of the excitation signal. The excitation channel gating module receives instructions from the main control and processing module and uses low on-resistance analog multi-channel to select and switch the injection mode in the electrode array, injects the current signal into the object under test through the corresponding electrode, and establishes a sensitive area. The measurement channel gating module receives instructions from the main control and processing module to select and switch the measurement mode of the electrode array, and sends the extracted voltage signal of the object under test to the signal modulation module. The signal modulation module processes the voltage signal input from the measurement channel gating module into a digital signal through an instrument amplifier circuit, a filter circuit, a demodulation circuit, a variable gain amplifier circuit, a low-pass filter and an A/D conversion circuit, and transmits the digital voltage signal to the computer module in real time through the main control and processing module and the communication module. The computer reconstructs the collected voltage data and current data through an adaptive extended Kalman filter algorithm;

B.用优化自适应扩展卡尔曼滤波生物电阻抗成像方法进行人体下肢电阻抗图像的重建,其技术方案如下:B. The optimized adaptive extended Kalman filter bioimpedance imaging method is used to reconstruct the electrical impedance image of the human lower limbs. The technical scheme is as follows:

第一步,建立基于真实结构先验信息的人体下肢数学模型:The first step is to establish a mathematical model of the human lower limbs based on real structural prior information:

(1.1)腿部CT图像预处理:(1.1) Leg CT image preprocessing:

采用改进Perona&Malik模型基于偏微分方程的图像方法消除边缘噪声以提高轮廓线提取精度,具体操作如下:The improved Perona&Malik model is used to eliminate edge noise based on partial differential equations to improve the accuracy of contour extraction. The specific operations are as follows:

设x0(a,b)为腿部的CT灰度图像,引入时间变量t∈[0,T],改进的Perona&Malik偏微分方程为如下公式(1)所示,Assume x 0 (a, b) is the CT grayscale image of the leg, introduce the time variable t∈[0,T], and the improved Perona&Malik partial differential equation is shown in the following formula (1):

公式(1)中,Gτ为高斯平滑模板,τ为高斯核的尺度,为图像梯度模,c为扩散系数用于控制扩散速度;In formula (1), G τ is the Gaussian smoothing template, τ is the scale of the Gaussian kernel, is the image gradient modulus, c is the diffusion coefficient used to control the diffusion speed;

由此完成腿部CT图像预处理;Thus, the leg CT image preprocessing is completed;

(1.2)获得腿部及内部各组织的边缘图像:(1.2) Obtain edge images of the legs and internal tissues:

采用腐蚀、膨胀的图像处理的阈值分割算法,首先对上述步骤(1.1)腿部CT图像预处理后的图像进行二值化处理,然后去除检查床提取腿部轮廓,再利用去除检查床的图像减去腿部轮廓图像,即得到腿部轮廓图像,同样操作,得到肌肉轮廓图像、脂肪轮廓图像和骨头轮廓图像,最后通过对腿部轮廓、肌肉轮廓、脂肪轮廓和骨头轮廓的融合,获得腿部及内部各组织的边缘图像;The threshold segmentation algorithm of the image processing of corrosion and expansion is adopted. First, the image of the leg CT image preprocessed in the above step (1.1) is binarized. Then, the examination bed is removed to extract the leg contour. Then, the leg contour image is subtracted from the image without the examination bed to obtain the leg contour image. The muscle contour image, fat contour image and bone contour image are obtained by the same operation. Finally, the edge image of the leg and its internal tissues is obtained by fusing the leg contour, muscle contour, fat contour and bone contour.

(1.3)提取腿部及内部各组织的边缘图像的轮廓线坐标:(1.3) Extract the contour coordinates of the edge image of the leg and internal tissues:

对上述步骤(1.2)获得的腿部及内部各组织的边缘图像采用基于二值图像的轮廓提取算法提取腿部及内部各组织的边缘图像的轮廓线坐标,具体操作方法如下:The edge image of the leg and its internal tissues obtained in the above step (1.2) is used to extract the contour line coordinates of the edge image of the leg and its internal tissues using a contour extraction algorithm based on a binary image. The specific operation method is as follows:

设y(c,d)为上述步骤(1.2)获得的腿部及内部各组织的边缘图像的像素点,Y(c,d)为应用二值化规则处理后获得的腿部及内部各组织的边缘图像的像素点,用如下所示公式(2)判断当前像素是否为腿部、肌肉、脂肪和骨头轮廓边界像素,Let y(c, d) be the pixel point of the edge image of the leg and its internal tissues obtained in the above step (1.2), and Y(c, d) be the pixel point of the edge image of the leg and its internal tissues obtained after applying the binarization rule. Use the following formula (2) to determine whether the current pixel is a leg, muscle, fat, or bone contour boundary pixel.

公式(2)中,当Y(c,d)=0时,当前像素不是轮廓边界像素点,不保留,当Y(c,d)=1时,当前像素是轮廓边界像素点,该当前像素点保留,应用此规则对上述步骤(1.2)得到的图像的每个像素进行处理,保留在图像中的像素为轮廓线坐标,由此完成了腿部及内部各组织的边缘图像的轮廓线坐标的提取;In formula (2), when Y(c, d) = 0, the current pixel is not a contour boundary pixel and is not retained. When Y(c, d) = 1, the current pixel is a contour boundary pixel and is retained. This rule is applied to process each pixel of the image obtained in step (1.2) above. The pixels retained in the image are the contour line coordinates, thereby completing the extraction of the contour line coordinates of the edge image of the leg and internal tissues.

(1.4)构建人体下肢仿真数学模型:(1.4) Constructing a mathematical model of human lower limb simulation:

基于上述步骤(1.3)中获得的腿部及内部各组织的边缘图像的轮廓线坐标,运用有限元仿真软件建立人体下肢仿真数学模型;Based on the contour line coordinates of the edge images of the legs and internal tissues obtained in the above step (1.3), a finite element simulation software is used to establish a simulation mathematical model of the human lower limbs;

至此,完成建立基于真实结构先验信息的人体下肢数学模型;At this point, the mathematical model of the human lower limbs based on real structural prior information has been established;

第二步,求解正问题:The second step is to solve the positive problem:

(2.1)定义人体下肢数学模型的物理特性;(2.1) Define the physical characteristics of the mathematical model of the human lower limbs;

首先电阻抗成像技术正问题所加电流场可看作稳态电流场来处理,则等效为Laplace边值问题:First, the current field applied in the positive problem of electrical impedance tomography can be treated as a steady-state current field, which is equivalent to a Laplace boundary value problem:

其中,σ是目标内部的电导率分布,是敏感场域Ω内部的电势分布,Where σ is the conductivity distribution inside the target, is the potential distribution inside the sensitive field Ω,

其次,定义所示第一步所建立的基于真实结构先验信息的人体下肢数学模型的物理特性,方法是:1)采用归一化的二维基于真实人体先验结构的模型;2)点状电极位于模型的边界节点上,电极个数为16个,电极的半径为0.015cm;3)注入50kHz,2.5mA的正弦波形激励电流;4)每个电极的接触阻抗为50Ω;5)设置模型各部分区域的电导率值,骨头电导率为0.02043S/m,脂肪电导率为0.02383S/m,肌肉电导率为0.34083S/m,皮肤表皮电导率为0.00020408S/m。Secondly, define the physical properties of the mathematical model of the human lower limbs based on the real structure prior information established in the first step shown, the method is: 1) use a normalized two-dimensional model based on the real human prior structure; 2) point electrodes are located on the boundary nodes of the model, the number of electrodes is 16, and the radius of the electrode is 0.015cm; 3) inject a 50kHz, 2.5mA sinusoidal waveform excitation current; 4) the contact impedance of each electrode is 50Ω; 5) set the conductivity value of each part of the model, the bone conductivity is 0.02043S/m, the fat conductivity is 0.02383S/m, the muscle conductivity is 0.34083S/m, and the skin epidermal conductivity is 0.00020408S/m.

(2.2)对人体下肢数学模型离散化处理;(2.2) Discretization of the mathematical model of the human lower limbs;

利用有限元方法将人体下肢数学模型剖分为较小的单元,离散后,二维人体下肢数值模型共10265个单元,41919个节点。The finite element method is used to divide the mathematical model of the human lower limbs into smaller units. After discretization, the two-dimensional human lower limb numerical model has a total of 10265 units and 41919 nodes.

(2.3)施加边界条件;(2.3) Apply boundary conditions;

考虑到实际情况,本发明的数学模型为完备电极模型,即考虑接触阻抗,所以边界条件为:Taking into account the actual situation, the mathematical model of the present invention is a complete electrode model, that is, considering the contact impedance, so the boundary conditions are:

Γ2:(无电极区)Γ 2 : (No electrode area)

(注入电极区) (Injection electrode area)

Γ3:(测量电极区)Γ 3 : (Measuring electrode area)

其中,zl是第l个测量电极的接触阻抗,是电极上测得的电压,Jn是由电极注入的电流密度,n为外法向单位矢量。Where z l is the contact impedance of the lth measuring electrode, is the voltage measured on the electrode, Jn is the current density injected by the electrode, and n is the outward normal unit vector.

(2.4)计算边界电压值;(2.4) Calculate the boundary voltage value;

由此完成求解正问题;This completes the solution to the positive problem;

第三步,用优化自适应扩展卡尔曼滤波算法求解逆问题:The third step is to use the optimized adaptive extended Kalman filter algorithm to solve the inverse problem:

(3.1)建立状态方程和观测方程:(3.1) Establish the state equation and observation equation:

(3.1.1)建立状态方程:(3.1.1) Establish the state equation:

所建立的状态方程如下公式(3)所示,The established state equation is shown in the following formula (3):

σk=Ak-1σk-1k-1 (3),σ k =A k-1 σ k-1k-1 (3),

公式(3)中,σk为k时刻阻抗值,σk-1为k-1时刻阻抗值,Ak-1∈Rm×m,m为有限元模型剖分后单元的个数,采用随机游走模式,则Ak-1=Im,Im为单位矩阵,ωk-1为k-1时刻的系统噪声,该系统噪声设置为白噪声序列,其满足如下公式(4),In formula (3), σ k is the impedance value at time k, σ k-1 is the impedance value at time k-1, A k-1 ∈R m×m , m is the number of units after the finite element model is segmented, and the random walk mode is adopted, then A k-1 =I m , I m is the unit matrix, ω k-1 is the system noise at time k-1, and the system noise is set as a white noise sequence, which satisfies the following formula (4),

E(ωk-1)=0,E(ωk-1ωk-1 T)=Qk-1 (4),E(ω k-1 )=0,E(ω k-1 ω k-1 T )=Q k-1 (4),

公式(4)中,E为数学期望符号,Qk-1为k-1时刻ωk-1的协方差矩阵;In formula (4), E is the mathematical expectation symbol, Q k-1 is the covariance matrix of ω k-1 at time k-1;

(3.1.2)建立观测方程:(3.1.2) Establish the observation equation:

(3.1.2.1)建立非线性方程:(3.1.2.1) Establish the nonlinear equation:

所建立的非线性方程如下公式(5)所示,The established nonlinear equation is shown in the following formula (5):

uk=Ukk)+νk (5),u k =U kk )+ν k (5),

公式(5)中,uk为边界电压测量向量,Ukk)为边界电压测量值与阻抗值之间的非线性关系,vk为k时刻观测噪声,vk与ωk-1不相关,设置为白噪声序列,其满足如下公式(6),In formula (5), uk is the boundary voltage measurement vector, Uk ( σk ) is the nonlinear relationship between the boundary voltage measurement value and the impedance value, vk is the observation noise at time k, vk is uncorrelated with ωk-1 and is set as a white noise sequence, which satisfies the following formula (6):

E(νk)=0,E(νkνk T)=Rk,E(ωkνk T)=0 (6),E(ν k )=0,E(ν k ν k T )=R k ,E(ω k ν k T )=0 (6),

公式(6)中,Rk为k时刻vk的协方差矩阵;In formula (6), R k is the covariance matrix of v k at time k;

(3.1.2.2)对(3.2.2.1)中的非线性方程进行一阶泰勒级数展开:(3.1.2.2) Perform a first-order Taylor series expansion on the nonlinear equation in (3.2.2.1):

如下公式(7)为对上述步骤(3.2.2.1)中的非线性方程进行的一阶泰勒级数展开,The following formula (7) is the first-order Taylor series expansion of the nonlinear equation in the above step (3.2.2.1),

uk=Uk0)+Jk0)·(σk0)+νk (7),u k =U k0 )+J k0 )·(σ k0 )+ν k (7),

公式(7)中,Jk0)为雅可比矩阵,其计算公式为如下公式(8)所示,In formula (7), J k0 ) is the Jacobian matrix, and its calculation formula is shown in the following formula (8):

(3.1.2.3)建立观测方程:(3.1.2.3) Establish the observation equation:

进而建立观测方程如下公式(9)所示,Then the observation equation is established as shown in the following formula (9):

zk=Jσkk (9),z k =Jσ kk (9),

公式(9)中,zk为边界电压测量值,J为灵敏度矩阵,σk为阻抗值;In formula (9), z k is the boundary voltage measurement value, J is the sensitivity matrix, and σ k is the impedance value;

(3.2)设置初始值σ0(3.2) Set the initial value σ 0 :

所设置的初始值σ0为如下公式(10)所示,The initial value σ 0 is set as shown in the following formula (10):

σ0=0,C0=∞ (10),σ 0 =0,C 0 =∞ (10),

公式(10)中,C0为误差协方差矩阵初始值;In formula (10), C 0 is the initial value of the error covariance matrix;

(3.3)由k-1时刻得到k时刻的目标状态预测方程:(3.3) The target state prediction equation at time k is obtained from time k-1:

由k-1时刻得到k时刻的目标状态预测方程如下公式(11)所示,The target state prediction equation at time k is obtained from time k-1 as shown in the following formula (11):

公式(11)中,为σk的先验估计,即预测值;In formula (11), is the prior estimate of σ k , i.e. the predicted value;

(3.4)计算k时刻误差协方差矩阵的先验估计 (3.4) Calculate the prior estimate of the error covariance matrix at time k

由如下公式(12)计算k时刻误差协方差矩阵的先验估计 The prior estimate of the error covariance matrix at time k is calculated by the following formula (12):

公式(12)中,γk为自适应修正系数,其计算方法如下公式(13)所示,In formula (12), γ k is the adaptive correction coefficient, and its calculation method is shown in the following formula (13):

公式(13)中,trace为迹符号,为新息序列的协方差矩阵,其的计算方法如下公式(14)所示,In formula (13), trace is the trace symbol, is the covariance matrix of the new information sequence, and its calculation method is shown in the following formula (14):

公式(14)中,ξk为新息序列,期计算方法如下公式(15)所示,In formula (14), ξ k is the new information sequence, and the calculation method is as shown in formula (15):

公式(15)中,zk为边界电压测量值,为zk的预测值;In formula (15), zk is the measured value of the boundary voltage, is the predicted value of z k ;

γk取值范围如下公式(16)所示,The value range of γ k is shown in the following formula (16):

(3.5)计算扩展卡尔曼增益矩阵:(3.5) Calculate the extended Kalman gain matrix:

由如下公式(17)计算扩展卡尔曼增益矩阵KkThe extended Kalman gain matrix K k is calculated by the following formula (17):

公式(17)中,Kk为卡尔曼增益矩阵;In formula (17), K k is the Kalman gain matrix;

(3.6)计算k时刻误差协方差矩阵:(3.6) Calculate the error covariance matrix at time k:

由如下k时刻的状态更新方程即公式(18)来计算k时刻的阻抗值σkThe impedance value σ k at time k is calculated by the following state update equation at time k, that is, formula (18):

(3.7)计算k时刻误差协方差矩阵Ck(3.7) Calculate the error covariance matrix C k at time k:

公式(19)中,I为单位矩阵;In formula (19), I is the unit matrix;

(3.8)判断是否继续递推预测,当确定为“是”时,回转至上述步骤(3.3),当确定为“否”时,则跳转至下面的第四步;(3.8) Determine whether to continue recursive prediction. If it is determined to be "yes", go back to the above step (3.3). If it is determined to be "no", jump to the fourth step below;

由此完成用优化自适应扩展卡尔曼滤波算法求解逆问题;Thus, the inverse problem is solved by using the optimized adaptive extended Kalman filter algorithm;

至此,完成用优化自适应扩展卡尔曼滤波生物电阻抗成像方法进行人体下肢电阻抗图像的重建;So far, the reconstruction of human lower limb electrical impedance images using the optimized adaptive extended Kalman filter bioelectrical impedance imaging method has been completed;

第四步,人体下肢电阻抗重建图像的输出:Step 4: Output of the human lower limb electrical impedance reconstruction image:

由上述A所述设置进行卡尔曼滤波生物电阻抗成像所用的装置来输出B所述的用自适应扩展卡尔曼滤波生物电阻抗成像方法进行人体下肢电阻抗图像的重建得到的胸腔电阻抗图像,具体实施过程如下:The apparatus for Kalman filter bioelectrical impedance imaging described in A is used to output the chest electrical impedance image obtained by reconstructing the electrical impedance image of the human lower limbs using the adaptive extended Kalman filter bioelectrical impedance imaging method described in B. The specific implementation process is as follows:

在计算机模块1写入激励人体腿部电流的幅值和频率,将激励信号通过电极阵列7施加至人体腿部即被测对象9表面,通过电极测量腿部电压信号并传入计算机,通过调用优化自适应扩展卡尔曼滤波算法程序成像;总控与处理模块3为本发明所以装置的核心,由通信模块2发出与接收来自计算机模块1的控制指令,实现对上述A所述装置的硬件系统的全局控制和协调运行工作;电压/电流恒流输出模块4用于将产生1kHz-1MHz范围内可调的正弦波信号,转换成幅值在0.1mA-5mA范围内可调节的电流信号,通过激励通道选通模块5,实现激励电极的开与关,使激励信号按照设定的方式流入相应的电极,注入被测对象;通过控制测量通道选通模块6实现测量电极的开与关,使测量电极中相应电极提取被测对象电压信号,便将信号送入信号调制模块8;再由信号调理模块8内部的仪表放大电路、滤波电路、解调电路、可变增益放大电路、低通滤波器和A/D转换电路对测量通道选通模块6输入过来的电压信号处理成数字信号;然后再将数字电压信号由通信模块2传入计算机模块1,将数字电压信号转换为模拟电压信号,通过优化自适应扩展卡尔曼滤波算法程序实现腿部电阻抗图像重建,最后通过计算机输出人体下肢电阻抗重建图像;The amplitude and frequency of the current that stimulates the human leg are written into the computer module 1, and the excitation signal is applied to the human leg, i.e., the surface of the object to be measured 9, through the electrode array 7. The leg voltage signal is measured through the electrode and transmitted to the computer, and imaging is performed by calling the optimized adaptive extended Kalman filter algorithm program; the general control and processing module 3 is the core of the device of the present invention, and the communication module 2 sends and receives control instructions from the computer module 1 to achieve global control and coordinated operation of the hardware system of the device described in A above; the voltage/current constant current output module 4 is used to convert the sine wave signal adjustable in the range of 1kHz-1MHz into a current signal with an amplitude adjustable in the range of 0.1mA-5mA, and realize the opening and closing of the excitation electrode through the excitation channel selection module 5, so that The excitation signal flows into the corresponding electrode in a set manner and is injected into the object to be measured; the measuring electrode is turned on and off by controlling the measuring channel gating module 6, so that the corresponding electrode in the measuring electrode extracts the voltage signal of the object to be measured, and then the signal is sent to the signal modulation module 8; the voltage signal input from the measuring channel gating module 6 is processed into a digital signal by the instrument amplifier circuit, filter circuit, demodulation circuit, variable gain amplifier circuit, low-pass filter and A/D conversion circuit inside the signal conditioning module 8; the digital voltage signal is then transmitted to the computer module 1 from the communication module 2, and the digital voltage signal is converted into an analog voltage signal, and the leg electrical impedance image reconstruction is realized by optimizing the adaptive extended Kalman filter algorithm program, and finally the human lower limb electrical impedance reconstruction image is output through the computer;

至此,完成用优化自适应扩展卡尔曼滤波生物电阻抗成像方法进行人体下肢电阻抗图像的重建,得到人体下肢电阻抗图像。At this point, the reconstruction of the human lower limb electrical impedance image using the optimized adaptive extended Kalman filter bioimpedance imaging method is completed, and the human lower limb electrical impedance image is obtained.

上述实施例中,进行生物电阻抗成像所用装置是通过公知途径获得的,所涉及的操作方法,所述改进Perona&Malik模型基于偏微分方程的图像方法是本技术领域中所公知的。In the above-mentioned embodiment, the device used for bioelectrical impedance imaging is obtained through a well-known way, and the operation method involved, and the imaging method based on partial differential equations of the improved Perona & Malik model are well known in the technical field.

Claims (4)

1.一种优化自适应扩展卡尔曼滤波生物电阻抗成像方法,其特征在于具体步骤如下:1. An optimized adaptive extended Kalman filter bioelectrical impedance imaging method is characterized in that the specific steps are as follows: A.设置进行优化自适应扩展卡尔曼滤波电阻抗成像所用的装置:A. Setup for optimization of the adaptive extended Kalman filter electrical impedance imaging apparatus used: 进行优化自适应扩展卡尔曼滤波电阻抗成像所用装置采用模块化设计,是串联与并联混合式的结构,其构成包括计算机模块、通信模块、总控与处理模块、电压/电流恒流输出模块、激励通道选通模块、测量通道选通模块、电极阵列和信号调制模块;计算机模块用来控制总控与处理模块和自适应扩展卡尔曼滤波成像算法的程序运行,总控与处理模块通过通信模块接收来自计算机模块的指令并通过数据总线、地址总线和控制总线实现对电阻抗成像装置系统的控制与协调各模块之间的工作,实时精准完成对硬件系统各模块的控制并通过通信模块及时反馈给计算机模块信息以做出相应调整,电压/电流转换恒流输出模块用于产生正弦电压信号,再经过隔离、滤波、电压增益电路、电压/电流转换恒流源电路,将电压转换成电流,总控与处理模块通过通信模块控制该模块电压信号的频率、幅值和相位,实施对激励信号频率、幅值和相位的调整,激励通道选通模块接收来自总控与处理模块的指令采用低导通电阻的模拟多路来选择和切换电极阵列中的注入模式,将电流信号通过相应的电极注入被测对象,建立敏感区域,测量通道选通模块接收来自总控与处理模块的指令选择和切换电极阵列的测量模式,将提取到的被测对象电压信号送到信号调制模块,信号调制模块通过仪表放大电路、滤波电路、解调电路、可变增益放大电路、低通滤波器和A/D转换电路,对测量通道选通模块输入过来的电压信号处理成数字信号,通过总控与处理模块与通信模块实时将数字电压信号传入计算机模块,计算机将采集的电压数据和电流数据通过自适应扩展卡尔曼滤波算法进行图像重建成像;The device used for optimization and adaptive extended Kalman filter electrical impedance imaging adopts a modular design, which is a hybrid structure of series and parallel, and its composition includes a computer module, a communication module, a master control and processing module, a voltage/current constant current output module, The excitation channel gating module, measurement channel gating module, electrode array and signal modulation module; the computer module is used to control the program operation of the general control and processing module and the adaptive extended Kalman filter imaging algorithm. The general control and processing module passes through the communication module Receive instructions from the computer module and realize the control of the electrical impedance imaging device system and coordinate the work between the modules through the data bus, address bus and control bus, and complete the control of each module of the hardware system accurately in real time and timely feedback through the communication module Give the computer module information to make corresponding adjustments, the voltage/current conversion constant current output module is used to generate sinusoidal voltage signals, and then through isolation, filtering, voltage gain circuit, voltage/current conversion constant current source circuit, the voltage is converted into current, The master control and processing module controls the frequency, amplitude and phase of the voltage signal of the module through the communication module, and adjusts the frequency, amplitude and phase of the excitation signal. The excitation channel gating module receives instructions from the master control and processing module using low The injection mode in the electrode array is selected and switched by the analog multiplex of the on-resistance, and the current signal is injected into the measured object through the corresponding electrode to establish a sensitive area. The measurement channel gating module receives the command selection and Switch the measurement mode of the electrode array, and send the extracted voltage signal of the measured object to the signal modulation module. The signal modulation module passes through the instrument amplifier circuit, filter circuit, demodulation circuit, variable gain amplifier circuit, low-pass filter and A/ The D conversion circuit processes the voltage signal input from the measurement channel gating module into a digital signal, and transmits the digital voltage signal to the computer module in real time through the master control and processing module and the communication module, and the computer passes the collected voltage data and current data through its own Adapt to the extended Kalman filter algorithm for image reconstruction imaging; B.用优化自适应扩展卡尔曼滤波生物电阻抗成像方法进行人体下肢电阻抗图像的重建,其步骤如下:B. Reconstructing the electrical impedance image of human lower limbs with the optimized adaptive extended Kalman filter bioelectrical impedance imaging method, the steps are as follows: 第一步,建立基于真实结构先验信息的人体下肢数学模型;The first step is to establish a mathematical model of human lower limbs based on the prior information of the real structure; 第二步,求解正问题;The second step is to solve the positive problem; 第三步,用优化自适应扩展卡尔曼滤波算法求解逆问题;The third step is to use the optimized adaptive extended Kalman filter algorithm to solve the inverse problem; 第四步,人体下肢电阻抗重建图像的输出:The fourth step is the output of the electrical impedance reconstruction image of the lower limbs of the human body: 由上述A所述设置进行优化自适应扩展卡尔曼滤波电阻抗成像所用的装置来输出B所述的用优化自适应扩展卡尔曼滤波生物电阻抗成像方法进行人体下肢电阻抗图像的重建得到胸腔电阻抗图像,具体实施过程如下:Optimizing the device used in the adaptive extended Kalman filter electrical impedance imaging described in the above-mentioned A to output the reconstruction of the electrical impedance image of the lower limbs of the human body using the optimized adaptive extended Kalman filter bioelectrical impedance imaging method described in B to obtain the chest cavity resistance Anti-image, the specific implementation process is as follows: 在计算机模块写入激励人体腿部电流的幅值和频率,将激励信号通过电极阵列施加至人体腿部即被测对象表面,通过电极测量腿部电压信号并传入计算机,通过调用优化自适应扩展卡尔曼滤波算法程序成像;总控与处理模块为上述装置的核心,由通信模块发出与接收来自计算机模块的控制指令,实现对上述A所述装置的硬件系统的全局控制和协调运行工作;电压/电流恒流输出模块用于将产生1kHz-1MHz范围内可调的正弦波信号,转换成幅值在0.1mA-5mA范围内可调节的电流信号,通过激励通道选通模块,实现激励电极的开与关,使激励信号按照设定的方式流入相应的电极,注入被测对象;通过控制测量通道选通模块实现测量电极的开与关,使测量电极中相应电极提取被测对象电压信号,便将信号送入信号调制模块;再由信号调理模块内部的仪表放大电路、滤波电路、解调电路、可变增益放大电路、低通滤波器和A/D转换电路对测量通道选通模块输入过来的电压信号处理成数字信号;然后再将数字电压信号由通信模块传入计算机模块,将数字电压信号转换为模拟电压信号,通过优化自适应扩展卡尔曼滤波算法程序实现腿部电阻抗图像重建,最后通过计算机输出人体下肢电阻抗重建图像;Write in the computer module the amplitude and frequency of the current that excites the leg of the human body, apply the excitation signal to the leg of the human body through the electrode array, that is, the surface of the measured object, measure the voltage signal of the leg through the electrode and transmit it to the computer, and optimize the self-adaptation by calling Extended Kalman filter algorithm program imaging; the main control and processing module is the core of the above-mentioned device, and the communication module sends and receives control instructions from the computer module to realize the overall control and coordinated operation of the hardware system of the above-mentioned device A; The voltage/current constant current output module is used to convert the sine wave signal adjustable in the range of 1kHz-1MHz into a current signal adjustable in the range of 0.1mA-5mA, and realize the excitation electrode by exciting the channel gating module On and off, so that the excitation signal flows into the corresponding electrode according to the set method, and injected into the measured object; by controlling the measurement channel gating module to realize the opening and closing of the measuring electrode, so that the corresponding electrode in the measuring electrode can extract the voltage signal of the measured object , the signal is sent to the signal modulation module; then the measurement channel gating module is controlled by the instrument amplifier circuit, filter circuit, demodulation circuit, variable gain amplifier circuit, low-pass filter and A/D conversion circuit inside the signal conditioning module The input voltage signal is processed into a digital signal; then the digital voltage signal is transferred from the communication module to the computer module, the digital voltage signal is converted into an analog voltage signal, and the electrical impedance image of the leg is realized by optimizing the adaptive extended Kalman filter algorithm program Reconstruction, and finally output the electrical impedance reconstruction image of human lower limbs through the computer; 至此,完成用优化自适应扩展卡尔曼滤波生物电阻抗成像方法进行人体下肢电阻抗图像的重建,得到人体下肢电阻抗图像。So far, the reconstruction of the electrical impedance image of the lower limbs of the human body using the optimized adaptive extended Kalman filter bioelectrical impedance imaging method is completed, and the electrical impedance image of the lower limbs of the human body is obtained. 2.根据权利要求1所述一种优化自适应扩展卡尔曼滤波生物电阻抗成像方法,其特征在于:所述建立基于真实结构先验信息的人体下肢数学模型的具体方法如下:2. according to claim 1, a kind of optimized adaptive extended Kalman filter bioelectrical impedance imaging method is characterized in that: the concrete method of described setting up the mathematical model of human lower limbs based on real structure prior information is as follows: (1.1)腿部CT图像预处理:(1.1) Leg CT image preprocessing: 采用改进Perona&Malik模型基于偏微分方程的图像方法消除边缘噪声以提高轮廓线提取精度,具体操作如下:The image method based on the partial differential equation of the improved Perona&Malik model is used to eliminate edge noise to improve the accuracy of contour line extraction. The specific operations are as follows: 设x0(a,b)为腿部的CT灰度图像,引入时间变量t∈[0,T],改进的Perona&Malik偏微分方程为如下公式(1)所示,Let x 0 (a,b) be the CT grayscale image of the leg, and introduce the time variable t∈[0,T], the improved Perona&Malik partial differential equation is shown in the following formula (1): 公式(1)中,Gτ为高斯平滑模板,τ为高斯核的尺度,为图像梯度模,c为扩散系数用于控制扩散速度;In formula (1), G τ is the Gaussian smoothing template, τ is the scale of the Gaussian kernel, is the image gradient mode, c is the diffusion coefficient used to control the diffusion speed; 由此完成腿部CT图像预处理;This completes the leg CT image preprocessing; (1.2)获得腿部及内部各组织的边缘图像:(1.2) Obtain the edge images of the legs and internal tissues: 采用腐蚀、膨胀的图像处理的阈值分割算法,首先对上述步骤(1.1)腿部CT图像预处理后的图像进行二值化处理,然后去除检查床提取腿部轮廓,再利用去除检查床的图像减去腿部轮廓图像,即得到腿部轮廓图像,同样操作,得到肌肉轮廓图像、脂肪轮廓图像和骨头轮廓图像,最后通过对腿部轮廓、肌肉轮廓、脂肪轮廓和骨头轮廓的融合,获得腿部及内部各组织的边缘图像;Using the image processing threshold segmentation algorithm of erosion and dilation, first, binarize the image preprocessed in the above step (1.1) leg CT image, then remove the examination bed to extract the leg contour, and then use the image of the removed examination bed Subtract the leg contour image to obtain the leg contour image, and perform the same operation to obtain the muscle contour image, fat contour image and bone contour image, and finally obtain the leg by fusing the leg contour, muscle contour, fat contour and bone contour Edge images of internal and internal organizations; (1.3)提取腿部及内部各组织的边缘图像的轮廓线坐标:(1.3) Extract the contour line coordinates of the edge images of the legs and internal tissues: 对上述步骤(1.2)获得的腿部及内部各组织的边缘图像采用基于二值图像的轮廓提取算法提取腿部及内部各组织的边缘图像的轮廓线坐标,具体操作方法如下:The leg and the edge images of the internal tissues obtained in the above steps (1.2) are extracted using a contour extraction algorithm based on binary images to extract the contour line coordinates of the leg and the edge images of the internal tissues. The specific operation method is as follows: 设y(c,d)为上述步骤(1.2)获得的腿部及内部各组织的边缘图像的像素点,Y(c,d)为应用二值化规则处理后获得的腿部及内部各组织的边缘图像的像素点,用如下所示公式(2)判断当前像素是否为腿部、肌肉、脂肪和骨头轮廓边界像素,Let y(c,d) be the pixel points of the edge image of the leg and internal tissues obtained in the above step (1.2), and Y(c,d) be the leg and internal tissues obtained after applying the binarization rule The pixel points of the edge image, use the following formula (2) to judge whether the current pixel is the boundary pixel of the leg, muscle, fat and bone contour, 公式(2)中,当Y(c,d)=0时,当前像素不是轮廓边界像素点,不保留,当Y(c,d)=1时,当前像素是轮廓边界像素点,该当前像素点保留,应用此规则对上述步骤(1.2)得到的图像的每个像素进行处理,保留在图像中的像素为轮廓线坐标,由此完成了腿部及内部各组织的边缘图像的轮廓线坐标的提取;In the formula (2), when Y(c, d)=0, the current pixel is not a contour border pixel point and is not reserved; when Y(c, d)=1, the current pixel is a contour border pixel point, the current pixel Point retention, apply this rule to process each pixel of the image obtained in the above step (1.2), the pixels retained in the image are the contour line coordinates, thus completing the contour line coordinates of the edge images of the legs and internal tissues extraction; (1.4)构建人体下肢仿真数学模型:(1.4) Construct the mathematical model of human lower limb simulation: 基于上述步骤(1.3)中获得的腿部及内部各组织的边缘图像的轮廓线坐标,运用有限元仿真软件建立人体下肢仿真数学模型;Based on the contour line coordinates of the leg and the edge image of each internal tissue obtained in the above step (1.3), use finite element simulation software to establish a human lower limb simulation mathematical model; 至此,完成建立基于真实结构先验信息的人体下肢数学模型。So far, the mathematical model of human lower limbs based on the prior information of the real structure has been established. 3.根据权利要求1所述一种优化自适应扩展卡尔曼滤波生物电阻抗成像方法,其特征在于求解正问题的具体方法如下:3. according to claim 1, a kind of optimized adaptive extended Kalman filter bioelectrical impedance imaging method is characterized in that the concrete method for solving positive problem is as follows: (2.1)定义人体下肢数学模型的物理特性;(2.1) Define the physical characteristics of the mathematical model of the lower limbs of the human body; (2.2)对人体下肢数学模型离散化处理;(2.2) Discretize the mathematical model of human lower limbs; (2.3)施加边界条件;(2.3) Apply boundary conditions; (2.4)计算边界电压值;(2.4) Calculate the boundary voltage value; 由此完成求解正问题。This completes the solution of the positive problem. 4.根据权利要求1所述一种优化自适应扩展卡尔曼滤波生物电阻抗成像方法,其特征在于用优化自适应扩展卡尔曼滤波算法求解逆问题的具体方法如下:4. according to claim 1, a kind of optimized adaptive extended Kalman filter bioelectrical impedance imaging method is characterized in that the concrete method of solving inverse problem with optimized adaptive extended Kalman filter algorithm is as follows: (3.1)建立状态方程和观测方程:(3.1) Establish state equation and observation equation: (3.1.1)建立状态方程:(3.1.1) Establish the state equation: 所建立的状态方程如下公式(3)所示,The established equation of state is shown in the following formula (3): σk=Ak-1σk-1k-1 (3),σ k = A k-1 σ k-1 + ω k-1 (3), 公式(3)中,σk为k时刻阻抗值,σk-1为k-1时刻阻抗值,Ak-1∈Rm×m,m为有限元模型剖分后单元的个数,采用随机游走模式,则Ak-1=Im,Im为单位矩阵,ωk-1为k-1时刻的系统噪声,该系统噪声设置为白噪声序列,其满足如下公式(4),In formula (3), σ k is the impedance value at time k, σ k-1 is the impedance value at time k-1, A k-1 ∈ R m×m , and m is the number of units after the finite element model is divided, using Random walk mode, then A k-1 =I m , Im is the identity matrix, ω k-1 is the system noise at k-1 moment, and the system noise is set as a white noise sequence, which satisfies the following formula (4), E(ωk-1)=0,E(ωk-1ωk-1 T)=Qk-1 (4),E(ω k-1 )=0,E(ω k-1 ω k-1 T )=Q k-1 (4), 公式(4)中,E为数学期望符号,Qk-1为k-1时刻ωk-1的协方差矩阵;In formula (4), E is the symbol of mathematical expectation, and Q k-1 is the covariance matrix of ω k-1 at time k-1; (3.1.2)建立观测方程:(3.1.2) Establish observation equation: (3.1.2.1)建立非线性方程:(3.1.2.1) Establish nonlinear equation: 所建立的非线性方程如下公式(5)所示,The established nonlinear equation is shown in the following formula (5), uk=Ukk)+νk (5),u k =U kk )+ν k (5), 公式(5)中,uk为边界电压测量向量,Ukk)为边界电压测量值与阻抗值之间的非线性关系,vk为k时刻观测噪声,vk与ωk-1不相关,设置为白噪声序列,其满足如下公式(6),In formula (5), u k is the boundary voltage measurement vector, U kk ) is the nonlinear relationship between the boundary voltage measurement value and the impedance value, v k is the observation noise at time k, v k and ω k-1 Irrelevant, set as a white noise sequence, which satisfies the following formula (6), E(νk)=0,E(νkνk T)=Rk,E(ωkνk T)=0 (6),E(ν k )=0, E(ν k ν k T )=R k , E(ω k ν k T )=0 (6), 公式(6)中,Rk为k时刻vk的协方差矩阵;In formula (6), R k is the covariance matrix of v k at time k ; (3.1.2.2)对(3.1.2.1)中的非线性方程进行一阶泰勒级数展开:(3.1.2.2) Perform a first-order Taylor series expansion of the nonlinear equation in (3.1.2.1): 如下公式(7)为对上述步骤(3.1.2.1)中的非线性方程进行的一阶泰勒级数展开,uk=Uk0)+Jk0)·(σk0)+νk (7),The following formula (7) is the first-order Taylor series expansion of the nonlinear equation in the above step (3.1.2.1), u k =U k0 )+J k0 )·(σ k0 )+ν k (7), 公式(7)中,Jk0)为雅可比矩阵,其计算公式为如下公式(8)所示,In formula (7), J k0 ) is the Jacobian matrix, and its calculation formula is shown in the following formula (8): (3.1.2.3)建立观测方程:(3.1.2.3) Establish observation equation: 进而建立观测方程如下公式(9)所示,Then establish the observation equation as shown in the following formula (9): zk=Jσkk (9),z k = Jσ k + ν k (9), 公式(9)中,zk为边界电压测量值,J为灵敏度矩阵,σk为阻抗值;In formula (9), z k is the measured value of the boundary voltage, J is the sensitivity matrix, and σ k is the impedance value; (3.2)设置初始值σ0(3.2) Set the initial value σ 0 : 所设置的初始值σ0为如下公式(10)所示,The set initial value σ 0 is shown in the following formula (10), σ0=0,C0=∞ (10),σ 0 =0, C 0 =∞ (10), 公式(10)中,C0为误差协方差矩阵初始值;In the formula (10), C 0 is the initial value of the error covariance matrix; (3.3)由k-1时刻得到k时刻的目标状态预测方程:(3.3) Obtain the target state prediction equation at time k from time k-1: 由k-1时刻得到k时刻的目标状态预测方程如下公式(11)所示,The target state prediction equation at time k obtained from time k-1 is shown in the following formula (11): 公式(11)中,为σk的先验估计,即预测值;In formula (11), is the prior estimate of σ k , that is, the predicted value; (3.4)计算k时刻误差协方差矩阵的先验估计 (3.4) Calculate the prior estimate of the error covariance matrix at time k 由如下公式(12)计算k时刻误差协方差矩阵的先验估计 The prior estimate of the error covariance matrix at time k is calculated by the following formula (12): 公式(12)中,γk为自适应修正系数,其计算方法如下公式(13)所示,In the formula (12), γ k is the adaptive correction coefficient, and its calculation method is shown in the following formula (13): 公式(13)中,trace为迹符号,为新息序列的协方差矩阵,其的计算方法如下公式(14)所示,In formula (13), trace is the trace symbol, is the covariance matrix of the innovation sequence, and its calculation method is shown in the following formula (14): 公式(14)中,ξk为新息序列,其计算方法如下公式(15)所示,In formula (14), ξ k is the innovation sequence, and its calculation method is shown in the following formula (15): 公式(15)中,zk为边界电压测量值,为zk的预测值;In the formula (15), z k is the measured value of the boundary voltage, is the predicted value of z k ; γk取值范围如下公式(16)所示,The value range of γ k is shown in the following formula (16): (3.5)计算扩展卡尔曼增益矩阵:(3.5) Calculate the extended Kalman gain matrix: 由如下公式(17)计算扩展卡尔曼增益矩阵KkThe extended Kalman gain matrix K k is calculated by the following formula (17), 公式(17)中,Kk为卡尔曼增益矩阵;In the formula (17), K k is the Kalman gain matrix; (3.6)计算k时刻误差协方差矩阵:(3.6) Calculate the error covariance matrix at time k: 由如下k时刻的状态更新方程即公式(18)来计算k时刻的阻抗值σkThe impedance value σ k at time k is calculated by the following state update equation at time k, that is, formula (18), (3.7)计算k时刻误差协方差矩阵Ck(3.7) Calculate the error covariance matrix C k at time k : 公式(19)中,I为单位矩阵;In formula (19), I is identity matrix; (3.8)判断是否继续递推预测,当确定为“是”时,回转至上述步骤(3.3),当确定为“否”时,则跳转至下面的第四步;(3.8) Judging whether to continue the recursive prediction, when it is determined to be "yes", go back to the above step (3.3), when it is determined to be "no", then jump to the fourth step below; 由此完成用优化自适应扩展卡尔曼滤波算法求解逆问题。In this way, the inverse problem is solved with the optimized adaptive extended Kalman filter algorithm.
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