CN111938641B - Optimized self-adaptive extended Kalman filtering bioelectrical impedance imaging method - Google Patents
Optimized self-adaptive extended Kalman filtering bioelectrical impedance imaging method Download PDFInfo
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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
Technical Field
The technical scheme of the invention relates to measuring the electrical impedance of a certain part of a body, in particular to an optimized self-adaptive extended Kalman filtering bioelectrical impedance imaging method.
Background
Electrical impedance imaging (Electrical Impedance Tomography, EIT) is a low cost, non-invasive imaging technique to obtain electrical potential on a surface by injecting a suitable current pattern through contact electrodes placed on the surface of the object, thereby measuring surface potential values with high temporal resolution to estimate electrical properties, such as conductivity distribution, inside the cross-section of the object. Electrical impedance imaging techniques have been used in industry, geophysics, and other fields of engineering and application science. In geophysics, it is used to locate underground mineral resource distributions. In oil recovery, it has been used to monitor the flow of injection fluids into the earth. Bioelectrical impedance imaging (Biological Electrical Impedance Imaging Tomography, BEIIT) is a technique in which excitation current is applied to the skin of a human body to obtain a response voltage, and an image is generated from the current value and the voltage value to represent the internal conductivity distribution of the human body. Bioelectrical impedance imaging techniques have been used in medicine to monitor the inhaled air distribution of mechanically ventilated patients in intensive care units, and have also been reported in literature to be applied to gastric emptying, brain function monitoring, breast imaging and pulmonary function assessment. Although electrical impedance imaging techniques have not been used to date to replace positron emission tomography, computed tomography, and the like in medical institutions, they have potential clinical application value because they are a non-invasive, rapid-response, and low-cost imaging technique that does not cause any side effects as compared to other medical imaging techniques that use harmful radiation.
However, the inverse problem with existing bioelectrical impedance imaging techniques is highly ill-conditioned compared to techniques using other radiological medical imaging techniques. This is because the first, underdetermined, limited number of electrodes has a limited current flow path, the unknown amount of solution is much greater than the condition number, and the two are not matched, so the solution is not unique; secondly, the electric potential in the field is a function of the electric conductivity distribution, and the electric conductivity is a nonlinear problem through the surface voltage measurement value; thirdly, the instability is caused, the boundary potential is insensitive to the change of the internal conductivity in the field, the inverse problem solving is essentially a derivative, and the small change of the measured boundary voltage value can cause the huge change of the internal conductivity, so that the solving process is unstable. From the above analysis, it is known that the inverse problem of the electrical impedance resolution imaging technique has serious discomfort. The stability and the calculation precision of reconstruction calculation can be improved by selecting an effective algorithm, and the purposes of high resolution and short imaging time of bioelectrical impedance imaging are achieved. The human body from the earth gravity environment to the weightlessness or overweight environment can cause the transfer of body fluid, which is divided into extracellular fluid and intracellular fluid. When extracellular fluid and intracellular fluid are transferred, the conductivity of each tissue of a human body can be changed, and the electrical impedance imaging technology is used for generating cross-sectional images of different parts of the human body, so that continuous monitoring and periodic evaluation of the health state of a spaceman flying on orbit for a long time can be realized, and a dynamic imaging mode is selected for the scene. Dynamic imaging modes are specifically classified into classical algorithms and novel image reconstruction algorithms, such as neural networks and genetic algorithms. Classical algorithms are classified into non-iterative and iterative methods, with: linear back projection algorithm, newton-Raphsom algorithm, landweber algorithm, conjugate gradient algorithm, truncated singular value decomposition algorithm, and improved algorithm based on different regularization methods. However, these algorithms cannot solve the problems of artifact, low resolution, low anti-interference capability, high requirement on targets and continuous imaging at the same time, such as the large and small time and compact structure of human lower limbs and the change of conductivity, and how to acquire bioelectrical impedance imaging technical images with small continuous distortion to reflect the actual leg conductivity distribution, so that providing valuable information for body fluid research becomes the current problem to be solved urgently.
The bioelectrical impedance imaging technology disclosed in the prior art comprises the following steps: CN106037650a discloses a bioelectrical impedance imaging method of mixed variation, the method uses different weights of the regular and total variation regularization of the gihonov to determine the objective function of the mixed variation algorithm, applies the optimized L curve to adaptively adjust regularization parameters, solves the inverse problem by the steepest descent method and reconstructs the thoracic impedance image, the above-mentioned prior art scheme has the defects of over-idealized experimental model, single target, uniform conductivity distribution and low noise immunity; CN103462605a discloses a bioelectrical impedance imaging method, in the calculation of positive problems, non-uniform subdivision is adopted, the inverse problem adopts a standard particle swarm method to obtain an electrical impedance distribution value close to a true value, the electrical impedance distribution value is used as an initial value of a regularized gauss-newton algorithm, and an image is reconstructed through the regularized gauss-newton algorithm, so that the technical scheme has the defects of high accuracy and small calculation amount of the reconstructed image;
the Kalman Filtering (KF) algorithm is a novel image reconstruction algorithm based on numerical optimal estimation by using the covariance recursion operation of the predicted value of the previous moment and the measured value of the current moment, and in the updating and solving process, the filter Kalman gain weight can change the value of the filter Kalman gain weight along with different moments, and only the covariance value of the previous moment is reserved, so that the operation speed is high, and the solving accuracy is high. The performance of the kalman filter algorithm depends on the accuracy of the mathematical model of the system and the integrity of the noise statistics. However, in practical application, an accurate and uniform mathematical model cannot be established, the noise characteristics of the model are difficult to be properly described, and the model does not have self-adaptive stress on noise statistical variation, so that the unstable accuracy of the Kalman filtering algorithm is reduced or even diverged, and most importantly, the model is only aimed at a linear system. In order to solve the non-linearity problem, an extended kalman filter (Extended Kalman Filtering, EKF) algorithm is proposed, which is also the most widely used method in non-linear systems. The extended Kalman filtering algorithm utilizes Taylor series expansion to locally linearize the nonlinear system, and expands the application range of the Kalman filtering equation. The extended kalman filter algorithm retains many of the computational efficiency advantages associated with kalman filtering. Because the extended Kalman filtering algorithm expands the low-order Taylor series of the nonlinear function, the high-order part is truncated, so that the precision can not meet the system requirement when the method is applied.
The prior art disclosed Kalman filtering algorithm uses the following techniques: CN101499173B discloses a method for reconstructing a kalman filtering image in PET imaging, which comprises obtaining a sinogram of an original projection line by a PET positron emission tomography scanner, then establishing a state space system, obtaining radioactivity distribution by a kalman filtering method based on the state space to reconstruct an image, wherein the technical scheme has the defects of large operation amount and low reconstruction speed; CN106097285B discloses an ECT image reconstruction method based on adaptive extended kalman filtering, where the scheme has the defect that when a system model, a system input has deviation or actual data mutation, the kalman gain cannot be corrected online in real time, so that the accuracy of the algorithm may lose the original performance; vauhkonen et al, 1998 introduced the Kalman filtering algorithm into electrical impedance tomography; in 2010, xue Yongwen et al published paper "application of modified extended kalman filter in EIT", and in which extended kalman equation set given in paper "Electrical Impedance tomography Using The ExtebdedKalman Filter" Flavio Celso Trigo et al is modified, the above technical solution has the defect that as the measurement frequency increases, the relative error of the image is larger and larger, distortion occurs, and the difference between the absolute value of the predicted value and the actual value of the algorithm is gradually increased, that is, the filter diverges.
In a word, the existing disclosed bioelectrical impedance imaging technology has the defects of low noise resistance, high accuracy of reconstructed images and small calculated amount, and the existing disclosed Kalman filtering algorithm applied to reconstructed images has the defect that the accuracy of the algorithm may lose the original performance and the divergence of a filter.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: the method comprises the steps of establishing a human lower limb mathematical model based on real structure priori information; 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.
The technical scheme adopted by the invention for solving the technical problems is as follows: an optimized self-adaptive extended Kalman filtering bioelectrical impedance imaging method comprises the following specific steps:
A. the device for optimizing the adaptive extended Kalman filtering electrical impedance imaging is arranged:
the device for carrying out the optimized self-adaptive extended Kalman filtering electrical impedance imaging adopts a modularized design and is of a serial and parallel hybrid structure, and the device comprises a computer module, a communication module, a general 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 for controlling the program operation of the general control and processing module and the self-adaptive extended Kalman filtering imaging algorithm, the general control and processing module receives instructions from the computer module through the communication module and controls and coordinates the operation among the modules of the electrical impedance imaging device system through the data bus, the address bus and the control bus, the control of the hardware system is accurately finished in real time and timely fed back to the computer module information through the communication module to make corresponding adjustment, the voltage/current conversion constant current output module is used for generating sinusoidal voltage signals, the voltage is converted into current through the isolation, filtering, voltage gain circuit and the voltage/current conversion constant current source circuit, the general control and processing module controls the frequency, the amplitude and the phase of the voltage signals of the module through the communication module, the excitation signal frequency, amplitude and phase are regulated, the excitation channel gating module receives the instruction from the general control and processing module, adopts low on-resistance analog multipath to select and switch the injection mode in the electrode array, injects current signals into the tested object through corresponding electrodes, establishes a sensitive area, the measurement channel gating module receives the instruction from the general control and processing module to select and switch the measurement mode of the electrode array, sends the extracted tested object voltage signals to the signal modulation module, the signal modulation module processes the voltage signals input by the measurement channel gating module into digital signals through the instrument amplifying circuit, the filter circuit, the demodulation circuit, the variable gain amplifying circuit, the low-pass filter and the A/D conversion circuit, and transmits the digital voltage signals into the computer module in real time through the general control and processing module and the communication module, the computer carries out image reconstruction imaging on the acquired voltage data and current data through a self-adaptive extended Kalman filtering algorithm;
B. The reconstruction of the human lower limb electrical impedance image is carried out by using an optimized self-adaptive extended Kalman filtering bioelectrical impedance imaging method, and the technical scheme is as follows:
firstly, establishing a human lower limb mathematical model based on real structure priori information;
secondly, solving a positive problem;
thirdly, solving an inverse problem by using an optimized self-adaptive extended Kalman filtering algorithm;
fourth, outputting the human body lower limb electrical impedance reconstruction image:
the device for performing Kalman filtering bioelectrical impedance imaging is arranged in the A to output the thoracic cavity impedance image obtained by reconstructing the human lower limb impedance image by using the self-adaptive expansion Kalman filtering bioelectrical impedance imaging method in the B, and the specific implementation process is as follows:
writing the amplitude and frequency of the current exciting the legs of the human body in the computer module, applying excitation signals to the legs of the human body, namely the surface of the tested object through the electrode array, measuring leg voltage signals through the electrodes, transmitting the leg voltage signals into the computer, and calling an optimized self-adaptive extended Kalman filtering algorithm program for imaging; the general control and processing module is the core of the device, and the communication module sends and receives the control instruction from the computer module to realize the global control and the coordinated operation work of the hardware system of the device A; the voltage/current constant current output module is used for converting an adjustable sine wave signal within the range of 1kHz-1MHz into a current signal with an adjustable amplitude within the range of 0.1mA-5mA, and the excitation channel gating module is used for realizing the on-off of an excitation electrode so that the excitation signal flows into the corresponding electrode according to a set mode and is injected into a measured object; the on-off of the measuring electrodes is realized by controlling the measuring channel gating module, so that the corresponding electrodes in the measuring electrodes extract the voltage signals of the measured object, and the signals are sent to the signal modulation module; then the instrument amplifying circuit, the filter circuit, the demodulation circuit, the variable gain amplifying circuit, the low-pass filter and the A/D conversion circuit in the signal conditioning module process the voltage signal input by the measuring channel gating module into a digital signal; then the digital voltage signal is transmitted into a computer module through a communication module, the digital voltage signal is converted into an analog voltage signal, the reconstruction of the electrical impedance image of the leg is realized through optimizing the self-adaptive expansion Kalman filtering algorithm program, and finally, the reconstructed image of the electrical impedance of the lower limb of the human body is output through a computer;
The reconstruction of the human lower limb electrical impedance image by using the optimized self-adaptive expansion Kalman filtering bioelectrical impedance imaging method is completed, and the human lower limb electrical impedance image is obtained.
The specific method for establishing the human lower limb mathematical model based on the real structure priori information in the first step is as follows:
(1.1) leg CT image preprocessing:
the image method based on partial differential equation of the improved Perona & Malik model is adopted to eliminate edge noise so as to improve the contour extraction precision, and the specific operation is as follows:
let x be 0 (a, b) introducing a time variable t E [0, T for CT gray scale images of legs]Improved Perona&The Malik partial differential equation is shown in the following formula (1),
in the formula (1), G τ For a gaussian smoothing template, τ is the scale of the gaussian kernel,c is a diffusion coefficient for controlling the diffusion speed;
thus completing the preprocessing of the CT images of the legs;
(1.2) obtaining an edge image of each of the leg and the internal tissues:
the method comprises the steps of (1) performing binarization treatment on an image subjected to pretreatment of a leg CT image in the step (1.1) by adopting a threshold segmentation algorithm for image processing of corrosion and expansion, removing an inspection bed to extract a leg outline, subtracting the leg outline image from the image of the inspection bed to obtain a leg outline image, performing the same operation to obtain a muscle outline image, a fat outline image and a bone outline image, and finally obtaining edge images of the leg and each tissue in the leg through fusion of the leg outline, the muscle outline, the fat outline and the bone outline;
(1.3) extracting contour coordinates of edge images of the leg and the internal tissues:
and (3) extracting contour coordinates of the leg and the edge images of the internal tissues by adopting a contour extraction algorithm based on binary images on the leg and the edge images of the internal tissues obtained in the step (1.2), wherein the specific operation method is as follows:
let Y (c, d) be the pixel points of the edge image of the leg and each tissue inside obtained in the above step (1.2), Y (c, d) be the pixel points of the edge image of the leg and each tissue inside obtained after applying binarization rule processing, judge whether the current pixel is the boundary pixel of the leg, muscle, fat and bone contour by the following formula (2),
in the formula (2), when Y (c, d) =0, the current pixel is not a contour boundary pixel point, and is not reserved, when Y (c, d) =1, the current pixel is a contour boundary pixel point, and the current pixel point is reserved, and the rule is applied to process each pixel of the image obtained in the step (1.2), and the pixels reserved in the image are contour line coordinates, so that the extraction of the contour line coordinates of the edge images of the leg and each tissue inside is completed;
(1.4) constructing a human lower limb simulation mathematical model:
based on the contour line coordinates of the edge images of the leg and each tissue in the leg and the inner tissue obtained in the step (1.3), establishing a human lower limb simulation mathematical model by using finite element simulation software;
Thus, the establishment of the human lower limb mathematical model based on the prior information of the real structure is completed.
The specific method for solving the positive problem in the second step is as follows:
(2.1) defining physical characteristics of a mathematical model of the lower limb of the human body;
(2.2) discretizing the mathematical model of the lower limb of the human body;
(2.3) applying a boundary condition;
(2.4) calculating a boundary voltage value;
thereby completing the solving of the positive problem.
The method for optimizing the self-adaptive extended Kalman filter bioelectrical impedance imaging comprises the following specific steps of:
(3.1) establishing a state equation and an observation equation:
(3.1.1) establishing a state equation:
the established state equation is shown in the following formula (3),
σ k ＝A k-1 σ k-1 +ω k-1 (3)，
in the formula (3), sigma k For the impedance value at time k, sigma k-1 For the impedance value at time k-1, A k-1 ∈R m×m M is the number of units after finite element model subdivision, and A is the number of units after finite element model subdivision by adopting a random walk mode k-1 ＝I m ，I m Is a unitary matrix omega k-1 Is the system noise at time k-1, which is set as a white noise sequence, which satisfies the following equation (4),
E(ω k-1 )＝0,E(ω k-1 ω k-1 T )＝Q k-1 (4)，
in the formula (4), E is a mathematical desired symbol, Q k-1 For time ω of k-1 k-1 Is a covariance matrix of (a);
(3.1.2) establishing an observation equation:
(3.1.2.1) establishing a nonlinear equation:
the established nonlinear equation is shown in the following equation (5),
u k ＝U k (σ k )+ν k (5)，
in the formula (5), u k For measuring vector of boundary voltage, U k (σ k ) V is a nonlinear relationship between the boundary voltage measurement and the impedance value k For observing noise at time k, v k And omega k-1 Uncorrelated, set as a white noise sequence, which satisfies the following equation (6),
E(ν k )＝0,E(ν k ν k T )＝R k ,E(ω k ν k T )＝0 (6)，
in the formula (6), R k For time v of k k Is a covariance matrix of (a);
(3.1.2.2) first-order Taylor series expansion of the nonlinear equation in (3.2.2.1):
the following equation (7) is a first order taylor series expansion of the nonlinear equation in the above step (3.2.2.1),
u k ＝U k (σ 0 )+J k (σ 0 )·(σ k -σ 0 )+ν k (7)，
in the formula (7), J k (σ 0 ) Is a jacobian matrix, the calculation formula is shown in the following formula (8),
(3.1.2.3) establishing the observation equation:
and then an observation equation is established as shown in the following formula (9),
z k ＝Jσ k +ν k (9)，
in the formula (9), z k For the boundary voltage measurements, J is the sensitivity matrix, σ k Is an impedance value;
(3.2) setting an initial value sigma 0 ：
The set initial value sigma 0 As shown in the following formula (10),
σ 0 ＝0,C 0 ＝∞ (10)，
in the formula (10), C 0 An initial value of an error covariance matrix;
(3.3) obtaining a target state prediction equation of the k moment from the k-1 moment:
the target state prediction equation for the k time from the k-1 time is shown in the following equation (11),
In the formula (11), the color of the sample is,is sigma (sigma) k I.e. the predicted value;
(3.4) calculating a priori estimates of the k-time error covariance matrix
A priori estimates of the k-time error covariance matrix are calculated from equation (12) below
In the formula (12), gamma k For the adaptive correction coefficient, the calculation method is as shown in the following formula (13),
in equation (13), trace is a trace symbol,covariance matrix of innovation sequence, its meterThe calculation method is shown in the following formula (14),
in the formula (14), xi k For the innovation sequence, the calculation method is shown in the following formula (15),
in the formula (15), z k As a measure of the boundary voltage,is z k Is a predicted value of (2);
γ k the range of values is shown in the following formula (16),
(3.5) calculating an extended kalman gain matrix:
calculating an extended Kalman gain matrix K from the following equation (17) k ，
In the formula (17), K k Is a Kalman gain matrix;
(3.6) calculating a k moment error covariance matrix:
the impedance value sigma at the k time is calculated from the following state update equation at the k time, equation (18) k ，
(3.7) calculating the k-time error covariance matrix C k ：
In the formula (19), I is an identity matrix;
(3.8) judging whether to continue recursive prediction, turning to the step (3.3) when the determination is yes, and jumping to the following fourth step when the determination is no;
Thus, the inverse problem is solved by using an optimized self-adaptive extended Kalman filtering algorithm.
The optimized self-adaptive extended Kalman filtering bioelectrical impedance imaging method is characterized in that a device for carrying out bioelectrical impedance imaging is obtained through a known way, and the related operation method is realized, and the image method based on partial differential equation of the improved Perona & Malik model is known in the technical field.
The beneficial effects of the invention are as follows: compared with the prior art, the method has the following substantial characteristics and remarkable progress:
(1) The CN106037650A hybrid variational bioelectrical impedance imaging method is an invention patent applied earlier by the applicant, and practice proves that the invention patent applied earlier has the defects of over-idealized 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 invention builds a mathematical model based on the prior information of the lower limbs of a real human body, has good imaging effect on multiple targets and uneven conductivity distribution, has good stability in the reconstruction process of an algorithm, introduces a self-adaptive correction coefficient to adjust the proportion of a predicted value, improves the proportion of new measured data, effectively and accurately tracks the dynamic change trend of a target area and calculates the specific state of the target area, improves the image reconstruction resolution, ensures the accuracy and real-time performance of the algorithm, and can quickly and stably converge in real time when the data is changed stepwise. The technical solutions that are now claimed by the present invention are not readily available to those skilled in the art on the basis of CN106037650 a.
(2) Compared with a bioelectrical impedance imaging method of CN103462605A, the bioelectrical impedance imaging method has the outstanding substantial characteristics and remarkable progress that the self-adaptive correction coefficient is obtained by utilizing the innovation covariance calculation, the calculated amount is small, and the calculation process is simple.
(3) Compared with a Kalman filtering image reconstruction method in PET imaging of CN101499173B, the method has the outstanding substantial characteristics and remarkable progress that the self-adaptive correction coefficient is obtained by utilizing the innovation covariance calculation, and the complexity of an extended Kalman filtering algorithm is not increased.
(4) Compared with an iterative expansion increment Kalman filtering method of CN103312297A, the iterative expansion increment Kalman filtering method has the outstanding substantive characteristics and remarkable progress that the defect that priori information is difficult to obtain is overcome, the online prediction can be effectively performed, the divergence and the non-convergence of an algorithm are restrained, and the stability and the accuracy of the algorithm are improved.
(5) In 2010 Xue Yongwen et al, the paper "application of modified extended kalman filter in EIT", in which Flavio Celso Trigo et al, in paper "Electrical Impedance tomography Using The Extebded Kalman Filter", modified the set of extended kalman equations given, the solution provided by this paper was effective in one-step imaging, but when the relative error of the image is larger and distortion occurs with increasing number of measurements, the absolute value between the predicted value and the actual value of the algorithm is gradually increased. Aiming at the problem, the invention introduces the optimized self-adaptive correction coefficient to weaken the memory length of the algorithm and improve the occupied weight of observed quantity, and adjusts the Kalman gain matrix on line so that the innovation sequence is kept orthogonal to improve the stability of the Kalman algorithm in electrical impedance imaging. Compared with the technical scheme disclosed in the paper 'application of modified extended Kalman filter in EIT', the invention has outstanding substantive characteristics and remarkable progress that the weight of the expansion observation data of the optimized self-adaptive correction coefficient reaches the effect of the real-time correction observation value in the estimated value, when the state is suddenly changed, such as the difference between the resistivity values of the muscle part and the skeleton part is great, the innovation sequence is positively correlated with the error covariance matrix, the innovation sequence is increased, the error covariance matrix is increased, the self-adaptive correction coefficient is also increased, the position of the innovation sequence in reconstruction is emphasized, the weight of old data is reduced, and the calculation amount of the self-adaptive correction coefficient is small and easy to realize and has real-time performance.
(6) The invention improves the imaging speed and the image resolution of the reconstruction of the human lower limb image, introduces the self-adaptive correction coefficient in the reconstruction process, has small calculated amount, simple calculation process and strong adaptability, and improves the accuracy, the stability and the instantaneity of the algorithm.
(7) The application range of the method is not limited to the field of electrical impedance imaging, and the method can be applied to the fields of geotechnical engineering, resource and environmental protection and the like for detecting objects.
(8) The method comprises the steps of combining a bioelectrical impedance imaging method with a Kalman filtering method to form a new technical scheme, splitting the model into small units by a finite element method through establishing a human lower limb mathematical model based on real structure priori information, applying boundary conditions to calculate boundary voltage values, solving inverse problems by the finite element mathematical model by using a self-adaptive extended Kalman filtering algorithm and reconstructing leg images, introducing an optimized self-adaptive correction coefficient to improve the weight occupied by observed quantity in the reconstruction process, adjusting a Kalman gain matrix on line, improving the stability of the Kalman algorithm in impedance imaging, overcoming the defects that the existing disclosed bioelectrical impedance imaging technology has low noise resistance and cannot simultaneously have high accuracy of reconstructed images and small calculated amount, and the existing Kalman filtering algorithm applied to the reconstructed images has the defect that the algorithm accuracy may lose the original performance and the filter divergence.
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The invention will be further described with reference to the drawings and examples.
FIG. 1 is a schematic flow chart of reconstructing an electrical impedance image of a lower limb of a human body by using an optimized adaptive extended Kalman filter bioelectrical impedance imaging method in the method of the invention.
Fig. 2 is a schematic flow chart of "building a mathematical model of a human lower limb based on real structure prior information" in fig. 1.
Fig. 3 is a schematic flow chart of "solving a problem" in fig. 1.
Fig. 4 is a schematic flow chart of "solving the inverse problem with optimized adaptive extended kalman filter algorithm" in fig. 1.
FIG. 5 is a schematic diagram of the structure of the apparatus for performing Kalman filtering bioelectrical impedance imaging in the method of the present invention.
Fig. 6 is a mathematical model of an electrical impedance image reconstructed from an electrical impedance image of a lower limb of a human body output in the method of the present invention.
In the figure, a computer module, a communication module, a general control and processing module, a voltage/current constant current output module, an excitation channel gating module, a measurement channel gating module, an electrode array, a signal modulation module and a measured object are respectively arranged in sequence, wherein the computer module, the communication module, the general control and processing module, the voltage/current constant current output module, the excitation channel gating module, the measurement channel gating module, the electrode array and the signal modulation module are respectively arranged in sequence, and the measured object is arranged in sequence.
Detailed Description
The embodiment shown in fig. 1 shows that in the method of the invention, the optimized self-adaptive expansion kalman filter bioelectrical impedance imaging method is used for reconstructing the electrical impedance image of the lower limb of the human body: establishing a human lower limb mathematical model based on real structure priori information, solving a positive problem, solving an inverse problem by using an optimized self-adaptive extended Kalman filtering algorithm, and outputting a human lower limb electrical impedance image.
The embodiment shown in fig. 2 shows that the flow of "building a mathematical model of a lower limb of a human body based on prior information of a real structure" in fig. 1 is: the method comprises the steps of preprocessing leg CT images, obtaining edge images of legs and internal tissues, extracting outline coordinate structures of the edge images of the legs and the internal tissues, and constructing a human lower limb simulation mathematical model.
The embodiment shown in fig. 3 shows that the flow of "solving a positive problem" in fig. 1 is: defining physical characteristics of a human lower limb mathematical model, discretizing the human lower limb mathematical model, applying boundary conditions, and calculating boundary voltage values.
The embodiment shown in fig. 4 shows that the flow of "solving the inverse problem with optimized adaptive extended kalman filter algorithm" in fig. 1 is: establishing a state equation and an observation equation, and setting an initial value sigma 0 Obtaining a target state prediction equation of k moment from k-1 moment, and calculating prior estimation of k moment error covariance matrixCalculating an extended Kalman gain matrix, calculating a k moment error covariance matrix, and calculating a k moment error covariance matrix C k Judging whether to continue recursive prediction? When the determination is yes, turning to the step of obtaining the target state prediction equation of the k moment from the k-1 moment, and when the determination is no, jumping to the following fourth step: and outputting the electrical impedance image of the lower limb of the human body.
The embodiment shown in fig. 5 shows that the structure of the device used for carrying out the Kalman filtering bioelectrical impedance imaging by the method of the invention is composed of a computer module 1, a communication module 2, a general 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 for controlling the operation of the master control and processing module 3 and optimizing the self-adaptive extended Kalman filtering algorithm program, the master control and processing module 3 controls and coordinates the modules of the bioelectrical impedance imaging device system through a data bus, an address bus and a control bus, the control of each module of the hardware system is accurately finished in real time and timely fed back to the relevant information of the computer module 1 through the communication module 2 to make corresponding adjustment, the voltage/current constant current output module 4 is used for generating sinusoidal voltage signals, then the voltage is converted into current through an isolation, filtering, voltage gain circuit and a voltage/current conversion constant current source circuit, the excitation channel gating module 5 adopts a multipath analog switch with low on resistance to select and switch injection modes in electrodes, the current signals are injected into a measured object 9 through corresponding electrodes, the measurement channel gating module 6 is used for selecting a measurement mode of the electrodes, the electrode array 7 is placed on the surface of the measured object 9 to extract voltage signals induced on the surface of the measured object 9 and is transmitted to the signal modulation module 8, the signal modulation module 8 is used for generating sinusoidal voltage signals, the voltage signals are transmitted into the instrument amplification circuit, the filtering circuit, the demodulation circuit, the variable gain circuit, the voltage gain circuit and the voltage conversion circuit and the voltage/current conversion constant current source circuit are used for collecting the voltage signals through the computer algorithm module 1, the self-adaptive image processing algorithm is carried out through the computer algorithm, and the self-adaptive image processing module 1 is used for reconstructing the image signals, and the image is self-adaptively processed through the computer algorithm, and the image processing module is used for collecting the image signals and the image is suitable for the image, and the image and has high quality.
FIG. 6 shows an image of a leg mathematical model reconstructed by the optimized adaptive extended Kalman filtering algorithm, which shows that the optimized adaptive extended Kalman filtering algorithm adopted by the invention has good stability in the reconstruction process, and the optimized adaptive correction coefficient obtained by calculation of the innovation covariance is introduced to adjust the innovation weight, so that the weight of old measurement data is reduced, the calculated amount is smaller than that of the traditional calculation method, the complexity of the calculation process is low, the image reconstruction with more complexity can be adapted, the effective accurate and timely prediction of the change trend and output can be ensured when the data is mutated, and the accuracy, the stability and the instantaneity of the algorithm are improved, thereby achieving the purposes of improving the imaging speed and the image resolution of the image reconstruction.
Examples
The optimized self-adaptive extended Kalman filter bioelectrical impedance imaging method comprises the following specific steps:
A. the device for optimizing the adaptive extended Kalman filtering electrical impedance imaging is arranged:
the device for carrying out the optimized self-adaptive extended Kalman filtering electrical impedance imaging adopts a modularized design, is in a serial and parallel mixed structure as shown in figure 5, and comprises a computer module, a communication module, a general 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 for controlling the program operation of the general control and processing module and the self-adaptive extended Kalman filtering imaging algorithm, the general control and processing module receives instructions from the computer module through the communication module and controls and coordinates the operation among the modules of the electrical impedance imaging device system through the data bus, the address bus and the control bus, the control of the hardware system is accurately finished in real time and timely fed back to the computer module information through the communication module to make corresponding adjustment, the voltage/current conversion constant current output module is used for generating sinusoidal voltage signals, the voltage is converted into current through the isolation, filtering, voltage gain circuit and the voltage/current conversion constant current source circuit, the general control and processing module controls the frequency, the amplitude and the phase of the voltage signals of the module through the communication module, the excitation signal frequency, amplitude and phase are regulated, the excitation channel gating module receives the instruction from the general control and processing module, adopts low on-resistance analog multipath to select and switch the injection mode in the electrode array, injects current signals into the tested object through corresponding electrodes, establishes a sensitive area, the measurement channel gating module receives the instruction from the general control and processing module to select and switch the measurement mode of the electrode array, sends the extracted tested object voltage signals to the signal modulation module, the signal modulation module processes the voltage signals input by the measurement channel gating module into digital signals through the instrument amplifying circuit, the filter circuit, the demodulation circuit, the variable gain amplifying circuit, the low-pass filter and the A/D conversion circuit, and transmits the digital voltage signals into the computer module in real time through the general control and processing module and the communication module, the computer carries out image reconstruction imaging on the acquired voltage data and current data through a self-adaptive extended Kalman filtering algorithm;
B. The reconstruction of the human lower limb electrical impedance image is carried out by using an optimized self-adaptive extended Kalman filtering bioelectrical impedance imaging method, and the technical scheme is as follows:
firstly, establishing a human lower limb mathematical model based on real structure priori information:
(1.1) leg CT image preprocessing:
the image method based on partial differential equation of the improved Perona & Malik model is adopted to eliminate edge noise so as to improve the contour extraction precision, and the specific operation is as follows:
let x be 0 (a, b) introducing a time variable t E [0, T for CT gray scale images of legs]Improved Perona&The Malik partial differential equation is shown in the following formula (1),
in the formula (1), G τ For a gaussian smoothing template, τ is the scale of the gaussian kernel,c is a diffusion coefficient for controlling the diffusion speed;
thus completing the preprocessing of the CT images of the legs;
(1.2) obtaining an edge image of each of the leg and the internal tissues:
the method comprises the steps of (1) performing binarization treatment on an image subjected to pretreatment of a leg CT image in the step (1.1) by adopting a threshold segmentation algorithm for image processing of corrosion and expansion, removing an inspection bed to extract a leg outline, subtracting the leg outline image from the image of the inspection bed to obtain a leg outline image, performing the same operation to obtain a muscle outline image, a fat outline image and a bone outline image, and finally obtaining edge images of the leg and each tissue in the leg through fusion of the leg outline, the muscle outline, the fat outline and the bone outline;
(1.3) extracting contour coordinates of edge images of the leg and the internal tissues:
and (3) extracting contour coordinates of the leg and the edge images of the internal tissues by adopting a contour extraction algorithm based on binary images on the leg and the edge images of the internal tissues obtained in the step (1.2), wherein the specific operation method is as follows:
let Y (c, d) be the pixel points of the edge image of the leg and each tissue inside obtained in the above step (1.2), Y (c, d) be the pixel points of the edge image of the leg and each tissue inside obtained after applying binarization rule processing, judge whether the current pixel is the boundary pixel of the leg, muscle, fat and bone contour by the following formula (2),
in the formula (2), when Y (c, d) =0, the current pixel is not a contour boundary pixel point, and is not reserved, when Y (c, d) =1, the current pixel is a contour boundary pixel point, and the current pixel point is reserved, and the rule is applied to process each pixel of the image obtained in the step (1.2), and the pixels reserved in the image are contour line coordinates, so that the extraction of the contour line coordinates of the edge images of the leg and each tissue inside is completed;
(1.4) constructing a human lower limb simulation mathematical model:
based on the contour line coordinates of the edge images of the leg and each tissue in the leg and the inner tissue obtained in the step (1.3), establishing a human lower limb simulation mathematical model by using finite element simulation software;
Thus, the establishment of the mathematical model of the lower limb of the human body based on the prior information of the real structure is completed;
secondly, solving a positive problem:
(2.1) defining physical characteristics of a mathematical model of the lower limb of the human body;
firstly, the current field added to the positive problem of the electrical impedance imaging technology can be regarded as a steady-state current field to be treated, and the current field is equivalent to the Laplace boundary value problem:
where σ is the conductivity distribution inside the target,is the potential distribution inside the sensitive field Ω,
secondly, defining the physical characteristics of the human lower limb mathematical model based on the prior information of the real structure, which is established in the first step, wherein the method comprises the following steps: 1) Adopting a normalized two-dimensional model based on a real human body priori structure; 2) The dot electrodes are positioned on boundary nodes of the model, the number of the electrodes is 16, and the radius of the electrodes is 0.015cm; 3) Injecting 50kHz,2.5mA sine wave excitation current; 4) The contact resistance of each electrode was 50Ω; 5) Conductivity values of the various partial areas of the model were set, with bone conductivity 0.02043S/m, fat conductivity 0.02383S/m, muscle conductivity 0.34083S/m and skin epidermis conductivity 0.00020408S/m.
(2.2) discretizing the mathematical model of the lower limb of the human body;
the finite element method is utilized to divide the human lower limb mathematical model into smaller units, and after the human lower limb mathematical model is discretized, the two-dimensional human lower limb numerical model is divided into 10265 units and 41919 nodes.
(2.3) applying a boundary condition;
in consideration of practical situations, the mathematical model of the invention is a complete electrode model, namely, the contact impedance is considered, so the boundary conditions are as follows:
Γ 2 :(electrode-free region)
(injection electrode region)
Γ 3 :(measuring electrode region)
Wherein z is l Is the contact impedance of the first measuring electrode,is the voltage measured on the electrode, J n Is the current density injected by the electrode, n is the external normal unit vector.
(2.4) calculating a boundary voltage value;
thereby completing solving the positive problem;
thirdly, solving an inverse problem by using an optimized self-adaptive extended Kalman filtering algorithm:
(3.1) establishing a state equation and an observation equation:
(3.1.1) establishing a state equation:
the established state equation is shown in the following formula (3),
σ k ＝A k-1 σ k-1 +ω k-1 (3)，
in the formula (3), sigma k For the impedance value at time k, sigma k-1 For the impedance value at time k-1, A k-1 ∈R m×m M is the number of units after finite element model subdivision, and A is the number of units after finite element model subdivision by adopting a random walk mode k-1 ＝I m ，I m Is a unitary matrix omega k-1 Is the system noise at time k-1, which is set as a white noise sequence, which satisfies the following equation (4),
E(ω k-1 )＝0,E(ω k-1 ω k-1 T )＝Q k-1 (4)，
in the formula (4), E is a mathematical desired symbol, Q k-1 For time ω of k-1 k-1 Is a covariance matrix of (a);
(3.1.2) establishing an observation equation:
(3.1.2.1) establishing a nonlinear equation:
the established nonlinear equation is shown in the following equation (5),
u k ＝U k (σ k )+ν k (5)，
In the formula (5), u k For measuring vector of boundary voltage, U k (σ k ) V is a nonlinear relationship between the boundary voltage measurement and the impedance value k For observing noise at time k, v k And omega k-1 Uncorrelated, set as a white noise sequence, which satisfies the following equation (6),
E(ν k )＝0,E(ν k ν k T )＝R k ,E(ω k ν k T )＝0 (6)，
in the formula (6), R k For time v of k k Is a covariance matrix of (a);
(3.1.2.2) first-order Taylor series expansion of the nonlinear equation in (3.2.2.1):
the following equation (7) is a first order taylor series expansion of the nonlinear equation in the above step (3.2.2.1),
u k ＝U k (σ 0 )+J k (σ 0 )·(σ k -σ 0 )+ν k (7)，
in the formula (7), J k (σ 0 ) Is a jacobian matrix, the calculation formula is shown in the following formula (8),
(3.1.2.3) establishing the observation equation:
and then an observation equation is established as shown in the following formula (9),
z k ＝Jσ k +ν k (9)，
in the formula (9), z k For the boundary voltage measurements, J is the sensitivity matrix, σ k Is an impedance value;
(3.2) setting an initial value sigma 0 ：
The set initial value sigma 0 As shown in the following formula (10),
σ 0 ＝0,C 0 ＝∞ (10)，
in the formula (10), C 0 An initial value of an error covariance matrix;
(3.3) obtaining a target state prediction equation of the k moment from the k-1 moment:
the target state prediction equation for the k time from the k-1 time is shown in the following equation (11),
in the formula (11), the color of the sample is,is sigma (sigma) k I.e. the predicted value;
(3.4) calculating a priori estimates of the k-time error covariance matrix
A priori estimates of the k-time error covariance matrix are calculated from equation (12) below
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In the formula (12), gamma k For the adaptive correction coefficient, the calculation method is as shown in the following formula (13),
in equation (13), trace is a trace symbol,the covariance matrix of the innovation sequence is calculated by the following formula (14),
in the formula (14), xi k For the innovation sequence, the phase calculation method is shown in the following formula (15),
in the formula (15), z k As a measure of the boundary voltage,is z k Is a predicted value of (2);
γ k the range of values is shown in the following formula (16),
(3.5) calculating an extended kalman gain matrix:
calculating an extended Kalman gain matrix K from the following equation (17) k ，
In the formula (17), K k Is a Kalman gain matrix;
(3.6) calculating a k moment error covariance matrix:
the impedance value sigma at the k time is calculated from the following state update equation at the k time, equation (18) k ，
(3.7) calculating the k-time error covariance matrix C k ：
In the formula (19), I is an identity matrix;
(3.8) judging whether to continue recursive prediction, turning to the step (3.3) when the determination is yes, and jumping to the following fourth step when the determination is no;
thus, the inverse problem is solved by using an optimized self-adaptive extended Kalman filtering algorithm;
So far, the reconstruction of the human lower limb electrical impedance image by using the optimized self-adaptive expansion Kalman filtering bioelectrical impedance imaging method is completed;
fourth, outputting the human body lower limb electrical impedance reconstruction image:
the device for performing Kalman filtering bioelectrical impedance imaging is arranged in the A to output the thoracic cavity impedance image obtained by reconstructing the human lower limb impedance image by using the self-adaptive expansion Kalman filtering bioelectrical impedance imaging method in the B, and the specific implementation process is as follows:
writing the amplitude and frequency of the current exciting the legs of the human body in the computer module 1, applying an excitation signal to the legs of the human body, namely the surface of the measured object 9 through the electrode array 7, measuring leg voltage signals through the electrodes, transmitting the leg voltage signals into the computer, and imaging through calling an optimized self-adaptive extended Kalman filtering algorithm program; the general control and processing module 3 is the core of the device, and the communication module 2 sends and receives the control instruction from the computer module 1 to realize the global control and the coordinated operation of the hardware system of the device A; the voltage/current constant current output module 4 is used for converting a sine wave signal which is adjustable within the range of 1kHz-1MHz into a current signal with the amplitude which is adjustable within the range of 0.1mA-5mA, and realizes the on-off of an excitation electrode through the excitation channel gating module 5, so that the excitation signal flows into the corresponding electrode according to a set mode and is injected into a measured object; the on-off of the measuring electrodes is realized by controlling the measuring channel gating module 6, so that the corresponding electrodes in the measuring electrodes extract the voltage signals of the measured object, and the signals are sent to the signal modulation module 8; then the instrument amplifying circuit, the filter circuit, the demodulation circuit, the variable gain amplifying circuit, the low-pass filter and the A/D conversion circuit in the signal conditioning module 8 process the voltage signal input by the measurement channel gating module 6 into a digital signal; then, the digital voltage signal is transmitted into a computer module 1 through a communication module 2, the digital voltage signal is converted into an analog voltage signal, the reconstruction of the electrical impedance image of the leg is realized through optimizing the self-adaptive expansion Kalman filtering algorithm program, and finally, the reconstructed image of the electrical impedance of the lower limb of the human body is output through a computer;
The reconstruction of the human lower limb electrical impedance image by using the optimized self-adaptive expansion Kalman filtering bioelectrical impedance imaging method is completed, and the human lower limb electrical impedance image is obtained.
In the above embodiments, the apparatus for performing bioelectrical impedance imaging is obtained by a known method, and the related operation method, the improved Perona & Malik model image method based on partial differential equation, is known in the art.
Claims (4)
1. An optimized self-adaptive extended Kalman filtering bioelectrical impedance imaging method is characterized by comprising the following specific steps:
A. the device for optimizing the adaptive extended Kalman filtering electrical impedance imaging is arranged:
the device for carrying out the optimized self-adaptive extended Kalman filtering electrical impedance imaging adopts a modularized design and is of a serial and parallel hybrid structure, and the device comprises a computer module, a communication module, a general 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 for controlling the program operation of the general control and processing module and the self-adaptive extended Kalman filtering imaging algorithm, the general control and processing module receives instructions from the computer module through the communication module and controls and coordinates the operation among the modules of the electrical impedance imaging device system through the data bus, the address bus and the control bus, the control of the hardware system is accurately finished in real time and timely fed back to the computer module information through the communication module to make corresponding adjustment, the voltage/current conversion constant current output module is used for generating sinusoidal voltage signals, the voltage is converted into current through the isolation, filtering, voltage gain circuit and the voltage/current conversion constant current source circuit, the general control and processing module controls the frequency, the amplitude and the phase of the voltage signals of the module through the communication module, the excitation signal frequency, amplitude and phase are regulated, the excitation channel gating module receives the instruction from the general control and processing module, adopts low on-resistance analog multipath to select and switch the injection mode in the electrode array, injects current signals into the tested object through corresponding electrodes, establishes a sensitive area, the measurement channel gating module receives the instruction from the general control and processing module to select and switch the measurement mode of the electrode array, sends the extracted tested object voltage signals to the signal modulation module, the signal modulation module processes the voltage signals input by the measurement channel gating module into digital signals through the instrument amplifying circuit, the filter circuit, the demodulation circuit, the variable gain amplifying circuit, the low-pass filter and the A/D conversion circuit, and transmits the digital voltage signals into the computer module in real time through the general control and processing module and the communication module, the computer carries out image reconstruction imaging on the acquired voltage data and current data through a self-adaptive extended Kalman filtering algorithm;
B. The reconstruction of the human lower limb electrical impedance image is carried out by using an optimized self-adaptive extended Kalman filtering bioelectrical impedance imaging method, and the method comprises the following steps:
firstly, establishing a human lower limb mathematical model based on real structure priori information;
secondly, solving a positive problem;
thirdly, solving an inverse problem by using an optimized self-adaptive extended Kalman filtering algorithm;
fourth, outputting the human body lower limb electrical impedance reconstruction image:
the device for optimizing the self-adaptive expansion Kalman filter impedance imaging by the arrangement of the A is used for outputting the reconstruction of the lower limb impedance image of the human body by using the optimizing self-adaptive expansion Kalman filter bioelectrical impedance imaging method to obtain the thoracic cavity impedance image, and the specific implementation process is as follows:
writing the amplitude and frequency of the current exciting the legs of the human body in the computer module, applying excitation signals to the legs of the human body, namely the surface of the tested object through the electrode array, measuring leg voltage signals through the electrodes, transmitting the leg voltage signals into the computer, and calling an optimized self-adaptive extended Kalman filtering algorithm program for imaging; the general control and processing module is the core of the device, and the communication module sends and receives control instructions from the computer module to realize the global control and the coordinated operation work of the hardware system of the device A; the voltage/current constant current output module is used for converting an adjustable sine wave signal within the range of 1kHz-1MHz into a current signal with an adjustable amplitude within the range of 0.1mA-5mA, and the excitation channel gating module is used for realizing the on-off of an excitation electrode so that the excitation signal flows into the corresponding electrode according to a set mode and is injected into a measured object; the on-off of the measuring electrodes is realized by controlling the measuring channel gating module, so that the corresponding electrodes in the measuring electrodes extract the voltage signals of the measured object, and the signals are sent to the signal modulation module; then the instrument amplifying circuit, the filter circuit, the demodulation circuit, the variable gain amplifying circuit, the low-pass filter and the A/D conversion circuit in the signal conditioning module process the voltage signal input by the measuring channel gating module into a digital signal; then the digital voltage signal is transmitted into a computer module through a communication module, the digital voltage signal is converted into an analog voltage signal, the reconstruction of the electrical impedance image of the leg is realized through optimizing the self-adaptive expansion Kalman filtering algorithm program, and finally, the reconstructed image of the electrical impedance of the lower limb of the human body is output through a computer;
The reconstruction of the human lower limb electrical impedance image by using the optimized self-adaptive expansion Kalman filtering bioelectrical impedance imaging method is completed, and the human lower limb electrical impedance image is obtained.
2. An optimized adaptive extended kalman filter bioelectrical impedance imaging method as claimed in claim 1, wherein: the specific method for establishing the human lower limb mathematical model based on the real structure priori information comprises the following steps:
(1.1) leg CT image preprocessing:
the image method based on partial differential equation of the improved Perona & Malik model is adopted to eliminate edge noise so as to improve the contour extraction precision, and the specific operation is as follows:
let x be 0 (a, b) introducing a time variable t E [0, T for CT gray scale images of legs]Improved Perona&The Malik partial differential equation is shown in the following formula (1),
in the formula (1), G τ For a gaussian smoothing template, τ is the scale of the gaussian kernel,c is a diffusion coefficient for controlling the diffusion speed;
thus completing the preprocessing of the CT images of the legs;
(1.2) obtaining an edge image of each of the leg and the internal tissues:
the method comprises the steps of (1) performing binarization treatment on an image subjected to pretreatment of a leg CT image in the step (1.1) by adopting a threshold segmentation algorithm for image processing of corrosion and expansion, removing an inspection bed to extract a leg outline, subtracting the leg outline image from the image of the inspection bed to obtain a leg outline image, performing the same operation to obtain a muscle outline image, a fat outline image and a bone outline image, and finally obtaining edge images of the leg and each tissue in the leg through fusion of the leg outline, the muscle outline, the fat outline and the bone outline;
(1.3) extracting contour coordinates of edge images of the leg and the internal tissues:
and (3) extracting contour coordinates of the leg and the edge images of the internal tissues by adopting a contour extraction algorithm based on binary images on the leg and the edge images of the internal tissues obtained in the step (1.2), wherein the specific operation method is as follows:
let Y (c, d) be the pixel points of the edge image of the leg and each tissue inside obtained in the above step (1.2), Y (c, d) be the pixel points of the edge image of the leg and each tissue inside obtained after applying binarization rule processing, judge whether the current pixel is the boundary pixel of the leg, muscle, fat and bone contour by the following formula (2),
in the formula (2), when Y (c, d) =0, the current pixel is not a contour boundary pixel point, and is not reserved, when Y (c, d) =1, the current pixel is a contour boundary pixel point, and the current pixel point is reserved, and the rule is applied to process each pixel of the image obtained in the step (1.2), and the pixels reserved in the image are contour line coordinates, so that the extraction of the contour line coordinates of the edge images of the leg and each tissue inside is completed;
(1.4) constructing a human lower limb simulation mathematical model:
based on the contour line coordinates of the edge images of the leg and each tissue in the leg and the inner tissue obtained in the step (1.3), establishing a human lower limb simulation mathematical model by using finite element simulation software;
Thus, the establishment of the human lower limb mathematical model based on the prior information of the real structure is completed.
3. The optimized adaptive extended kalman filter bioelectrical impedance imaging method according to claim 1, wherein the specific method for solving the positive problem is as follows:
(2.1) defining physical characteristics of a mathematical model of the lower limb of the human body;
(2.2) discretizing the mathematical model of the lower limb of the human body;
(2.3) applying a boundary condition;
(2.4) calculating a boundary voltage value;
thereby completing the solving of the positive problem.
4. The optimized adaptive extended kalman filter bioelectrical impedance imaging method as set forth in claim 1, wherein the specific method for solving the inverse problem by using the optimized adaptive extended kalman filter algorithm is as follows:
(3.1) establishing a state equation and an observation equation:
(3.1.1) establishing a state equation:
the established state equation is shown in the following formula (3),
σ k ＝A k-1 σ k-1 +ω k-1 (3)，
in the formula (3), sigma k For the impedance value at time k, sigma k-1 For the impedance value at time k-1, A k-1 ∈R m×m M is the number of units after finite element model subdivision, and A is the number of units after finite element model subdivision by adopting a random walk mode k-1 ＝I m ，I m Is a unitary matrix omega k-1 Is the system noise at time k-1, which is set as a white noise sequence, which satisfies the following equation (4),
E(ω k-1 )＝0,E(ω k-1 ω k-1 T )＝Q k-1 (4)，
in the formula (4), E is a mathematical desired symbol, Q k-1 For time ω of k-1 k-1 Is a covariance matrix of (a);
(3.1.2) establishing an observation equation:
(3.1.2.1) establishing a nonlinear equation:
the established nonlinear equation is shown in the following equation (5),
u k ＝U k (σ k )+ν k (5)，
in the formula (5), u k For measuring vector of boundary voltage, U k (σ k ) V is a nonlinear relationship between the boundary voltage measurement and the impedance value k For observing noise at time k, v k And omega k-1 Uncorrelated, set as a white noise sequence, which satisfies the following equation (6),
E(ν k )＝0,E(ν k ν k T )＝R k ,E(ω k ν k T )＝0 (6)，
in the formula (6), R k For time v of k k Is a covariance matrix of (a);
(3.1.2.2) first-order Taylor series expansion of the nonlinear equation in (3.1.2.1):
the following equation (7) is a first-order Taylor series expansion of the nonlinear equation in the above step (3.1.2.1), u k ＝U k (σ 0 )+J k (σ 0 )·(σ k -σ 0 )+ν k (7)，
In the formula (7), J k (σ 0 ) Is a jacobian matrix, the calculation formula is shown in the following formula (8),
(3.1.2.3) establishing the observation equation:
and then an observation equation is established as shown in the following formula (9),
z k ＝Jσ k +ν k (9)，
in the formula (9), z k For the boundary voltage measurements, J is the sensitivity matrix, σ k Is an impedance value;
(3.2) setting an initial value sigma 0 ：
The set initial value sigma 0 As shown in the following formula (10),
σ 0 ＝0,C 0 ＝∞ (10)，
in the formula (10), C 0 An initial value of an error covariance matrix;
(3.3) obtaining a target state prediction equation of the k moment from the k-1 moment:
The target state prediction equation for the k time from the k-1 time is shown in the following equation (11),
in the formula (11), the color of the sample is,is sigma (sigma) k I.e. the predicted value;
(3.4) calculating a priori estimates of the k-time error covariance matrix
A priori estimates of the k-time error covariance matrix are calculated from equation (12) below
In the formula (12), gamma k For adaptive correction coefficients, calculatedThe method is shown in the following formula (13),
in equation (13), trace is a trace symbol,the covariance matrix of the innovation sequence is calculated by the following formula (14),
in the formula (14), xi k For the innovation sequence, the calculation method is shown in the following formula (15),
in the formula (15), z k As a measure of the boundary voltage,is z k Is a predicted value of (2);
γ k the range of values is shown in the following formula (16),
(3.5) calculating an extended kalman gain matrix:
calculating an extended Kalman gain matrix K from the following equation (17) k ，
Formula (VI)(17) In (K) k Is a Kalman gain matrix;
(3.6) calculating a k moment error covariance matrix:
the impedance value sigma at the k time is calculated from the following state update equation at the k time, equation (18) k ，
(3.7) calculating the k-time error covariance matrix C k ：
In the formula (19), I is an identity matrix;
(3.8) judging whether to continue recursive prediction, turning to the step (3.3) when the determination is yes, and jumping to the following fourth step when the determination is no;
Thus, the inverse problem is solved by using an optimized self-adaptive extended Kalman filtering algorithm.
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