CN106821380B - Biomedical electrical impedance imaging method and device based on the regularization of multiplying property - Google Patents
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Abstract
The invention discloses a kind of biomedical electrical impedance imaging methods and device based on the regularization of multiplying property, wherein method includes: to arrange multiple electrodes around object to be imaged, and in measurement process, two electrodes in constant current drive multiple electrodes and the potential difference on other electrodes in multiple electrodes is measured in turn, to obtain a frame measurement data；The data error item of electrical impedance imaging problem is calculated according to measurement data and Forward simulation data, and cost functional is calculated according to preset multiplying property regular terms and data error term；By alternative manner minimization cost functional to carry out image reconstruction.This method can retain the edge configuration of organism organ well, so that reconstruction image is had " piecemeal constant " characteristic, and have good noise robustness.
Description
Technical Field
The invention relates to the technical field of biomedical electrical impedance imaging, in particular to a biomedical electrical impedance imaging method and device based on multiplicative regularization.
Background
With the progress of science and technology, the medical imaging technology has been developed. These techniques provide imaging information for biological tissue research and clinical diagnosis, such as medical imaging techniques of X-ray imaging, ultrasonic imaging, magnetic resonance imaging, infrared imaging, radionuclide imaging, optical imaging, electrical impedance tomography, and the like, by extracting information on the morphology, structure, and certain physiological functions of tissues or organs in a living body through interaction of certain energy with the living body. Among them, Electrical Impedance Tomography (EIT) is a technique for imaging by using Electrical Impedance characteristics of an object to be detected. The technology has the advantages of high time resolution, low cost, light equipment, non-invasion, no radiation and the like, thereby being a technology with attractive prospect.
However, in practical applications, when the electrical impedance imaging technology is used to reconstruct morphological images of tissues or organs in a living body, the image reconstruction problem is often seriously ill-conditioned because the obtained measurement data is limited and is usually less than the number of unknowns to be inverted. To improve this morbidity, in the related art, the problem is generally regularized. Among them, there are various regularization methods, such as Tikhonov regularization, Total Variation (Total Variation) regularization, etc.
However, although the conventional regularization method can improve the ill-posed problem of reconstruction, it has some disadvantages. For example, Tikhonov regularization makes the boundaries of biological organs too smooth; the original total variation regularization term has no differentiability, so that image reconstruction is difficult to perform by using a Newton method.
In addition, the traditional additive regularization method needs to set a parameter in the target functional to adjust the relative weight of the data error term and the regularization term. However, the parameter values need to be determined by rather cumbersome numerical experiments, which greatly increases the computational complexity of the imaging algorithm.
Disclosure of Invention
The object of the present invention is to solve at least to some extent one of the above mentioned technical problems.
To this end, a first object of the present invention is to propose a biomedical electrical impedance imaging method based on multiplicative regularization. The method can well reserve the edge form of the organism organ, so that the reconstructed image has the characteristic of a blocking constant and has good anti-noise performance.
The second purpose of the invention is to provide a biomedical electrical impedance imaging device based on multiplicative regularization.
In order to achieve the above object, a biomedical electrical impedance imaging method based on multiplicative regularization in an embodiment of the first aspect of the invention includes the following steps: arranging a plurality of electrodes around an object to be imaged, and in the measuring process, sequentially exciting two electrodes in the plurality of electrodes by constant current and measuring the potential difference on other electrodes in the plurality of electrodes to obtain a frame of measuring data; calculating a data error term of the electrical impedance imaging problem according to the measurement data and the forward simulation data, and calculating a target functional according to a preset multiplicative regular term and the data error term; minimizing the target functional by an iterative method for image reconstruction.
According to the biomedical electrical impedance imaging method based on multiplicative regularization, a constant current source is used for exciting and measuring two electrodes in a plurality of electrodes in turn to obtain measurement data, a data error term of an electrical impedance imaging problem is calculated according to the measurement data and forward simulation data, a target functional is calculated according to a preset multiplicative regularization term and the data error term, and then the target functional is minimized through an iteration method to carry out image reconstruction, so that the edge form of an organism organ is well reserved, a reconstructed image has the characteristic of a block constant and has good anti-noise performance.
In order to achieve the above object, a biomedical electrical impedance imaging apparatus based on multiplicative regularization according to an embodiment of a second aspect of the present invention includes: the measuring module is used for arranging a plurality of electrodes around an object to be imaged, and in the measuring process, alternately exciting two electrodes in the plurality of electrodes at constant current and measuring the potential difference of other electrodes in the plurality of electrodes to obtain a frame of measuring data; the calculation module is used for calculating a data error term of the electrical impedance imaging problem according to the measurement data and the forward simulation data, and calculating a target functional according to a preset multiplicative regular term and the data error term; and the image reconstruction module is used for minimizing the target functional through an iterative method so as to reconstruct the image.
According to the biomedical electrical impedance imaging device based on multiplicative regularization, the constant current source is used for exciting and measuring two electrodes in the plurality of electrodes in turn to obtain measurement data, a data error term of an electrical impedance imaging problem is calculated according to the measurement data and forward simulation data, a target functional is calculated according to a preset multiplicative regularization term and the data error term, and then the target functional is minimized through an iteration method to carry out image reconstruction, so that the edge form of an organism organ is well reserved, a reconstructed image has the characteristic of a block constant, and the reconstructed image has good anti-noise performance.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which,
FIG. 1 is a flow chart of a biomedical electrical impedance imaging method based on multiplicative regularization according to an embodiment of the invention;
FIG. 2 is an exemplary diagram of a simulation model constructed by a biomedical electrical impedance imaging method based on multiplicative regularization according to an embodiment of the invention;
FIG. 3(a) is a diagram illustrating the image reconstruction result without noise according to an embodiment of the present invention;
FIG. 3(b) is a diagram illustrating the image reconstruction result when applying noise according to an embodiment of the present invention;
FIG. 3(c) is a diagram illustrating the image reconstruction result when noise is applied according to another embodiment of the present invention;
fig. 4 is a schematic structural diagram of a biomedical electrical impedance imaging device based on multiplicative regularization according to an embodiment of the invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
The following describes a biomedical electrical impedance imaging method and device based on multiplicative regularization according to an embodiment of the invention with reference to the accompanying drawings.
Fig. 1 is a flow chart of a biomedical electrical impedance imaging method based on multiplicative regularization according to an embodiment of the invention. As shown in fig. 1, the biomedical electrical impedance imaging method based on multiplicative regularization may include:
s101, arranging a plurality of electrodes around an object to be imaged, and in the measuring process, exciting two electrodes in the plurality of electrodes by constant current in turn and measuring the potential difference on other electrodes in the plurality of electrodes to obtain one frame of measuring data.
Specifically, in order to acquire a reconstructed image of an object to be imaged, a plurality of electrodes may be arranged around the object to be imaged, and during measurement, two electrodes of the plurality of electrodes are excited at a constant current in turn and potential differences on the other electrodes of the plurality of electrodes are measured to obtain one frame of measurement data. Examples are as follows:
assuming that a plurality of electrodes are arranged around the chest of a human body, in the measuring process, constant current excitation is applied to two electrodes of the plurality of electrodes, the potential difference of other electrodes is measured, meanwhile, the positions of the excitation electrodes are continuously changed, corresponding measurement is carried out, and finally, a frame of measurement data is obtained and can be recorded as a vector m.
The number of the plurality of electrodes in this embodiment may be 16, or may be other numbers, and is not limited herein.
It should be noted that, in this embodiment, besides arranging a plurality of electrodes on the chest of the human body, a plurality of electrodes may also be arranged on the brain of the human body, and the specific arrangement positions may be arranged at corresponding positions of the human body according to actual needs, and the arrangement positions of the plurality of electrodes are not specifically limited herein.
Further, in the present embodiment, for the determined constant current excitation, the potential distribution in the object to be imaged needs to satisfy the following poisson equation and boundary conditions:
at the boundary electrode l (2)
Elsewhere on the border (3)
Wherein phi is the potential distribution in the object to be imaged, sigma is the conductivity distribution thereof, IlFor current through electrode l, n is the boundary normalAnd r is a spatial coordinate. The partial differential equation can be solved by a finite element method, and the potential difference of the electrodes on the boundary can be obtained.
And S102, calculating a data error term of the electrical impedance imaging problem according to the measurement data and the forward simulation data, and calculating a target functional according to a preset multiplicative regular term and the data error term.
Specifically, after the measurement data is obtained, the data error term of the electrical impedance imaging problem may be calculated by subtracting the forward simulation data and the measurement data.
Wherein, the data error term of the electrical impedance imaging problem can be obtained by the following formula:
data error term | | | S (σ) -m | | non-woven phosphor2 (4)
Wherein, σ is the conductivity to be inverted, S (-) is a forward operator for solving the positive problem, and m is the measurement data.
And then, a target functional can be calculated according to a preset multiplicative regular term and a data error term.
It should be noted that, in the present embodiment, the preset multiplicative regularization term is set based on the total variation principle, and the multiplicative regularization term may include various forms, such as L2Norm regularization term, weighting L2Norm regularization terms, etc.
The specific implementation process of calculating the target functional according to the preset multiplicative regular term and the data error term may include the following steps:
and multiplying the data error term and a multiplicative regular term based on a total variation principle to obtain a target functional. The calculation of the target functional may be achieved by the following formula:
Cn(σ)＝||S(σ)-m||2×Rn(σ) (5)
wherein, Cn(σ) is the target functional, σ is the conductivity to be inverted, S (-) is the forward direction to solve the positive problemOperator, m is measured data, Rn(σ) is a multiplicative regularization term, and n is the number of iterations.
And S103, minimizing the target functional through an iteration method to reconstruct the image.
In particular, minimizing the target functional may be accomplished in a number of ways. For example, the steepest descent method, the gauss-newton method, the conjugate gradient method, and the like. Of course, there are other iterative methods, which are not described in detail herein.
The minimization target functional will be described in detail below using a gauss-newton method as an example.
Firstly, solving a gradient vector g of a target functionaln(sigma.) and Hessian matrix Gn(σ), which can be written specifically as:
wherein,is the gradient vector of the multiplicative regularization term,the hessian matrix is a multiplicative regular term, J (sigma) is a Jacobian matrix, sigma is discrete conductivity to be inverted, S (·) is a discretized forward operator for solving a positive problem, m is measurement data, and n is iteration times.
It should be noted that the jacobian matrix can be obtained quickly by equation (8):
where Ω is the problem solving area, φiFor the potential distribution, u, generated in the region omega upon excitation of the ith counter electrodejδ σ (e) is a characteristic function of cell e for the potential distribution generated in region Ω when the jth pair of electrodes is excited.
Secondly, the conductivity to be inverted can be updated by searching for directions as follows:
Δσn＝-[Gn]-1·gn (9)
wherein, gnGradient vector, G, of the target functionalnIs the hessian matrix of the target functional.
Furthermore, after the target functional is minimized through the iterative method, a reconstructed image of the object to be imaged can be obtained.
In order to perform performance verification on the reconstruction method, a simulation model is further constructed in the embodiment of the invention, and a finite element subdivision of the simulation model is shown in fig. 2. The background conductivity in this model was 0.25S/m, the conductivity of the included semicircle with sharp edges was 0.1S/m, and the 16 dots around the model represent the electrodes. The finite element method is utilized to solve the positive problem through the model to generate simulation measurement data, and then the performance of the reconstruction method can be verified according to the generated simulation measurement data.
Further, the simulation model can be used for reconstructing images of the object to be imaged under different noise levels. See, in particular, fig. 3(a) -3 (c). Wherein, fig. 3(a) is a schematic diagram of the image reconstruction result of the simulation measurement data when no noise is applied; FIG. 3(b) is a graph showing the result of image reconstruction of simulated measurement data with 1% noise applied; fig. 3(c) is a graph showing the result of image reconstruction when 2% noise is applied to the simulation measurement data. The image reconstruction in fig. 3(a) -3 (c) uses a different grid from that in fig. 2.
Based on the above image reconstruction examples of the object to be imaged under different noise levels, it can be seen that the edges of the contents of the simulation model can be clearly reconstructed, the reconstructed image has the characteristic of "blocking constant", and when the noise level applied to the simulation measurement data is relatively high, for example, 2%, the edges of the image can also be better reconstructed, so that the biomedical electrical impedance imaging method based on multiplicative regularization in the embodiment of the present invention has good anti-noise performance.
In summary, according to the biomedical electrical impedance imaging method based on multiplicative regularization, two electrodes in a plurality of electrodes are excited in turn by using a constant current source and measured to obtain measurement data, a data error term of an electrical impedance imaging problem is calculated according to the measurement data and forward simulation data, a target functional is calculated according to a preset multiplicative regularization term and the data error term, and then the target functional is minimized by an iteration method to perform image reconstruction, so that the edge morphology of a biological organ is well preserved, a reconstructed image has a 'block constant' characteristic, and good anti-noise performance is achieved. In addition, compared with an additive regularization mode, the multiplicative regularization mode disclosed by the invention does not need to set a parameter in the target functional to adjust the relative weights of the data error term and the regularization term, and the relative weights of the data error term and the regularization term can be dynamically adjusted in the process of minimizing the target functional, so that the step of determining the parameter value through a rather complicated numerical experiment is omitted.
In order to realize the embodiment, the invention also provides a biomedical electrical impedance imaging device based on multiplicative regularization.
Fig. 4 is a schematic structural diagram of a biomedical electrical impedance imaging device based on multiplicative regularization according to an embodiment of the invention.
As shown in fig. 4, the biomedical electrical impedance imaging device based on multiplicative regularization may include: a measurement module 110, a calculation module 120 and an image reconstruction module 130.
The measuring module 110 is configured to arrange a plurality of electrodes around an object to be imaged, and in a measuring process, sequentially and constantly energize two electrodes of the plurality of electrodes and measure potential differences of other electrodes of the plurality of electrodes to obtain a frame of measurement data.
Specifically, in order to acquire a reconstructed image of an object to be imaged, a plurality of electrodes may be arranged around the object to be imaged, and during measurement, two electrodes of the plurality of electrodes are excited at a constant current in turn and potential differences on the other electrodes of the plurality of electrodes are measured to obtain one frame of measurement data. Examples are as follows:
assuming that a plurality of electrodes are arranged around the chest of a human body, in the measuring process, constant current excitation is applied to two electrodes of the plurality of electrodes, the potential difference of other electrodes is measured, meanwhile, the positions of the excitation electrodes are continuously changed, corresponding measurement is carried out, and finally, a frame of measurement data is obtained and can be recorded as a vector m.
The number of the plurality of electrodes in this embodiment may be 16, or may be other numbers, and is not limited herein.
It should be noted that, in this embodiment, besides arranging a plurality of electrodes on the chest of the human body, a plurality of electrodes may also be arranged on the brain of the human body, and the specific arrangement positions may be arranged at corresponding positions of the human body according to actual needs, and the arrangement positions of the plurality of electrodes are not specifically limited herein.
Further, in the present embodiment, for the determined constant current excitation, the potential distribution in the object to be imaged needs to satisfy the following poisson equation and boundary conditions:
at the boundary electrode l (2)
Elsewhere on the border (3)
Wherein phi is the potential distribution in the object to be imaged, sigma is the conductivity distribution thereof, IlFor the current through electrode l, n is the boundary normal and r is the spatial coordinate. The partial differential equation can be solved by a finite element method, and the potential difference of the electrodes on the boundary can be obtained.
The calculation module 120 is configured to calculate a data error term of the electrical impedance imaging problem according to the measurement data and the forward simulation data, and calculate a target functional according to a preset multiplicative regularization term and the data error term;
specifically, the calculation module 120 may further calculate a data error term of the electrical impedance imaging problem after obtaining the measurement data.
Wherein, the data error term of the electrical impedance imaging problem can be obtained by the following formula:
data error term | | | S (σ) -m | | non-woven phosphor2 (4)
Wherein, σ is the conductivity to be inverted, S (-) is a forward operator for solving the positive problem, and m is the measurement data.
And then, a target functional can be calculated according to a preset multiplicative regular term and a data error term.
It should be noted that, in the present embodiment, the preset multiplicative regularization term is set based on the total variation principle, and the multiplicative regularization term may include various forms, such as L2Norm regularization term, weighting L2Norm regularization terms, etc.
The specific implementation process of calculating the target functional according to the preset multiplicative regular term and the data error term may include the following steps:
and multiplying the data error term and a multiplicative regular term based on a total variation principle to obtain a target functional. The calculation of the target functional may be achieved by the following formula:
Cn(σ)＝||S(σ)-m||2×Rn(σ) (5)
wherein, Cn(sigma) is the target functional, sigma is the conductivity to be inverted, S (-) is the forward operator to solve the positive problem, m is the measured data, Rn(σ) is a multiplicative regularization term, and n is the number of iterations.
The image reconstruction module 130 is configured to minimize the target functional by an iterative method for image reconstruction. In particular, minimizing the target functional may be accomplished in a number of ways. For example, the steepest descent method, the gauss-newton method, or the conjugate gradient method. Of course, there are other iterative methods, which are not described in detail herein.
The minimization target functional will be described in detail below using a gauss-newton method as an example.
Firstly, solving a gradient vector g of a target functionaln(sigma.) and Hessian matrix Gn(σ), which can be written specifically as:
wherein,is the gradient vector of the multiplicative regularization term,hessian matrix which is a multiplicative regularization term, J (sigma) is a Jacobian matrix, sigma is the discrete conductivity to be inverted, and S (DEG) is the front of the discretized positive problem solving methodAnd (5) calculating an operator, wherein m is measurement data and n is iteration number.
It should be noted that the jacobian matrix can be obtained quickly by equation (8):
where Ω is the problem solving area, φiFor the potential distribution, u, generated in the region omega upon excitation of the ith counter electrodejδ σ (e) is a characteristic function of cell e for the potential distribution generated in region Ω when the jth pair of electrodes is excited.
Secondly, the conductivity to be inverted can be updated by searching for directions as follows:
Δσn＝-[Gn]-1·gn (9)
wherein, gnGradient vector, G, of the target functionalnIs the hessian matrix of the target functional.
Further, the image reconstruction module 130 may obtain a reconstructed image of the object to be imaged after minimizing the target functional by the iterative method described above.
In order to perform performance verification on the reconstruction method, a simulation model is further constructed in the embodiment of the invention, and a finite element subdivision of the simulation model is shown in fig. 2. The background conductivity in this model was 0.25S/m, the conductivity of the included semicircle with sharp edges was 0.1S/m, and the 16 dots around the model represent the electrodes. The finite element method is utilized to solve the positive problem through the model to generate simulation measurement data, and then the performance of the reconstruction method can be verified according to the generated simulation measurement data.
Further, the simulation model can be used for reconstructing images of the object to be imaged under different noise levels. See, in particular, fig. 3(a) -3 (c). Wherein, fig. 3(a) is a schematic diagram of the image reconstruction result of the simulation measurement data when no noise is applied; FIG. 3(b) is a graph showing the result of image reconstruction of simulated measurement data with 1% noise applied; fig. 3(c) is a graph showing the result of image reconstruction when 2% noise is applied to the simulation measurement data. The image reconstruction in fig. 3(a) -3 (c) uses a different grid from that in fig. 2.
Based on the above image example of reconstructing the object to be imaged under different noise levels, it can be seen that the edge of the simulation model inclusion can be clearly reconstructed, and the reconstructed image has the characteristic of "blocking constant", and when the noise level applied to the simulation measurement data is relatively high, for example, 2%, the edge of the image can also be better reconstructed, so that the biomedical electrical impedance imaging method based on multiplicative regularization in the embodiment of the present invention has good anti-noise performance.
According to the biomedical electrical impedance imaging device based on multiplicative regularization, the constant current source is used for exciting and measuring two electrodes in the plurality of electrodes in turn to obtain measurement data, a data error term of an electrical impedance imaging problem is calculated according to the measurement data and forward simulation data, a target functional is calculated according to a preset multiplicative regularization term and the data error term, and then the target functional is minimized through an iteration method to carry out image reconstruction, so that the edge form of an organism organ is well reserved, a reconstructed image has the characteristic of a block constant, and the reconstructed image has good anti-noise performance. In addition, compared with an additive regularization mode, the multiplicative regularization mode disclosed by the invention does not need to set a parameter in the target functional to adjust the relative weights of the data error term and the regularization term, and the relative weights of the data error term and the regularization term can be dynamically adjusted in the process of minimizing the target functional, so that the step of determining the parameter value through a rather complicated numerical experiment is omitted.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and alternate implementations are included within the scope of the preferred embodiment of the present invention in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present invention.
The logic and/or steps represented in the flowcharts or otherwise described herein, e.g., an ordered listing of executable instructions that can be considered to implement logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic device) having one or more wires, a portable computer diskette (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). Additionally, the computer-readable medium could even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured, via for instance optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner if necessary, and then stored in a computer memory.
It should be understood that portions of the present invention may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.
It will be understood by those skilled in the art that all or part of the steps carried by the method for implementing the above embodiments may be implemented by hardware related to instructions of a program, which may be stored in a computer readable storage medium, and when the program is executed, the program includes one or a combination of the steps of the method embodiments.
In addition, functional units in the embodiments of the present invention may be integrated into one processing module, or each unit may exist alone physically, or two or more units are integrated into one module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode. The integrated module, if implemented in the form of a software functional module and sold or used as a stand-alone product, may also be stored in a computer readable storage medium.
The storage medium mentioned above may be a read-only memory, a magnetic or optical disk, etc. Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.
Claims (8)
1. A biomedical electrical impedance imaging method based on multiplicative regularization is characterized by comprising the following steps:
arranging a plurality of electrodes around an object to be imaged, and in the measuring process, sequentially exciting two electrodes in the plurality of electrodes by constant current and measuring the potential difference on other electrodes in the plurality of electrodes to obtain a frame of measuring data;
calculating a data error term of the electrical impedance imaging problem according to the measurement data and the forward simulation data, and calculating a target functional according to a preset multiplicative regular term and the data error term, wherein the preset multiplicative regular term is set based on a total variation principle, and the target functional is calculated according to the preset multiplicative regular term and the data error term, and the method comprises the following steps:
multiplying the data error term and the multiplicative regular term based on the total variation principle to obtain the target functional;
minimizing the target functional by an iterative method for image reconstruction.
2. The biomedical electrical impedance imaging method based on multiplicative regularization as recited in claim 1, wherein a data error term of the electrical impedance imaging problem is calculated by the following formula:
data error term | | | S (σ) -m | | non-woven phosphor2
Wherein σ is the conductivity to be inverted, S (-) is a forward operator for solving the positive problem, and m is the measurement data.
3. The biomedical electrical impedance imaging method based on multiplicative regularization as recited in claim 1, wherein for the determined constant-current excitation, the potential distribution within the object to be imaged satisfies the following poisson equation and boundary conditions:
at the boundary at the electrode l
Elsewhere on the border
Wherein, phi is the potential distribution in the object to be imaged, sigma is the conductivity distribution, omega is the area of the object to be imaged, IlFor the current through electrode l, n is the boundary normal and r is the spatial coordinate.
4. The biomedical electrical impedance imaging method based on multiplicative regularization as recited in claim 1, wherein the iterative method comprises any one of a steepest descent method, a newton method, a conjugate gradient method.
5. A biomedical electrical impedance imaging device based on multiplicative regularization, comprising:
the measuring module is used for arranging a plurality of electrodes around an object to be imaged, and in the measuring process, alternately exciting two electrodes in the plurality of electrodes at constant current and measuring the potential difference of other electrodes in the plurality of electrodes to obtain a frame of measuring data;
a calculating module, configured to calculate a data error term of an electrical impedance imaging problem according to the measurement data and forward simulation data, and calculate a target functional according to a preset multiplicative regularization term and the data error term, where the preset multiplicative regularization term is set based on a total variation principle, and the calculating module is specifically configured to:
multiplying the data error term and the multiplicative regular term based on the total variation principle to obtain the target functional;
and the image reconstruction module is used for minimizing the target functional through an iterative method so as to reconstruct the image.
6. The biomedical electrical impedance imaging device based on multiplicative regularization as recited in claim 5, wherein a data error term of the electrical impedance imaging problem is calculated by the following formula:
data error term | | | S (σ) -m | | non-woven phosphor2
Wherein σ is the conductivity to be inverted, S (-) is a forward operator for solving the positive problem, and m is the measurement data.
7. The biomedical electrical impedance imaging device based on multiplicative regularization as recited in claim 5, wherein for the determined constant-current excitation, the potential distribution within the object to be imaged satisfies the following poisson equation and boundary conditions:
at the boundary at the electrode l
Elsewhere on the border
Wherein, phi is the potential distribution in the object to be imaged, sigma is the conductivity distribution, omega is the area of the object to be imaged, IlFor the current through electrode l, n is the boundary normal and r is the spatial coordinate.
8. The biomedical electrical impedance imaging device based on multiplicative regularization as recited in claim 5, wherein the iterative method comprises any one of a steepest descent method, a newton method, a conjugate gradient method.
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