CN117577274A - EIT image reconstruction method, device and equipment based on spatial spectrum kernel function - Google Patents
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Abstract
The invention discloses an EIT image reconstruction method, device and equipment based on a spatial spectrum kernel function. According to the invention, the spatial spectrum kernel function of the spatial correlation information and the frequency domain correlation information of the synchronous coding image is constructed and then embedded into the multi-frequency EIT image reconstruction model, the prior guidance of the spatial domain and the frequency domain can be implicitly introduced, the noise interference of the EIT spatial domain and the frequency domain can be synchronously restrained, the EIT image deformation problem caused by the characteristic of the electromagnetic field 'soft field' is avoided, and the multi-frequency bioelectrical impedance tomography image reconstruction with high precision, low noise and high quality is realized.
Description
Technical Field
The invention relates to the field of biomedical signal detection, the field of biosensors and the field of biomedical images, in particular to an EIT image reconstruction method, an EIT image reconstruction device and EIT image reconstruction equipment based on a spatial frequency spectrum kernel function.
Background
The medical electrical impedance tomography (Electrical Impedance Tomography, EIT) is a novel noninvasive imaging technology for carrying out human internal structure distribution imaging based on bioelectrical impedance characteristics, and the electrical impedance distribution of human internal tissues is estimated by measuring the electrical information change caused by applying low-frequency weak alternating current signals on the surface of a human body, so that the physiological function information and the structure distribution information of the internal tissues and organs are obtained. EIT has been widely studied and promoted to clinical medical applications such as lung ventilation and lung perfusion monitoring, wind detection in brain, and tumor screening by virtue of its advantages of non-invasiveness, non-radiation, low cost, high time resolution, portability, etc.
The medical basis for imaging the interior of the human body using EIT is the electrical properties of biological tissue. The human body is composed of different tissues and organs, each of which is composed of different cells and cell matrices. Because the cell membrane of the basic structure of the cell has selective semipermeable property, and a large amount of sodium ions and potassium ions with charges are distributed on two sides of the membrane, the biological tissue can be automatically discharged outwards along with the progress of life activities, and simultaneously, the biological tissue can also make corresponding electrical response under the action of external stimulus. Thus, the human body can be equivalently a complex electrical conductor, exhibiting bioimpedance characteristics. The bioimpedance is a complex number consisting of a resistance value R (real part) and a reactance value X (imaginary part), which are determined by the conductive fluid and cell membrane in the human body, respectively. The biological impedance characteristics of the same tissue can be obviously changed along with the physiological and pathological changes of the same tissue, and different biological tissues can show obviously different electrical responses to the same external stimulation signal due to the differences in chemical composition, physiological structure, water content, size, shape and the like, so that the same external stimulation signal further shows unique electrical impedance characteristics. In addition, due to the selective semi-permeability of the cell membrane, the cell membrane presents a capacitance characteristic, so that the transmission path of exciting current in the human body can be changed along with the frequency change of externally applied signals, namely, low-frequency exciting electric signals can only be transmitted outside the cell membrane, and high-frequency exciting electric signals can penetrate the cell membrane and simultaneously be transmitted inside and outside the cell membrane. Thus, the electrical characteristics of biological tissue not only show great differences due to the differences in their own characteristics, but also changes in the physiological and pathological states, and also show unique electrical impedance spectrum information with the frequency of the applied signal. Therefore, the multi-frequency EIT is utilized to acquire the broadband electrical impedance spectrum data of the biological tissue, so that different biological tissues can be distinguished more accurately, and the physiological and pathological states of the tissues can be identified more accurately.
EIT biological imaging systems generally consist of an electrode sensor, a data acquisition system, and a computer. The imaging process of the technology comprises the steps of placing a group of array electrode plates at the boundary of an imaging target area before use; applying excitation alternating current signals to one electrode plate for excitation, and simultaneously receiving and collecting corresponding response electric signals at other electrode plates; repeating the above processes until all the electrode plates complete the excitation-response process, forming a group of complete boundary measurement electrical data; acquiring an EIT system response matrix based on the sensor geometry and the quasi-static electromagnetic field environment; and combining the system response matrix, and obtaining the EIT image representing the distribution condition of the human body by using a reconstruction algorithm. The external excitation applied by the multi-frequency EIT is an alternating current signal at a plurality of excitation frequencies. The EIT reconstructed image has higher time resolution, however, because the data volume of EIT boundary measurement data is far less than the data volume of electrical impedance distribution data of the internal position of the EIT, the reconstruction process of solving the internal electrical impedance distribution image from the boundary measurement data by combining a system response matrix is a serious ill-defined problem, so the EIT reconstructed image quality has higher sensitivity to noise. For multi-frequency bioelectrical impedance spectral imaging, a large amount of noise exists in both the spatial and spectral domains. In order to inhibit noise interference in the reconstruction process and improve EIT reconstructed image quality, a method for setting various local image prior conditions to carry out constraint in the image reconstruction process is a common solving means. However, because the signal-to-noise ratio of the bioelectrical response signal is low, and the EIT has a soft field characteristic, namely the sensitivity of the EIT field is higher near the boundary of the sensor and lower near the center of the field, the EIT image reconstruction method for carrying out local condition constraint based on single image mode information faces a technical bottleneck which is difficult to break through, so that a large improvement space still exists for the quality of the EIT image, and the precision of bioelectrical impedance spectrum data acquired based on the multi-frequency EIT image still does not reach clinical requirements.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides an EIT image reconstruction method, an EIT image reconstruction device and EIT image reconstruction equipment based on a spatial frequency spectrum kernel function, so as to realize high-precision, low-noise and high-quality image reconstruction of multi-frequency bioelectrical impedance tomography and accurate analysis of bioelectrical impedance spectrum data under a broadband condition.
The technical scheme adopted by the invention is as follows:
an EIT image reconstruction method based on a spatial spectrum kernel function comprises the following steps:
acquiring EIT system boundary measurement data under multi-frequency excitation;
constructing a target loss function between EIT system boundary measurement data under multi-frequency excitation and internal electrical characteristic distribution parameters K alpha to be reconstructed, and performing iterative reconstruction by minimizing the target loss function until the number of iterative steps preset or the iterative convergence condition is met, so as to obtain an optimal solution of a coefficient vector alpha, and obtaining a high-precision, low-noise and high-quality multi-frequency bioelectrical impedance chromatographic image by dip dyeing; k is a space frequency spectrum kernel function and is obtained by calculating a Cronecker product of a space domain kernel function constructed based on a space feature vector corresponding to a pixel point i on each frequency frame image in a multi-frequency EIT image set to be reconstructed and a frequency domain kernel function constructed based on the corresponding frequency spectrum feature vector; the spatial feature vector corresponding to the pixel point i on each frequency frame image in the multi-frequency EIT image set to be reconstructed is the pixel point intensity value of a single Zhang Jiepou structural image which is acquired in the same batch and has the same image size, and the corresponding frequency spectrum feature vector is the boundary measurement data value of the corresponding frequency frame image.
Further, the multi-frequency excitation signal is an alternating current electric signal in a frequency range from 1 kilohertz to 10 megahertz.
Further, the target loss function is expressed as follows:
wherein J is a system response matrix, and b is boundary measurement data.
Further, the single Zhang Jiepou structural image which is acquired in the same batch and has the same image size is a CT image or an ultrasonic image.
Further, the constructed spatial domain kernel function is a gaussian kernel function or a polynomial kernel function.
Further, the constructed frequency domain kernel function adopts a Gaussian kernel function or a sigmoid kernel function.
The invention utilizes the kernel function, can measure the relation between two data points by calculating the similarity or inner product value of the two data points in the high-dimensional characteristic space, and can further convert the nonlinear problem of the low dimension into the linear problem in the high-dimensional space. The spatial spectrum kernel function can convert nonlinear spatial spectrum correlation information of the multi-frequency EIT image into linear expression of an image domain, and apply spatial spectrum correlation prior constraint in the process of solving the unknown electrical impedance distribution condition, so as to guide the optimized reconstruction of the image.
Based on the same principle, the invention also provides an EIT image reconstruction device, which comprises:
the data acquisition module is used for acquiring EIT system boundary measurement data under multi-frequency excitation;
the feature generation module is used for identifying a group of low-dimensional features and forming a space spectrum feature vector set aiming at pixel points i on each frequency frame image omega in the multi-frequency EIT image set to be reconstructedThe method comprises the steps of carrying out a first treatment on the surface of the Wherein f i The spatial feature vector corresponding to the pixel point i on the frequency frame image omega is represented by the pixel point intensity value of a single Zhang Jiepou structure image which is acquired in the same batch and has the same image size; />Representing the frequency spectrum characteristic vector corresponding to the frequency frame image omega, and representing the frequency spectrum characteristic vector by adopting the boundary measurement data value of the frequency frame image omega;
the kernel function construction module is used for calculating a space domain kernel function constructed based on the space feature vector corresponding to the pixel point i on each frequency frame image in the multi-frequency EIT image set to be reconstructed and a Cronecker product of the frequency domain kernel constructed based on the corresponding frequency spectrum feature vector to obtain a space spectrum kernel function K;
the image reconstruction module is used for constructing a target loss function between EIT system boundary measurement data under multi-frequency excitation and internal electrical property distribution parameters K alpha to be reconstructed, and carrying out iterative reconstruction by minimizing the target loss function until the number of iterative steps preset or the iterative convergence condition is met, so as to obtain an optimal solution of the coefficient vector alpha, and further obtain the multi-frequency bioelectrical impedance chromatographic image with high precision, low noise and high quality.
An electronic device comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor realizes the EIT image reconstruction method based on the spatial spectrum kernel function when executing the computer program.
A storage medium containing computer executable instructions that when executed by a computer processor implement an EIT image reconstruction method based on a spatial spectrum kernel as described above.
The beneficial effects of the invention are as follows: the method provided by the invention is used for constructing the spatial spectrum kernel function of the spatial correlation priori information and the frequency domain correlation priori information of the coded image, and then embedding the spatial spectrum kernel function into the multi-frequency EIT image reconstruction model, so that the multi-frequency bioelectrical impedance tomography image reconstruction purpose with high precision, low noise and high quality is achieved. The spatial spectrum kernel function provided by the invention has the decoupling property of a spatial domain and a frequency domain, can acquire clearer and more accurate information such as image structures, details and the like from single Zhang Jiepou structure type images (such as CT images and ultrasonic images) which are acquired in the same batch as the EIT images and have the same image size, and excavates the relevance among multi-frequency frame images, encodes the spatial domain and the frequency domain information into an EIT image reconstruction model, synchronously suppresses noise interference of the EIT spatial domain and the frequency domain, avoids image deformation caused by a soft field, and improves the multi-frequency EIT image reconstruction quality.
Drawings
FIG. 1 is a flow chart of an EIT image reconstruction method based on a spatial spectrum kernel function;
FIG. 2 is a schematic flow chart of an EIT image reconstruction method based on a spatial spectrum kernel function provided in an embodiment of the invention;
FIG. 3 is a schematic structural diagram of an EIT image reconstruction device according to the present invention;
FIG. 4 is a schematic diagram of a data acquisition module according to an embodiment of the present invention;
FIG. 5 is a perspective view and a top view of a sensing device including both an ultrasonic sensor and an EIT sensor according to an embodiment of the present invention;
fig. 6 is a schematic structural diagram of an electronic device according to the present invention.
Detailed Description
Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, the same numbers in different drawings refer to the same or similar elements, unless otherwise indicated. The implementations described in the following exemplary examples are not representative of all implementations consistent with the present application. Rather, they are merely examples of apparatus and methods consistent with some aspects of the present application as detailed in the accompanying claims.
The terminology used in the present application is for the purpose of describing particular embodiments only and is not intended to be limiting of the present application. As used in this application and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and/or" as used herein refers to and encompasses any or all possible combinations of one or more of the associated listed items.
The bioelectrical impedance spectrum information can accurately reflect the physiological and pathological states of biological tissues and can be used for distinguishing different biological tissues, so that the acquisition of the bioelectrical impedance spectrum information based on the EIT imaging technology has great significance for a plurality of clinical applications such as tumor screening, brain monitoring and the like. However, since the image reconstruction process of EIT is a ill-condition underdetermined problem, that is, a small measurement error can cause a huge change of an imaging result, and an electrical response signal generated by biological tissue under external stimulus is weak, the measurement signal obtained by the EIT system contains a large amount of noise signals besides a real response signal, so that a bioelectrical impedance reconstructed image obtained based on the existing method shows limited image precision. In addition, due to the "soft-field" nature of the electromagnetic field, the single EIT linearization response matrix based reconstructed image also faces the problem of target deformation. In view of these problems, the present invention proposes an EIT image reconstruction method based on a spatial spectrum kernel function, as shown in fig. 1, including:
acquiring EIT system boundary measurement data under multi-frequency excitation;
and constructing a target loss function between EIT system boundary measurement data under multi-frequency excitation and internal electrical characteristic distribution parameters K alpha to be reconstructed, and performing iterative reconstruction by minimizing the target loss function until the number of iterative steps preset or the iterative convergence condition is met, so as to obtain an optimal solution of the coefficient vector alpha, and obtain a high-precision, low-noise and high-quality multi-frequency bioelectrical impedance tomographic image. K is a space frequency spectrum kernel function and is obtained by calculating a Cronecker product of a space domain kernel function constructed based on a space feature vector corresponding to a pixel point i on each frequency frame image in a multi-frequency EIT image set to be reconstructed and a frequency domain kernel function constructed based on the corresponding frequency spectrum feature vector; the spatial feature vector corresponding to the pixel point i on each frequency frame image in the multi-frequency EIT image set to be reconstructed is the pixel point intensity value of a single Zhang Jiepou structural image which is acquired in the same batch and has the same image size, and the corresponding frequency spectrum feature vector is the boundary measurement data value of the corresponding frequency frame image.
The invention provides a method for constructing a spatial frequency spectrum kernel function to acquire spatial correlation priori information and frequency domain correlation priori information of a multi-frequency EIT image, and synchronously codes the spatial correlation priori information and the frequency domain correlation priori information into an image reconstruction model of the multi-frequency EIT, namely a target loss function, so as to implement effective prior guidance and constraint, thereby realizing the great improvement of EIT image quality and the accurate analysis of bioelectrical impedance spectrum information.
The process according to the invention is described in detail below with reference to the drawings and to specific examples.
Fig. 2 is a schematic flow chart of an EIT image reconstruction method based on a spatial spectrum kernel function, which specifically includes the following steps:
step one: acquiring EIT system boundary measurement data under multi-frequency excitation;
wherein the multi-frequency excitation signal is an alternating current electric signal in a frequency range from 1 kilohertz to 10 megahertz.
Step two: and constructing a target loss function between boundary measurement data of the EIT system under multi-frequency excitation and an internal electrical characteristic distribution parameter K alpha to be reconstructed, and then minimizing the target loss function to finish iterative reconstruction until the number of iterative steps is preset or the iterative convergence condition is met, so as to obtain an optimal solution of the coefficient vector alpha, and further obtain a high-precision, low-noise and high-quality multi-frequency bioelectrical impedance chromatographic image.
Specifically, the target loss function based on the spatial spectrum kernel function is constructed by the following method:
(1) Firstly, aiming at the image intensity of a pixel point i on each frequency frame image omega in a multi-frequency EIT image set to be reconstructedIdentifying a set of low-dimensional features and forming a set of spatial spectral feature vectors +.>；
Specifically, a set of vectors including spatial features f is formed i And spectral feature vectorsIs a spatial spectrum feature vectorCollect->. Wherein the spatial feature vector f i The pixel intensity values of single Zhang Jiepou structural images (such as CT images and ultrasonic images) which are acquired in the same batch with the EIT images and have the same image size are used for exploring the spatial correlation among the pixels, and the spatial correlation prior formed by the structural and detail information acquired from the high-quality images is guided and encoded into an EIT image reconstruction model by utilizing a kernel function so as to inhibit noise interference of a spatial domain and correct image deformation caused by a soft field. Spectral feature vector->And (3) for each boundary measurement data value corresponding to each frequency frame image omega, the boundary measurement data value is used for exploring the correlation among different frequency frame images and encoding the correlation prior information into an EIT image reconstruction model by utilizing a kernel function so as to inhibit the influence of frequency domain noise.
(2) Using a basis function or conversion functionLow-dimensional feature vector set +.>Mapping into high-dimensional feature space, i.e. EIT image space, to obtain a high-dimensional feature vector +.>In addition, by combining a weight vector theta, EIT image data ++in a high-dimensional feature space as a 'tag value' is established>Spatial spectral feature vector +.>Is a linear relation of (2)And based on linear relation, expanding and changingAlternatively, a spatial spectrum kernel function which simultaneously encodes the prior information of the spatial domain correlation and the frequency domain correlation is obtained>Wherein ω, ω 'e W, I, I' e I, W is a frequency set of the adopted multi-frequency excitation signal, and I is a set of pixel points on the corresponding frequency frame image;
wherein the basis functionFor mapping the target object to a mapping function of arbitrary dimension space, which is implicitly defined by the kernel of the kernel function, no explicit expression is required, i.e. no explicit base function +.>In a specific form, also without calculationSpecific values of (3). The weight vector theta is located at and +.>The vector with weight of the same high-dimensional feature space has the expression +.>Wherein alpha is a coefficient vector consisting of a plurality of +.>Coefficient composition->Representation->The corresponding coefficients, S, represent the total number of pixels in the image of single Zhang Pinlv frames, and Ω represents the total number of spectrums. EIT image data in high-dimensional feature space +.>Spatial spectral feature vector +.>The linear relation of (2) is expanded and changed, and the method can be obtained:
wherein the spatial spectrum kernel functionNamely, a space spectrum characteristic vector in a low-dimensional spaceAs an input vector and back to the function of the vector dot product in the high-dimensional feature space. Which can be used for decoupling space domain and time-space domain and recording K S As a spatial domain kernel function, K Ω Is a frequency domain kernel function, then->，/>Is a kronecker product operator. The space domain kernel function is a Gaussian kernel function or a polynomial kernel function, and the frequency domain kernel function is a Gaussian kernel function or a sigmoid kernel function. Taking a gaussian kernel function as an example, the spatial spectrum kernel function expression is:
，
，
wherein sigma S A gaussian kernel parameter, i.e., a standard deviation, representing a spatial domain kernel function; accordingly, sigma Ω Gaussian kernel parameters representing the frequency domain kernel function.
The kernel function itself can be regarded as a computational skill that maps features to high dimensions and computes complex computations of inner products in the high dimensionsThe process is converted into a simple solving process of directly calculating the inner product of the characteristic and then carrying out higher-order operation, so that the method does not need to define a basis functionIn particular the form of the expression (c).
(3) Reuse of spatial spectrum kernel functionsCharacterizing EIT image data in a high-dimensional feature space>And embedding the new image data expression which codes the spatial frequency spectrum correlation priori information into an EIT forward model to form a nucleated forward model, and combining the forward model and a system response matrix to construct a target loss function between EIT system boundary measurement data under multi-frequency excitation and internal electrical characteristic distribution parameters to be reconstructed.
In particular, EIT image data is characterized by a spatial spectral kernel function, i.eEmbedding the expression into the EIT forward model is as follows:
wherein J is a system response matrix, and b is boundary measurement data. Combining the forward model, constructing a target loss function between EIT system boundary measurement data under multi-frequency excitation and internal electrical property distribution parameters to be reconstructed:
and finishing iterative reconstruction by minimizing the target loss function until the preset iterative step number is reached or the iterative convergence condition is met, so that the high-precision, low-noise and high-quality multi-frequency bioelectrical impedance tomography image can be obtained.
Specifically, the iterative process of the objective loss function described above may be expanded to:
t represents the number of iterative steps,is the coefficient vector at step t+1, < >>For the coefficient vector at step T, T is transposed, < >>Is the difference in boundary measurements between the two steps.
The invention also provides an embodiment of an EIT image reconstruction device corresponding to the embodiment of the EIT image reconstruction method based on the spatial spectrum kernel function.
Referring to fig. 3, a schematic structural diagram of an EIT image reconstruction apparatus according to an embodiment of the present invention includes:
the data acquisition module is used for acquiring EIT system boundary measurement data under multi-frequency excitation; fig. 4 is a schematic structural diagram of a data acquisition module in this embodiment, which includes a plurality of EIT sensors, a data acquisition system and a computer, wherein the EIT sensors, the data acquisition system and the computer are connected with each other, and the data acquisition system acquires signals at the EIT sensors under the instruction of the computer and transmits the signals to the computer for data storage to obtain the boundary measurement data of the EIT system under the multi-frequency excitation.
The feature generation module is used for identifying a group of low-dimensional features and forming a space spectrum feature vector set aiming at pixel points i on each frequency frame image omega in the multi-frequency EIT image set to be reconstructedThe method comprises the steps of carrying out a first treatment on the surface of the Wherein f i Representing the spatial feature vector corresponding to the pixel point i on the frequency frame image omega, and acquiring the spatial feature vector corresponding to the pixel point i on the frequency frame imageThe pixel point intensity values of the single Zhang Jiepou structural image which are acquired in the same batch and have the same image size are used for representing; />Representing the frequency spectrum characteristic vector corresponding to the frequency frame image omega, and representing the frequency spectrum characteristic vector by adopting the boundary measurement data value of the frequency frame image omega;
the kernel function construction module is used for calculating a space domain kernel function constructed based on the space feature vector corresponding to the pixel point i on each frequency frame image in the multi-frequency EIT image set to be reconstructed and a Cronecker product of the frequency domain kernel constructed based on the corresponding frequency spectrum feature vector to obtain a space spectrum kernel function K;
the image reconstruction module is used for constructing a target loss function between EIT system boundary measurement data under multi-frequency excitation and internal electrical property distribution parameters K alpha to be reconstructed, carrying out iterative reconstruction by minimizing the target loss function until the number of iterative steps set in advance is reached or the iterative convergence condition is met, obtaining the optimal solution of the coefficient vector alpha, and further obtaining the multi-frequency bioelectrical impedance chromatographic image with high precision, low noise and high quality.
Further, the data acquisition module further includes a sensor for acquiring single Zhang Jiepou structural images acquired in the same batch and having identical image sizes, as shown in fig. 5, which is a perspective view and a top view of a sensing device including both an ultrasonic sensor and an EIT sensor.
For the device embodiments, reference is made to the description of the method embodiments for the relevant points, since they essentially correspond to the method embodiments. The apparatus embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purposes of the present invention. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
Corresponding to the embodiment of the EIT image reconstruction method based on the spatial spectrum kernel function, the invention further provides electronic equipment, which comprises one or more processors and is used for realizing the EIT image reconstruction method based on the spatial spectrum kernel function in the embodiment.
As shown in fig. 6, a hardware configuration diagram of an arbitrary device with data processing capability where an EIT image reconstruction apparatus provided by the present invention is located, except for a processor, a memory, a network interface, and a nonvolatile memory shown in fig. 6, the arbitrary device with data processing capability where the apparatus is located in the embodiment generally includes other hardware according to an actual function of the arbitrary device with data processing capability, which is not described herein again.
The embodiment of the invention also provides a computer readable storage medium, on which a program is stored, which when executed by a processor, implements the EIT image reconstruction method based on the spatial spectrum kernel function in the above embodiment.
The computer readable storage medium may be an internal storage unit, such as a hard disk or a memory, of any of the data processing enabled devices described in any of the previous embodiments. The computer readable storage medium may be any device having data processing capability, for example, a plug-in hard disk, a Smart Media Card (SMC), an SD Card, a Flash memory Card (Flash Card), or the like, which are provided on the device. Further, the computer readable storage medium may include both internal storage units and external storage devices of any data processing device. The computer readable storage medium is used for storing the computer program and other programs and data required by the arbitrary data processing apparatus, and may also be used for temporarily storing data that has been output or is to be output.
The above examples are intended to illustrate the invention, not to limit it. Other variations or modifications of the above teachings will be apparent to those of ordinary skill in the art. It is not necessary for all embodiments to be exhaustive. Any modifications and changes made to the present invention fall within the spirit of the invention and the scope of the appended claims.
Claims (10)
1. An EIT image reconstruction method based on a spatial spectrum kernel function is characterized by comprising the following steps:
acquiring EIT system boundary measurement data under multi-frequency excitation;
constructing a target loss function between EIT system boundary measurement data under multi-frequency excitation and internal electrical characteristic distribution parameters K alpha to be reconstructed, and performing iterative reconstruction by minimizing the target loss function until the number of iterative steps preset or the iterative convergence condition is met, so as to obtain an optimal solution of a coefficient vector alpha, thereby obtaining a high-precision, low-noise and high-quality multi-frequency bioelectrical impedance tomographic image; k is a space frequency spectrum kernel function and is obtained by calculating a Cronecker product of a space domain kernel function constructed based on a space feature vector corresponding to a pixel point i on each frequency frame image in a multi-frequency EIT image set to be reconstructed and a frequency domain kernel function constructed based on the corresponding frequency spectrum feature vector; the spatial feature vector corresponding to the pixel point i on each frequency frame image in the multi-frequency EIT image set to be reconstructed is the pixel point intensity value of a single Zhang Jiepou structural image which is acquired in the same batch and has the same image size, and the corresponding frequency spectrum feature vector is the boundary measurement data value of the corresponding frequency frame image.
2. The method of claim 1, wherein the multi-frequency excitation signal is an alternating current electrical signal in a frequency range of 1 kilohertz to 10 megahertz.
3. The method of claim 1, wherein the objective loss function is expressed as follows:
；
wherein J is a system response matrix, and b is boundary measurement data.
4. The method of claim 1, wherein the single Zhang Jiepou structural class image acquired in the same batch and having the same image size is a CT image or an ultrasound image.
5. The method of claim 1, wherein the constructed spatial domain kernel function employs a gaussian kernel function or a polynomial kernel function.
6. The method of claim 1, wherein the constructed frequency domain kernel function employs a gaussian kernel function or a sigmoid kernel function.
7. An EIT image reconstruction apparatus, comprising:
the data acquisition module is used for acquiring EIT system boundary measurement data under multi-frequency excitation;
the feature generation module is used for identifying a group of low-dimensional features and forming a space spectrum feature vector set aiming at pixel points i on each frequency frame image omega in the multi-frequency EIT image set to be reconstructedThe method comprises the steps of carrying out a first treatment on the surface of the Wherein f i The spatial feature vector corresponding to the pixel point i on the frequency frame image omega is represented by the pixel point intensity value of a single Zhang Jiepou structural image which is acquired in the same batch and has the same image size; />Representing the frequency spectrum characteristic vector corresponding to the frequency frame image omega, and representing the frequency spectrum characteristic vector by adopting the boundary measurement data value of the frequency frame image omega;
the kernel function construction module is used for calculating a space domain kernel function constructed based on the space feature vector corresponding to the pixel point i on each frequency frame image in the multi-frequency EIT image set to be reconstructed and a Cronecker product of the frequency domain kernel constructed based on the corresponding frequency spectrum feature vector to obtain a space spectrum kernel function K;
the image reconstruction module is used for constructing a target loss function between EIT system boundary measurement data under multi-frequency excitation and internal electrical property distribution parameters K alpha to be reconstructed, and carrying out iterative reconstruction by minimizing the target loss function until the number of iterative steps preset or the iterative convergence condition is met, so as to obtain an optimal solution of the coefficient vector alpha, and further obtain the multi-frequency bioelectrical impedance chromatographic image with high precision, low noise and high quality.
8. The apparatus of claim 7, wherein the objective loss function is expressed as follows:
；
wherein J is a system response matrix, and b is boundary measurement data.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the EIT image reconstruction method based on spatial spectrum kernel functions as claimed in any one of claims 1-6 when executing the computer program.
10. A storage medium containing computer executable instructions which when executed by a computer processor implement the EIT image reconstruction method based on a spatial spectrum kernel as claimed in any one of claims 1-6.
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