CN109758149B - Electrical impedance imaging method combining time difference imaging and frequency difference imaging - Google Patents

Electrical impedance imaging method combining time difference imaging and frequency difference imaging Download PDF

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CN109758149B
CN109758149B CN201910049961.4A CN201910049961A CN109758149B CN 109758149 B CN109758149 B CN 109758149B CN 201910049961 A CN201910049961 A CN 201910049961A CN 109758149 B CN109758149 B CN 109758149B
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杨琳
张学思
代萌
付峰
董秀珍
文治洪
王航
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Fourth Military Medical University FMMU
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Abstract

本发明公开了一种结合时差成像和频差成像的电阻抗成像方法，该方法通过采用两个不同时刻同一频率处的两组测量数据进行时差成像，获得成像目标体积变化而导致的成像目标(位于成像区域内)电阻抗变化，然后通过采用同一时刻不同频率处的两组测量数据进行频差成像，获得成像目标电导率变化而导致的成像目标(位于成像区域内)电阻抗变化，最终结合时差重构结果和频差重构结果计算在某一时刻的成像目标体积(三维成像)或者成像目标面积(二维成像)。本发明利用时差成像和频差成像的各自特点，能够计算成像目标(位于成像区域内)在某一时刻的体积(或面积)。

Figure 201910049961

The invention discloses an electrical impedance imaging method combining time-difference imaging and frequency-difference imaging. The method performs time-difference imaging by using two sets of measurement data at the same frequency at two different times to obtain the imaging target ( The electrical impedance changes in the imaging area), and then frequency difference imaging is performed by using two sets of measurement data at different frequencies at the same time to obtain the electrical impedance changes of the imaging target (located in the imaging area) caused by changes in the conductivity of the imaging target. The time difference reconstruction result and the frequency difference reconstruction result calculate the imaging target volume (three-dimensional imaging) or the imaging target area (two-dimensional imaging) at a certain moment. The present invention utilizes the respective characteristics of time difference imaging and frequency difference imaging, and can calculate the volume (or area) of the imaging target (located in the imaging area) at a certain moment.

Figure 201910049961

Description

一种结合时差成像和频差成像的电阻抗成像方法An Electrical Impedance Imaging Method Combining Time Difference Imaging and Frequency Difference Imaging

技术领域technical field

本发明属于电阻抗成像技术领域，涉及一种结合时差成像和频差成像的电阻抗成像方法。The invention belongs to the technical field of electrical impedance imaging, and relates to an electrical impedance imaging method combining time-difference imaging and frequency-difference imaging.

背景技术Background technique

基于不同生物组织具有不同电阻抗特性，以及同一种生物组织在不同生理和病理状态下的电阻抗特性也不同的原理，电阻抗断层成像技术(ElectricalImpedanceTomography，EIT)通过在被测体表面安放的电极施加一定的安全电流，同时采集边界电压响应信号，然后依据图像重构算法计算被测体内部的电阻抗分布或者电阻抗变化分布。依据成像方式，EIT可分为静态EIT成像、时差EIT成像和频差EIT成像。静态EIT以重构被测体内部的绝对电阻抗分布为目标，，但是其成像结果严重受被测体边界误差、电极位置误差、测量噪声等因素的影响，导致静态EIT成像在实际应用中困难很大。Based on the principle that different biological tissues have different electrical impedance characteristics, and the same biological tissue has different electrical impedance characteristics under different physiological and pathological states, electrical impedance tomography (Electrical Impedance Tomography, EIT) uses electrodes placed on the surface of the object to be measured. A certain safe current is applied, and the boundary voltage response signal is collected at the same time, and then the electrical impedance distribution or the electrical impedance variation distribution inside the measured body is calculated according to the image reconstruction algorithm. According to the imaging method, EIT can be divided into static EIT imaging, time difference EIT imaging and frequency difference EIT imaging. The goal of static EIT is to reconstruct the absolute electrical impedance distribution inside the measured body, but its imaging results are seriously affected by the boundary error of the measured body, electrode position error, measurement noise and other factors, which make static EIT imaging difficult in practical applications. very large.

但是，实际应用一直需要被测体内部的绝对阻抗分布，特别是对于被测体内部某一目标在某一时刻的绝对阻抗分布(也就是，面积或者体积信息)的需求一直存在。尽管时差EIT和频差EIT分别利用不同时刻和不同频率下的测量数据进行差分成像，可反映人体被测部位内部不同时刻和不同频率下的电阻抗分布变化，具有明显降低被测体边界误差、电极位置误差、测量噪声对成像结果影响的优点，但是时差EIT和频差EIT计算的都是电阻抗相对变化信息，无法直接反映人体被测部位内部成像目标在某一时刻的绝对阻抗(面积或者体积信息)。However, practical applications have always required the absolute impedance distribution inside the measured body, especially the demand for the absolute impedance distribution (that is, area or volume information) of a certain target inside the measured body at a certain time. Although the time difference EIT and the frequency difference EIT use the measurement data at different times and different frequencies to perform differential imaging, they can reflect the changes of the electrical impedance distribution inside the measured part of the human body at different times and at different frequencies. The advantages of electrode position error and measurement noise on imaging results, but time difference EIT and frequency difference EIT calculate the relative change information of electrical impedance, which cannot directly reflect the absolute impedance (area or volume information).

因此，亟需一种能够利用时差EIT和频差EIT成像的优点，可计算成像目标面积或者体积的电阻抗成像方法。Therefore, there is an urgent need for an electrical impedance imaging method that can utilize the advantages of time difference EIT and frequency difference EIT imaging to calculate the area or volume of the imaging target.

发明内容SUMMARY OF THE INVENTION

为了克服上述现有技术的缺点，本发明的目的在于提供一种结合时差成像和频差成像的电阻抗成像方法，该方法能够计算被测部位内部成像目标的体积或面积信息。In order to overcome the above-mentioned shortcomings of the prior art, the purpose of the present invention is to provide an electrical impedance imaging method combining time-difference imaging and frequency-difference imaging, which can calculate the volume or area information of the imaging target inside the measured part.

为了达到上述目的，本发明采用以下技术方案予以实现：In order to achieve the above object, the present invention adopts the following technical solutions to be realized:

本发明公开了一种结合时差成像和频差成像的电阻抗成像方法，首先，通过采用两个不同时刻同一频率处的两组测量数据进行时差成像，获得成像目标体积变化与成像目标电阻抗变化之间的对应关系，即得到时差重构结果；然后，通过采用同一时刻不同频率处的两组测量数据进行频差成像，获得成像目标电导率变化与成像目标电阻抗变化之间的关系，即频差重构结果；最终，结合时差重构结果和频差重构结果计算在某一时刻的成像目标体积或面积。The invention discloses an electrical impedance imaging method combining time-difference imaging and frequency-difference imaging. First, by using two sets of measurement data at the same frequency at two different times to perform time-difference imaging, the volume change of the imaging target and the electrical impedance change of the imaging target are obtained. Then, by using the two sets of measurement data at different frequencies at the same time to perform frequency difference imaging, the relationship between the change of the conductivity of the imaging target and the change of the electrical impedance of the imaging target is obtained, namely Frequency difference reconstruction result; finally, the imaging target volume or area at a certain moment is calculated by combining the time difference reconstruction result and the frequency difference reconstruction result.

优选地，上述的结合时差成像和频差成像的电阻抗成像方法，具体包括以下步骤：Preferably, the above-mentioned electrical impedance imaging method combining time difference imaging and frequency difference imaging specifically includes the following steps:

1)采用两种频率f1和f2的电流分别在两个不同时刻t1和t2进行激励，分别获得两种频率处、两个不同时刻的测量数据

Figure BDA0001950414890000021
和
Figure BDA0001950414890000022
其中
Figure BDA0001950414890000023
表示频率处x处、在y时刻的测量数据；1) The currents of two frequencies f 1 and f 2 are used for excitation at two different times t 1 and t 2 , respectively, and the measurement data at two frequencies and two different times are obtained respectively.
Figure BDA0001950414890000021
and
Figure BDA0001950414890000022
in
Figure BDA0001950414890000023
Represents the measurement data at x at the frequency and at time y;

2)利用两个不同时刻t1和t2、频率f1处的两组测量数据

Figure BDA0001950414890000024
和
Figure BDA0001950414890000025
的差分结果
Figure BDA0001950414890000026
进行图像重建，获得频率f1处、因成像目标体积随时间发生变化而引起的电阻抗变化
Figure BDA0001950414890000027
利用下式求解
Figure BDA0001950414890000028
2) Using two sets of measurement data at two different times t 1 and t 2 and frequency f 1
Figure BDA0001950414890000024
and
Figure BDA0001950414890000025
difference result of
Figure BDA0001950414890000026
Perform image reconstruction to obtain electrical impedance changes at frequency f 1 due to changes in the volume of the imaging target over time
Figure BDA0001950414890000027
Solve using the following formula
Figure BDA0001950414890000028

Figure BDA0001950414890000029
其中，S为敏感矩阵，
Figure BDA00019504148900000210
为正则化系数，L为正则化矩阵，
Figure BDA00019504148900000211
为重构矩阵，T为矩阵的转置；
Figure BDA0001950414890000029
Among them, S is the sensitivity matrix,
Figure BDA00019504148900000210
is the regularization coefficient, L is the regularization matrix,
Figure BDA00019504148900000211
is the reconstruction matrix, T is the transpose of the matrix;

3)利用两个不同时刻t1和t2、频率f2处的两组测量数据

Figure BDA00019504148900000212
和
Figure BDA00019504148900000213
的差分结果
Figure BDA00019504148900000214
进行图像重建，获得频率f2处、因成像目标体积随时间发生变化而引起的电阻抗变化
Figure BDA00019504148900000215
利用下式求解
Figure BDA00019504148900000216
3) Using two sets of measurement data at two different times t 1 and t 2 and frequency f 2
Figure BDA00019504148900000212
and
Figure BDA00019504148900000213
difference result of
Figure BDA00019504148900000214
Perform image reconstruction to obtain electrical impedance changes at frequency f 2 due to changes in the imaging target volume over time
Figure BDA00019504148900000215
Solve using the following formula
Figure BDA00019504148900000216

Figure BDA0001950414890000031
其中，
Figure BDA0001950414890000032
为重构矩阵，L为正则化矩阵，
Figure BDA0001950414890000033
为正则化系数；
Figure BDA0001950414890000031
in,
Figure BDA0001950414890000032
is the reconstruction matrix, L is the regularization matrix,
Figure BDA0001950414890000033
is the regularization coefficient;

4)利用t1时刻两种频率f1和f2处的两组测量数据

Figure BDA0001950414890000034
和
Figure BDA0001950414890000035
的差分结果
Figure BDA0001950414890000036
进行图像重建，获得时刻t1处、因成像目标电导率随频率变化而引起的电阻抗变化
Figure BDA0001950414890000037
利用下式求解
Figure BDA0001950414890000038
4) Use two sets of measurement data at two frequencies f 1 and f 2 at time t 1
Figure BDA0001950414890000034
and
Figure BDA0001950414890000035
difference result of
Figure BDA0001950414890000036
Perform image reconstruction to obtain the electrical impedance change at time t 1 due to the change of the conductivity of the imaging target with the frequency
Figure BDA0001950414890000037
Solve using the following formula
Figure BDA0001950414890000038

Figure BDA0001950414890000039
其中，
Figure BDA00019504148900000310
为重构矩阵，L为正则化矩阵，
Figure BDA00019504148900000311
为正则化系数；
Figure BDA0001950414890000039
in,
Figure BDA00019504148900000310
is the reconstruction matrix, L is the regularization matrix,
Figure BDA00019504148900000311
is the regularization coefficient;

5)利用t2时刻两种频率f1和f2处的两组测量数据

Figure BDA00019504148900000312
和
Figure BDA00019504148900000313
的差分结果
Figure BDA00019504148900000314
进行图像重建，获得时刻t2处、因成像目标电导率随频率变化而引起的电阻抗变化
Figure BDA00019504148900000315
利用下式求解
Figure BDA00019504148900000316
5) Use two sets of measurement data at two frequencies f 1 and f 2 at time t 2
Figure BDA00019504148900000312
and
Figure BDA00019504148900000313
difference result of
Figure BDA00019504148900000314
Perform image reconstruction to obtain the electrical impedance change at time t 2 due to the change of the conductivity of the imaging target with the frequency
Figure BDA00019504148900000315
Solve using the following formula
Figure BDA00019504148900000316

Figure BDA00019504148900000317
其中，
Figure BDA00019504148900000318
为重构矩阵，L为正则化矩阵，
Figure BDA00019504148900000319
为正则化系数；
Figure BDA00019504148900000317
in,
Figure BDA00019504148900000318
is the reconstruction matrix, L is the regularization matrix,
Figure BDA00019504148900000319
is the regularization coefficient;

6)基于成像目标的电阻抗变化与其体积和电导率特性成正比的关系，即：6) The electrical impedance change based on the imaging target is proportional to its volume and conductivity characteristics, namely:

Figure BDA00019504148900000320
Figure BDA00019504148900000320

Figure BDA00019504148900000321
Figure BDA00019504148900000321

Figure BDA00019504148900000322
Figure BDA00019504148900000322

Figure BDA00019504148900000323
Figure BDA00019504148900000323

根据下式计算t1时刻的成像目标体积

Figure BDA00019504148900000329
Figure BDA00019504148900000324
那么，
Figure BDA00019504148900000325
以及t2时刻的成像目标体积
Figure BDA00019504148900000326
其中，
Figure BDA00019504148900000327
和
Figure BDA00019504148900000328
为成像区域的重构结果之和，分别采用以下四式进行计算：
Figure BDA0001950414890000041
和
Figure BDA0001950414890000042
Calculate the imaging target volume at time t 1 according to the following formula
Figure BDA00019504148900000329
Figure BDA00019504148900000324
So,
Figure BDA00019504148900000325
and the imaging target volume at time t 2
Figure BDA00019504148900000326
in,
Figure BDA00019504148900000327
and
Figure BDA00019504148900000328
The sum of the reconstruction results of the imaging area is calculated by the following four formulas:
Figure BDA0001950414890000041
and
Figure BDA0001950414890000042

优选地，电阻抗成像正问题计算方程为：S·Δρ＝ΔV；Preferably, the calculation equation for the forward problem of electrical impedance imaging is: S·Δρ=ΔV;

其中，S是敏感矩阵，ΔV为待重构的边界测量数据变化向量，Δρ为成像目标的电阻抗变化，其与成像目标的体积C和电导率σf成正比，表示为Δρ∝C·σf。Among them, S is the sensitivity matrix, ΔV is the change vector of boundary measurement data to be reconstructed, Δρ is the electrical impedance change of the imaging target, which is proportional to the volume C of the imaging target and the conductivity σ f , expressed as Δρ∝C·σ f .

优选地，待重建的边界测量数据包含各种激励-测量模式条件下采集的数据。如上述的四个电压数据

Figure BDA0001950414890000043
和
Figure BDA0001950414890000044
在EIT领域中，有非常多的数据采集模式可以获得电压数据，本发明的方法可以适合所有采集模式下得到的数据。Preferably, the boundary measurement data to be reconstructed includes data collected under various excitation-measurement mode conditions. The four voltage data as above
Figure BDA0001950414890000043
and
Figure BDA0001950414890000044
In the field of EIT, there are many data acquisition modes to obtain voltage data, and the method of the present invention can be adapted to the data obtained in all acquisition modes.

优选地，两种不同频率为任意频段内的两个不同频率。Preferably, the two different frequencies are two different frequencies within any frequency band.

优选地，两个不同时刻为任意间隔的两个不同时刻。Preferably, the two different moments are two different moments at any interval.

优选地，在二维成像中，计算成像目标的面积；在三维成像中，计算成像目标的体积。Preferably, in the two-dimensional imaging, the area of the imaging target is calculated; in the three-dimensional imaging, the volume of the imaging target is calculated.

与现有技术相比，本发明具有以下有益效果：Compared with the prior art, the present invention has the following beneficial effects:

本发明提供的一种结合时差成像和频差成像的电阻抗成像方法，通过采用两个不同时刻同一频率处的两组测量数据进行时差成像，获得成像目标体积变化而导致的成像目标(位于成像区域内)电阻抗变化；然后通过采用同一时刻不同频率处的两组测量数据进行频差成像，获得成像目标电导率变化与成像目标电阻抗变化之间的关系，最终结合时差重构结果和频差重构结果计算在某一时刻的成像目标体积或面积(绝对阻抗分布)。现有技术只能重构获得两个不同时刻之间的成像目标体积变化或者两个不同频率之间的成像目标电导率变化，无法获得某一时刻成像目标的体积，而本发明通过结合时差成像和频差成像解决了该问题。本发明提供的一种结合时差成像和频差成像的电阻抗成像方法，可根据实际应用情况灵活应变：依据成像目标的电阻抗频谱特性，任意选择成像目标具有电导率差异的两个不同频率进行数据采集和成像；依据成像目标的体积变化情况，任意选择成像目标具有体积差异的两个不同时刻进行数据采集和成像。The present invention provides an electrical impedance imaging method combining time-difference imaging and frequency-difference imaging. By using two sets of measurement data at the same frequency at two different times to perform time-difference imaging, the imaging target (located in the imaging target) caused by the volume change of the imaging target is obtained. Then, by using two sets of measurement data at different frequencies at the same time to perform frequency difference imaging, the relationship between the changes in the conductivity of the imaging target and the changes in the electrical impedance of the imaging target is obtained. Finally, the time difference reconstruction results and the frequency difference are combined. The difference reconstruction result calculates the imaging target volume or area (absolute impedance distribution) at a certain time. The prior art can only reconstruct and obtain the volume change of the imaging target between two different moments or the conductivity change of the imaging target between two different frequencies, but cannot obtain the volume of the imaging target at a certain moment. And frequency difference imaging solves this problem. The present invention provides an electrical impedance imaging method combining time-difference imaging and frequency-difference imaging, which can be flexibly adapted according to the actual application situation: according to the electrical impedance spectral characteristics of the imaging target, two different frequencies with different electrical conductivity of the imaging target are arbitrarily selected for Data acquisition and imaging; according to the volume change of the imaging target, two different moments when the imaging target has a volume difference are arbitrarily selected for data acquisition and imaging.

附图说明Description of drawings

图1是本发明的方法流程图。Figure 1 is a flow chart of the method of the present invention.

图2是本发明用于计算仿真测量数据的仿真模型。FIG. 2 is a simulation model used for calculating simulation measurement data in the present invention.

图3是本发明的仿真重构模型。FIG. 3 is a simulation reconstruction model of the present invention.

图4是时差成像结果和频差成像结果，其中401和402分别为在两个频率处的时差成像结果，403和404为在两个时刻的频差成像结果。FIG. 4 shows the time difference imaging result and the frequency difference imaging result, wherein 401 and 402 are the time difference imaging results at two frequencies, respectively, and 403 and 404 are the frequency difference imaging results at two time instants.

具体实施方式Detailed ways

为了使本技术领域的人员更好地理解本发明方案，下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分的实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都应当属于本发明保护的范围。In order to make those skilled in the art better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only Embodiments are part of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

需要说明的是，本发明的说明书和权利要求书及上述附图中的术语“第一”、“第二”等是用于区别类似的对象，而不必用于描述特定的顺序或先后次序。应该理解这样使用的数据在适当情况下可以互换，以便这里描述的本发明的实施例能够以除了在这里图示或描述的那些以外的顺序实施。此外，术语“包括”和“具有”以及他们的任何变形，意图在于覆盖不排他的包含，例如，包含了一系列步骤或单元的过程、方法、系统、产品或设备不必限于清楚地列出的那些步骤或单元，而是可包括没有清楚地列出的或对于这些过程、方法、产品或设备固有的其它步骤或单元。It should be noted that the terms "first", "second" and the like in the description and claims of the present invention and the above drawings are used to distinguish similar objects, and are not necessarily used to describe a specific sequence or sequence. It is to be understood that the data so used may be interchanged under appropriate circumstances such that the embodiments of the invention described herein can be practiced in sequences other than those illustrated or described herein. Furthermore, the terms "comprising" and "having" and any variations thereof, are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those expressly listed Rather, those steps or units may include other steps or units not expressly listed or inherent to these processes, methods, products or devices.

下面结合附图对本发明做进一步详细描述：Below in conjunction with accompanying drawing, the present invention is described in further detail:

参照图1，本实施例给出一种结合时差成像和频差成像的电阻抗成像方法，分别采用两种不同频率的电流在两个不同时刻进行激励，获得两种频率处、两个不同时刻的测量数据，共四帧测量数据；其次，分别重构在两个频率处的时差图像，以及分别重构在两个不同时刻的频差图像；最后，基于上述四种重构结果分别计算在两个时刻的成像目标体积。Referring to FIG. 1, this embodiment provides an electrical impedance imaging method combining time difference imaging and frequency difference imaging, respectively using two different frequencies of currents to excite at two different times to obtain two frequencies at two different times. There are four frames of measurement data in total; secondly, the time difference images at two frequencies are reconstructed respectively, and the frequency difference images at two different times are respectively reconstructed; finally, based on the above four reconstruction results, the Imaging target volume at two time instants.

在本实施例中，以二维成像为例，假设一个成像部位为以半径12cm的圆域，圆域内有一成像目标。成像目标在第一个时刻t1第一种频率f1处的电导率为1.0S/m，在第一个时刻t1第二种频率f2处的电导率为1.05S/m，在第二个时刻第一种频率f1处的电导率为1.1S/m，在第二个时刻第二种频率f2处的电导率为1.15S/m；圆域内的电导率在所有时刻和所有频率处均为1.0S/m，如图2所示，图2中201为第一个时刻t1的仿真模型；图2中202为第二个时刻t1的仿真模型，成像目标的面积在两个时刻变化为0.873cm2(成像目标的面积在第一和第二时刻的面积分别为0.873cm2和1.746cm2)。当仿真模型所有参数设置完成后，根据电阻抗成像原理，分别生成在两个时刻和两个频率处的仿真测量数据，而且为了模拟真实情况，向仿真数据中添加一定的噪声，最终获得四帧测量数据：

Figure BDA0001950414890000061
Figure BDA0001950414890000062
和
Figure BDA0001950414890000063
In this embodiment, taking two-dimensional imaging as an example, it is assumed that an imaging site is a circular domain with a radius of 12 cm, and there is an imaging target in the circular domain. The conductivity of the imaging target at the first time t 1 at the first frequency f 1 is 1.0 S/m, and at the first time t 1 at the second frequency f 2 , the conductivity is 1.05 S/m, and at the first time The conductivity at the first frequency f 1 is 1.1 S/m at the two instants, and the conductivity at the second frequency f 2 at the second instant is 1.15 S/m; the conductivity in the circular domain is at all times and all The frequency is 1.0S/m, as shown in Figure 2, 201 in Figure 2 is the simulation model at the first time t 1 ; 202 in Figure 2 is the simulation model at the second time t 1 , the area of the imaging target is in The change at the two time instants was 0.873 cm 2 (the area of the imaging target was 0.873 cm 2 and 1.746 cm 2 at the first and second time instants, respectively). When all parameters of the simulation model are set, according to the principle of electrical impedance imaging, the simulation measurement data at two times and at two frequencies are generated respectively, and in order to simulate the real situation, a certain amount of noise is added to the simulation data, and finally four frames are obtained. Measurement data:
Figure BDA0001950414890000061
Figure BDA0001950414890000062
and
Figure BDA0001950414890000063

图3为用于重构图像的仿真重构模型，该模型由12层有限元组成，所有有限元网格均为规则的三角形剖分网格，圆域内电导率均匀分布，为1.0S/m。Figure 3 shows the simulation reconstruction model used to reconstruct the image. The model consists of 12 layers of finite elements. All finite element meshes are regular triangular meshes. The electrical conductivity in the circular domain is uniformly distributed and is 1.0S/m .

本发明提出的结合时差成像和频差成像的电阻抗成像方法，包括以下步骤：The electrical impedance imaging method combining time-difference imaging and frequency-difference imaging proposed by the present invention includes the following steps:

1)利用两个不同时刻(t1和t2)、频率f1处的两组测量数据

Figure BDA0001950414890000064
和
Figure BDA0001950414890000065
的差分结果
Figure BDA0001950414890000066
进行图像重建，利用下式重构在频率f1处、因成像目标体积随时间发生变化而引起的电阻抗变化
Figure BDA0001950414890000067
Figure BDA0001950414890000068
其中，S是敏感矩阵，L为正则化矩阵(本实施例中L＝diag(STS))，
Figure BDA0001950414890000069
为正则化系数(本实施例中
Figure BDA00019504148900000610
)，
Figure BDA00019504148900000611
为重构矩阵。
Figure BDA00019504148900000612
的重建结果如图4中401所示。1) Use two sets of measurement data at two different times (t 1 and t 2 ) and frequency f 1
Figure BDA0001950414890000064
and
Figure BDA0001950414890000065
difference result of
Figure BDA0001950414890000066
Perform image reconstruction and use the following equation to reconstruct the electrical impedance change at frequency f 1 due to the change of the imaging target volume over time
Figure BDA0001950414890000067
Figure BDA0001950414890000068
Among them, S is the sensitivity matrix, L is the regularization matrix (L=diag(S T S) in this embodiment),
Figure BDA0001950414890000069
is the regularization coefficient (in this example
Figure BDA00019504148900000610
),
Figure BDA00019504148900000611
is the reconstruction matrix.
Figure BDA00019504148900000612
The reconstruction result is shown as 401 in Figure 4.

2)利用两个不同时刻(t1和t2)、频率f2处的两组测量数据

Figure BDA00019504148900000613
和
Figure BDA00019504148900000614
的差分结果
Figure BDA0001950414890000071
进行图像重建，利用下式求解重构在频率f2处、因成像目标体积随时间发生变化而引起的电阻抗变化
Figure BDA0001950414890000072
Figure BDA0001950414890000073
其中，L为正则化矩阵(本实施例中L＝diag(STS))，
Figure BDA0001950414890000074
为正则化系数(本实施例中
Figure BDA0001950414890000075
)，
Figure BDA0001950414890000076
为重构矩阵。的重建结果如图4中402所示。2) Using two sets of measurement data at two different times (t 1 and t 2 ) and frequency f 2
Figure BDA00019504148900000613
and
Figure BDA00019504148900000614
difference result of
Figure BDA0001950414890000071
Perform image reconstruction, and use the following formula to solve and reconstruct the electrical impedance change at the frequency f 2 due to the change of the imaging target volume over time
Figure BDA0001950414890000072
Figure BDA0001950414890000073
Among them, L is the regularization matrix (L=diag(S T S) in this embodiment),
Figure BDA0001950414890000074
is the regularization coefficient (in this example
Figure BDA0001950414890000075
),
Figure BDA0001950414890000076
is the reconstruction matrix. The reconstruction result is shown as 402 in FIG. 4 .

3)利用t1时刻两种频率f1和f2处的两组测量数据

Figure BDA0001950414890000077
和
Figure BDA0001950414890000078
的差分结果
Figure BDA0001950414890000079
进行图像重建，利用下式重构在时刻t1处、因成像目标电导率随频率变化而引起的电阻抗变化
Figure BDA00019504148900000710
Figure BDA00019504148900000711
其中，L为正则化矩阵(本实施例中L＝diag(STS))，
Figure BDA00019504148900000712
为正则化系数(本实施例中
Figure BDA00019504148900000713
)，
Figure BDA00019504148900000714
为重构矩阵。的重建结果如图4中403所示。3) Use two sets of measurement data at two frequencies f 1 and f 2 at time t 1
Figure BDA0001950414890000077
and
Figure BDA0001950414890000078
difference result of
Figure BDA0001950414890000079
Perform image reconstruction, and use the following formula to reconstruct the electrical impedance change at time t 1 due to the change of the conductivity of the imaging target with the frequency
Figure BDA00019504148900000710
Figure BDA00019504148900000711
Among them, L is the regularization matrix (L=diag(S T S) in this embodiment),
Figure BDA00019504148900000712
is the regularization coefficient (in this example
Figure BDA00019504148900000713
),
Figure BDA00019504148900000714
is the reconstruction matrix. The reconstruction result is shown as 403 in Figure 4.

4)利用t2时刻两种频率f1和f2处的两组测量数据

Figure BDA00019504148900000715
和
Figure BDA00019504148900000716
的差分结果
Figure BDA00019504148900000717
进行图像重建，利用下式重构在时刻t2处、因成像目标电导率随频率变化而引起的电阻抗变化
Figure BDA00019504148900000718
Figure BDA00019504148900000719
其中，L为正则化矩阵(本实施例中L＝diag(STS))，
Figure BDA00019504148900000720
为正则化系数(本实施例中
Figure BDA00019504148900000721
)，
Figure BDA00019504148900000722
为重构矩阵。的重建结果如图4中404所示。4) Use two sets of measurement data at two frequencies f 1 and f 2 at time t 2
Figure BDA00019504148900000715
and
Figure BDA00019504148900000716
difference result of
Figure BDA00019504148900000717
Carry out image reconstruction, and use the following formula to reconstruct the electrical impedance change at time t 2 due to the change of the conductivity of the imaging target with the frequency
Figure BDA00019504148900000718
Figure BDA00019504148900000719
Among them, L is the regularization matrix (L=diag(S T S) in this embodiment),
Figure BDA00019504148900000720
is the regularization coefficient (in this example
Figure BDA00019504148900000721
),
Figure BDA00019504148900000722
is the reconstruction matrix. The reconstruction result is shown as 404 in Figure 4.

从图4中可以看出，尽管时差成像或频差成像结果能够反映成像目标的位置信息，但是无法准确获得成像目标的面积(或体积)信息。It can be seen from FIG. 4 that although the time difference imaging or frequency difference imaging results can reflect the position information of the imaging target, the area (or volume) information of the imaging target cannot be accurately obtained.

5)基于成像目标的电阻抗变化与其体积和电导率特性成正比的关系，根据下式计算t1时刻的成像目标体积，

Figure BDA00019504148900000723
以及t2时刻的成像目标体积
Figure BDA00019504148900000724
其中，
Figure BDA00019504148900000725
和
Figure BDA00019504148900000726
为成像区域的重构结果之和，分别采用以下四式进行计算：
Figure BDA0001950414890000081
Figure BDA0001950414890000082
和
Figure BDA0001950414890000083
经计算，
Figure BDA0001950414890000084
Figure BDA0001950414890000085
5) Based on the relationship between the electrical impedance change of the imaging target and its volume and conductivity characteristics, the imaging target volume at time t 1 is calculated according to the following formula,
Figure BDA00019504148900000723
and the imaging target volume at time t 2
Figure BDA00019504148900000724
in,
Figure BDA00019504148900000725
and
Figure BDA00019504148900000726
The sum of the reconstruction results of the imaging area is calculated by the following four formulas:
Figure BDA0001950414890000081
Figure BDA0001950414890000082
and
Figure BDA0001950414890000083
Calculated,
Figure BDA0001950414890000084
Figure BDA0001950414890000085

和

Figure BDA0001950414890000086
那么
Figure BDA0001950414890000087
本发明提出的方法的计算的两个时刻的成像目标面积与真实面积之间的误差分别为0.8％和1.03％，均小于5％(5％以内通常被认为是可接受范围)。所以本发明提出的结合时差成像和频差成像的电阻抗成像方法能够准确计算成像目标在不同时刻的面积(或体积)。and
Figure BDA0001950414890000086
So
Figure BDA0001950414890000087
The errors between the imaging target area and the real area calculated by the method proposed in the present invention are 0.8% and 1.03% respectively, both less than 5% (within 5% is generally regarded as an acceptable range). Therefore, the electrical impedance imaging method combining time difference imaging and frequency difference imaging proposed in the present invention can accurately calculate the area (or volume) of the imaging target at different times.

综上所述，本发明的方法通过采用两个不同时刻同一频率处的两组测量数据进行时差成像，获得成像目标体积变化而导致的成像目标(位于成像区域内)电阻抗变化，然后通过采用同一时刻不同频率处的两组测量数据进行频差成像，获得成像目标电导率变化而导致的成像目标(位于成像区域内)电阻抗变化，最终结合时差重构结果和频差重构结果计算在某一时刻的成像目标体积(三维成像)或者成像目标面积(二维成像)。本发明利用时差成像和频差成像的各自特点，能够计算成像目标(位于成像区域内)在某一时刻的体积(或面积)。To sum up, the method of the present invention performs time-difference imaging by using two sets of measurement data at the same frequency at two different times to obtain the electrical impedance change of the imaging target (located in the imaging area) caused by the volume change of the imaging target, and then using The two sets of measurement data at different frequencies at the same time are subjected to frequency difference imaging to obtain the electrical impedance change of the imaging target (located in the imaging area) caused by the change of the conductivity of the imaging target. The imaging target volume (3D imaging) or the imaging target area (2D imaging) at a certain moment. The present invention utilizes the respective characteristics of time difference imaging and frequency difference imaging, and can calculate the volume (or area) of the imaging target (located in the imaging area) at a certain moment.

以上内容仅为说明本发明的技术思想，不能以此限定本发明的保护范围，凡是按照本发明提出的技术思想，在技术方案基础上所做的任何改动，均落入本发明权利要求书的保护范围之内。The above content is only to illustrate the technical idea of the present invention, and cannot limit the protection scope of the present invention. Any changes made on the basis of the technical solution according to the technical idea proposed by the present invention all fall within the scope of the claims of the present invention. within the scope of protection.

Claims (6)

1. An electrical impedance imaging method combining time difference imaging and frequency difference imaging is characterized in that firstly, time difference imaging is carried out by adopting two groups of measurement data at the same frequency at two different moments to obtain the corresponding relation between the volume change of an imaging target and the electrical impedance change of the imaging target, and then a time difference reconstruction result is obtained; then, performing frequency difference imaging by adopting two groups of measurement data at different frequencies at the same moment to obtain the relation between the conductivity change of the imaging target and the electrical impedance change of the imaging target, namely a frequency difference reconstruction result; finally, calculating the imaging target volume or area at a certain moment by combining the time difference reconstruction result and the frequency difference reconstruction result;
the method comprises the following steps:
1) using two frequencies f1And f2Respectively at two different times t1And t2Exciting to obtain measured data at two frequencies and at two different times
Figure FDA0003386633630000011
And
Figure FDA0003386633630000012
wherein
Figure FDA0003386633630000013
Representing the measurement data at time y at frequency x;
2) using two different times t1And t2Frequency f1Two sets of measured data of
Figure FDA0003386633630000014
And
Figure FDA0003386633630000015
difference result of (2)
Figure FDA0003386633630000016
Carrying out image reconstruction to obtain frequency f1Electrical impedance change caused by time-dependent change of imaging target volume
Figure FDA0003386633630000017
Solving by
Figure FDA0003386633630000018
Figure FDA0003386633630000019
Wherein, S is a sensitive matrix,
Figure FDA00033866336300000110
for regularization coefficients, L is a regularization matrix,
Figure FDA00033866336300000111
for reconstructing the matrix, T is the transpose of the matrix;
3) by using two different phasesMoment t1And t2Frequency f2Two sets of measured data of
Figure FDA00033866336300000112
And
Figure FDA00033866336300000113
difference result of (2)
Figure FDA00033866336300000114
Carrying out image reconstruction to obtain frequency f2Electrical impedance change caused by time-dependent change of imaging target volume
Figure FDA00033866336300000115
Solving by
Figure FDA00033866336300000116
Figure FDA00033866336300000117
Wherein,
Figure FDA00033866336300000118
to reconstruct the matrix, L is a regularization matrix,
Figure FDA00033866336300000119
is a regularization coefficient;
4) using t1Two frequencies f of time1And f2Two sets of measured data of
Figure FDA00033866336300000120
And
Figure FDA00033866336300000121
difference result of (2)
Figure FDA00033866336300000122
Carrying out image reconstruction to obtain a moment t1Electrical impedance change caused by change of imaging target conductivity along with frequency change
Figure FDA00033866336300000123
Solving by
Figure FDA00033866336300000124
Figure FDA0003386633630000021
Wherein,
Figure FDA0003386633630000022
to reconstruct the matrix, L is a regularization matrix,
Figure FDA0003386633630000023
is a regularization coefficient;
5) using t2Two frequencies f of time1And f2Two sets of measured data of
Figure FDA0003386633630000024
And
Figure FDA0003386633630000025
difference result of (2)
Figure FDA0003386633630000026
Carrying out image reconstruction to obtain a moment t2Electrical impedance change caused by change of imaging target conductivity along with frequency change
Figure FDA0003386633630000027
Solving by
Figure FDA0003386633630000028
Figure FDA0003386633630000029
Wherein,
Figure FDA00033866336300000210
to reconstruct the matrix, L is a regularization matrix,
Figure FDA00033866336300000211
is a regularization coefficient;
6) based on the relationship that the electrical impedance change of an imaging target is in direct proportion to the volume and conductivity characteristics of the imaging target, namely:
Figure FDA00033866336300000212
Figure FDA00033866336300000213
Figure FDA00033866336300000214
Figure FDA00033866336300000215
calculating t from1Temporal imaging target volume
Figure FDA00033866336300000216
Figure FDA00033866336300000217
Then it is determined that,
Figure FDA00033866336300000218
and t2Temporal imaging target volume
Figure FDA00033866336300000219
Wherein,
Figure FDA00033866336300000220
and
Figure FDA00033866336300000221
the sum of the reconstruction results of the imaging region is calculated by the following four formulas:
Figure FDA00033866336300000222
and
Figure FDA00033866336300000223
2. an electrical impedance imaging method combining moveout imaging and frequency difference imaging according to claim 1, wherein the electrical impedance imaging positive problem calculation equation is: s · Δ ρ ═ Δ V;
wherein S is a sensitive matrix, Δ V is a change vector of boundary measurement data to be reconstructed, Δ ρ is an electrical impedance change of the imaging target, and the change vector is associated with a volume C and a conductivity σ of the imaging targetfIs proportional, and expressed as Δ ρ ∈ C · σf。
3. A method of electrical impedance imaging combining moveout imaging and frequency difference imaging according to claim 1, wherein the boundary measurement data to be reconstructed comprises data acquired under various excitation-measurement mode conditions.
4. An electrical impedance imaging method incorporating jet lag imaging and frequency difference imaging according to claim 1, wherein the two different frequencies are two different frequencies within any frequency band.
5. A method of electrical impedance imaging combining moveout imaging and frequency difference imaging according to claim 1, wherein the two different times are two different times at arbitrary intervals.
6. An electrical impedance imaging method combining time-of-arrival imaging and frequency-of-arrival imaging according to claim 1, wherein in two-dimensional imaging, the area of the imaged object is calculated; in three-dimensional imaging, a volume of an imaging target is calculated.
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