CN113362407A

CN113362407A - GAN enhanced magnetic induction imaging method and system based on complex value convolution

Info

Publication number: CN113362407A
Application number: CN202110503479.0A
Authority: CN
Inventors: 宣琦; 宋栩杰; 陈其军; 周洁韵; 韩瑞鑫; 张璐; 翔云; 邱君瀚
Original assignee: Zhejiang University of Technology ZJUT
Current assignee: Zhejiang University of Technology ZJUT
Priority date: 2021-05-10
Filing date: 2021-05-10
Publication date: 2021-09-07

Abstract

The invention discloses a method and a system for GAN enhanced magnetic induction imaging based on complex value convolution, which comprises the following steps: s1, collecting voltage sequence data, constructing a complex value neural network model, inputting the voltage sequence data into the complex value neural network model for training, and obtaining a preliminary conductivity distribution image; s2, constructing a confrontation generation network model, inputting the preliminary conductivity distribution image into the confrontation generation network model for training to obtain a generator for image enhancement; and S3, inputting the preliminary conductivity distribution image into the generator to obtain a high-precision target conductivity distribution image. According to the method, the countermeasure generation network model is used as an image optimization module to carry out image enhancement on the output of the complex value convolution network, the complex value characteristic of the voltage sequence data is fully utilized, the training efficiency of the neural network and the accuracy of conductivity reconstruction are improved, and further the resolution and the accuracy of the final image are improved.

Description

GAN enhanced magnetic induction imaging method and system based on complex value convolution

Technical Field

The invention relates to the field of biomedical imaging and deep learning, in particular to a GAN enhanced magnetic induction imaging method and system based on complex value convolution.

Background

The imaging techniques used for clinical diagnosis today are mainly ultrasonic imaging (ultrasound imaging), X-ray tomography (X-CT), Magnetic Resonance Imaging (MRI), Positron Emission Tomography (PET), and the like. While these detection techniques have provided a great impetus for human medicine, various limitations still exist. For example, it is expensive, inconvenient to operate, produces radiation, cannot be monitored in real time, etc. Particularly, with the economic development, the aging of the population in China is increasingly serious, and diseases such as cerebral hemorrhage, cerebral infarction and the like threaten the elderly population. The real-time image monitoring of the diseases has great significance for determining the etiology and observing the development of the disease, and the existing imaging technology can not realize real-time dynamic monitoring. Electrical Impedance Tomography (EIT) and Magnetic Induction Tomography (MIT) technologies are expected to solve this problem.

Electrical impedance tomography is an imaging technique that estimates electrical properties inside an object by means of measurements of the surface of the object. Generally, a current is injected into the surface of the object through an electrode, and the resulting electrode voltage is measured. And solving an inverse problem by using the obtained current and voltage information through a reconstruction algorithm, and calculating the conductivity and dielectric constant distribution in the object. The method is a noninvasive, non-radiative, correspondingly rapid and low-cost imaging method. Electrical impedance imaging technology has been widely used in the fields of industrial process imaging, biomedical imaging, and geological exploration due to its advantages.

Magnetic Induction Tomography is a non-contact and non-destructive electrical impedance Tomography technology with human body conductivity distribution as the imaging target, which can be referred to in the literature (GriffithH. magnetic Induction Tomography [ J ]. MeasSciTech,2001,12(8): 1126) 1131.). The MIT basic principle is an eddy current detection principle based on faraday electromagnetic induction theory, and detects the conductivity distribution and changes thereof of a target without contacting the target to be detected.

MIT is very similar to EIT, both of which target reconstructing the conductivity distribution in the field. However, unlike the EIT in which the electrode array needs to be in contact with the human body, which is very inconvenient when allergic or traumatic events occur, MIT avoids these problems, has better convenience, and can reduce the measurement error caused by contact with the human body. In addition, compared with EIT, the magnetic field excitation mode of MIT is easier to penetrate tissues with lower electric conductivity, such as the skull of a human body, so MIT has very great potential and is a research hotspot in the medical field.

For MIT, in the process of traditional reconstruction algorithm research, a positive problem and an inverse problem need to be considered, and the essence of the positive problem is to solve the side value problem of a time-harmonic open-domain quasi-static eddy current field, that is, the voltage value in the detection coil is obtained by knowing the conductivity distribution inside the measured object, the excitation current distribution in the excitation coil outside the conductor, the dielectric constant, the magnetic permeability and other information. The inverse problem is that the measured boundary voltage sequence is used for reducing the conductivity distribution in the field domain through a reconstruction algorithm, and the inverse problem is that a second-order partial differential equation is solved and is nonlinear; meanwhile, the method is also pathological, and the pathological state refers to that a tiny error on data can cause huge change of a solution, so that a plurality of solving methods become unstable, and finally, a reconstructed conductivity distribution image is inaccurate, an artifact is large, and imaging quality is not high.

In recent years, with the development of deep learning, researchers have tried to develop reconstruction algorithms using deep neural networks.

An article entitled "A Novel Algorithm for High-Resolution Magnetic index Based on Stacked Auto-Encoder for Biological Tissue Imaging" published in IEEE Access in 2019 proposes a neural network of a Stacked self-Encoder to solve the MIT problem. The paper compares the position and reconstruction accuracy of an anomaly based on SAE and back projection, simulates hemorrhagic stroke, and verifies the practicability of the proposed algorithm. The result shows that the reconstruction relative error based on the SAE network algorithm reaches 0.29%, the accuracy of abnormal reconstruction is improved, and the prediction time is reduced to 0.02 s. The SAE neural network reconstruction algorithm can autonomously learn the nonlinear relation between input and output, and can solve the problems of serious artifacts, complex calculation and the like existing in the traditional reconstruction algorithm.

The method proposed in this article shows good performance in simulation experiments, but the superiority of the method is not proved in the real data set, but the data collected in reality is often more complex compared with the simulation data because of the noise of various scenes such as temperature, electromagnetic interference and the like existing in the real world, which results in that the collected data are different even if the experimental object is not changed. Therefore, pursuing high performance on real data sets is obviously more challenging and better able to solve problems in practical applications.

Patent CN112001977A (an electrical impedance tomography image reconstruction method based on residual error network) proposes a residual error network to solve the inverse problem. The method attempts to replace the traditional algorithm with a deep learning method to improve the imaging quality. The patent comprises the following steps: adopting MIT equipment to manufacture a human skull model and a heterogeneous object, designing different frequencies to acquire data, wherein the MIT equipment has 16 electrodes which can work in an excitation state and a detection state respectively, so that 256 data are acquired by each frequency under the condition of single excitation and single receiving, 512 voltage data are acquired in total, meanwhile, a circular acquisition field is uniformly divided by 512 triangles, the relative conductivity distribution in the field is constructed by combining different position coordinates and the actual resistance value of a target object, and the residual network is the mapping from 512 voltage sequences to 512 conductivity distribution values; converting the acquired one-dimensional voltage sequence into a multi-channel matrix form similar to an image, wherein one frequency is one channel, and meanwhile, considering the influence among the frequencies, introducing a third channel matrix H3 which is obtained by calculating the first two channels according to a formula H3-H2-f 2-H1/f 1, wherein f2 and f1 are two excitation frequencies respectively; aiming at the particularity of the imaging problem, modifying a residual error network structure, and customizing a loss function for training; and generating data by using the training result, and processing and optimizing the image.

The invention applies a residual error network in deep learning to the inverse problem solution of MIT, but the information contained in a voltage sequence is not fully utilized, each voltage value acquired by MIT equipment comprises a real part and an imaginary part, wherein phase information is contained, and the invention only takes the amplitude of the voltage as useful information to be input into a neural network, and partial information of the voltage is lost. Meanwhile, the field is divided into 512 subdivision triangles, the resolution is not high, and a plurality of edges and corners exist around the image, so that the finally reconstructed image needs to be subjected to morphological opening operation, which is a rough processing mode.

Disclosure of Invention

The present invention provides a GAN enhanced magnetic induction imaging method and system based on complex convolution to overcome the above disadvantages of the prior art.

The inverse problem of MIT, image reconstruction, is the known detection of the voltage signal in the coil to reconstruct and visualize the conductivity distribution in the region of the object field. The method is not only nonlinear but also ill-conditioned, wherein the nonlinearity mainly means that the relation between the conductivity distribution in an object field and a voltage signal in a detection coil is nonlinear, and MIT needs to solve the inverse problem of a second-order partial micro equation. The small error of the ill-conditioned data mainly shown in the data can cause huge change of the solution, which makes the traditional solving methods such as Newton Raphson method and least square method become unstable, and finally causes inaccurate reconstructed conductivity distribution image, larger artifact, lower resolution and lower image quality. The deep learning algorithm provided by the invention solves the common problems of the traditional algorithm and has better performance compared with the traditional deep learning algorithm.

Although the complexity of the existing deep learning method in the MIT field is improved compared with the traditional algorithm, the reconstruction quality of the image is improved to a certain degree, a specific network structure is not provided according to the specificity of the MIT data, and the problem of insufficient data utilization is caused, so that the final imaging quality is influenced. According to the invention, a more reasonable complex value convolution neural network is introduced, parameter calculation among neurons follows a complex value operation rule, and the complex value characteristic of voltage sequence data is fully utilized, so that the training efficiency of the neural network and the accuracy of conductivity reconstruction are improved.

No matter the traditional method or the deep learning method is adopted, when the MIT inverse problem, i.e., the reconstructed conductivity distribution, is solved, the imaging region is usually divided into a limited number of units by a finite element method, and a single conductivity value represents the whole division unit, so that the reconstructed conductivity is usually low in resolution and coarse in granularity. The invention adopts a two-step structure, and uses the confrontation generation network model as an image optimization module to carry out image enhancement on the output of the complex value convolution network, thereby improving the resolution and precision of the final image.

In order to achieve the purpose, the invention provides the following scheme: the invention provides a GAN enhanced magnetic induction imaging method based on complex value convolution, which comprises the following steps:

s1, collecting voltage sequence data, constructing a complex value neural network model, inputting the voltage sequence data into the complex value neural network model for training, and obtaining a preliminary conductivity distribution image;

s2, constructing a confrontation generation network model, inputting the preliminary conductivity distribution image into the confrontation generation network model for training to obtain a generator for image enhancement;

and S3, inputting the preliminary conductivity distribution image into the generator to obtain a high-precision target conductivity distribution image.

Preferably, the specific process of acquiring the voltage sequence data in step S1 is as follows: and positioning a target object through a stepping motor, acquiring initial data, and then eliminating interference data to obtain the voltage sequence data.

Preferably, the step S1 of inputting the voltage sequence data into the complex neural network model includes:

s1.1, converting the voltage sequence data containing a real part and an imaginary part into complex value representation, and then carrying out complex value operation;

s1.2: calculating a loss function, updating model parameters, and repeatedly executing the step;

s1.3: the output vector of 1x512 is reduced to a conductivity distribution and smoothed.

Preferably, in step S1.3, the smoothing process is to average the value of each triangular region and the value of the adjacent triangular region to obtain smoothed data;

the formula of the smoothing process is as follows:

where m is the number of surrounding triangular cells, σ_iIs the conductivity value.

Step S2, the confrontation generation network model at least comprises a generator and a discriminator which pass through a function L_GAN(G，D)＝E_x[logD(x)]+E_x[log(1-D(G(z)))]Describing, wherein D is maximized to logD (x), G is minimized to log (1-D (G (z))), x is a label image, and z is random noise;

the generator output g (z) is a candidate image with a probability distribution of x, the candidate image being a previous distribution mapping from z;

the arbiter outputs D (x) or D (G (z)) for scalar scoring of the proximity of the inputs.

Preferably, the step S2 of inputting the preliminary conductivity distribution image into the challenge generation network model for training includes:

s2.1: the generator is trained.

S2.2: and training the discriminator.

S2.3: steps S2.1-S2.2 are alternated until the challenge generating network model is stable.

Preferably, step S3 further includes performing a quality evaluation on the high-precision target conductivity distribution map, wherein the quality evaluation is measured according to the intersection ratio and the centroid distance by converting the high-precision target conductivity distribution map into a binary map;

the formula of the intersection ratio is as follows:

wherein R is_objFor reconstructing objects in the image, G_objWhen IoU is equal to 1, the object in the label graph represents that the reconstructed image is consistent with the label condition;

the centroid distance is given by the formula:

wherein x and y are the x-axis and y-axis coordinates of the marked image, and x and y are calculated by the following formula:

the invention also provides a GAN enhanced magnetic induction tomography system based on complex value CNN, comprising:

the device comprises a data processing module, a complex value training module, an image enhancement module and an output module;

the data processing module is connected with the image enhancement module through the complex value training module and is used for acquiring voltage sequence data;

the complex value training module is connected with the output module through the image enhancement module and is used for inputting the voltage sequence data into a complex value neural network model for training;

the image enhancement module is used for inputting the preliminary conductivity distribution image into the confrontation generation network model for training to obtain a generator for image enhancement;

the output module is used for inputting the voltage sequence data into the complex value neural network model to obtain the preliminary conductivity distribution image, and then inputting the preliminary conductivity distribution image into the generator for image enhancement to obtain the high-precision target conductivity distribution map.

According to the method, the countermeasure generation network model is used as an image optimization module to carry out image enhancement on the output of the complex value convolution network, the complex value characteristic of the voltage sequence data is fully utilized, the training efficiency of the neural network and the accuracy of conductivity reconstruction are improved, and further the resolution and the accuracy of the final image are improved.

The invention has the advantages that:

many theoretical results are currently done on simulation data, i.e. simulation of the MIT problem by simulation software and experiments on the obtained data. The experimental environment is an ideal environment without noise, and the conclusion obtained by experimental verification shows that the experimental environment has a theoretical effect and is low in reference to practical application. In view of this, all data of the method are collected from actual equipment, and the model obtained through final training is also based on actual data, so that the method has a greater significance for actual application.

The method uses a complex neural network to extract features of the voltage sequence data. The complex-valued neural network is different from the existing neural network, and has the characteristics of complex-valued representation, compliance with complex-valued operation rules and the like. The convolution layer, the activation function and the like used in the method are subjected to complex value reconstruction, so that the information contained in the voltage sequence data can be utilized to the maximum extent, and the voltage sequence data which is not subjected to any processing contains a real part and an imaginary part, so that the amplitude, the phase and other information can be extracted from the voltage sequence data, and the method has rich expression capacity. The introduction of complex-valued structures is a targeted improvement to the solution of the MIT inverse problem, not just the migration of deep learning methods. Meanwhile, on the basis of a complex value structure, the method uses a skip-connection cascade structure, and the structure can fuse low-level features and high-level features, so that a network can learn multi-scale features.

The method adopts a two-step mode, and after the conductivity distribution is reconstructed by a complex neural network, the conductivity distribution is input into a generator obtained by GAN training for image enhancement, so that the finally obtained image has higher resolution and precision. When the MIT inverse problem is solved, a finite element method is often used for dividing a field to be measured into a limited number of subdivision regions, so that a reconstructed conductivity distribution image is coarse-grained, the deficiency is made up by introducing the GAN, and finally the generator can map the coarse-grained conductivity distribution image into an image with higher precision and resolution through the alternate training of the generator and the discriminator.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.

FIG. 1 is a flowchart of the MIT imaging method of the present invention;

FIG. 2 is a diagram of a complex CNN structure according to the present invention;

FIG. 3 is a graph comparing the final effects of the examples of the present invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.

Referring to fig. 1, the present embodiment provides a GAN enhanced magnetic induction imaging method based on complex-valued convolution, including the following steps:

s1: real data were collected and data sets were made, and we collected real world data sets using an MIT system with a circular field as the imaging area and plastic cartridges containing saline of different conductivities as the experimental subjects.

S1.1: experimental data were collected by using a mechanical device with a stepper motor.

S1.2: and eliminating interference data, and dividing a training set and a testing set.

And S2, inputting the voltage sequence data into a complex value neural network for training, wherein the training process is as follows.

S2.1: and converting the voltage sequence data containing the real part and the imaginary part into complex value representation and then carrying out complex value operation.

S2.2: and calculating a loss function, updating the model parameters and repeating the steps.

S2.3: the output vector of 1x512 is reduced to a conductivity distribution and smoothed.

S3: the countermeasure generation network (GAN) is trained by the picture generated at step S2. The GAN contains a generator and an arbiter, described by the following objective function.

L_GAN(G,D)＝E_x[logD(x)]+E_x[log(1-D(G(z)))] (5)

D is a discriminator in the GAN, G is a generator in the GAN, the discriminator is used for improving the identification precision of the discriminator, the generator is used for improving the quality of generated data of the generator, the discriminator cannot be identified, and the discriminator and the generator are in antagonistic training. D maximizes D (x) to drive it toward 1, and G minimizes D (G (z)) to drive it toward 0, x being the label image, and z being random noise. The generator output g (z) is a candidate image with a probability distribution of x, which is mapped from the previous distribution of z. The arbiter output D (x) or D (G (z)) is a scalar score of how close the input is, which is defined as the likelihood that the input belongs to x.

S3.1: training is confronted with generating generators in the generating network.

S3.2: training the discriminators in the countermeasure generation network.

S3.3: steps S3.1-S3.2 are performed alternately until the model is stable.

S4: and inputting the test set data into the model, and verifying the effect of the model.

In the step S1.1, the plastic cylinder filled with saline is fixed on the slide rail using three rigid rods, the center of the circular field is set as the origin, and the object is accurately moved and positioned using the stepping motor. We used two cylinders with diameters of 3cm and 3.5cm, respectively, and a triangular prism, all plastic cylinders having a height of 8cm, as shown in table 1 below. The two cylinders are moved and the results are recorded in 4mm steps, while the triangular prism is moved in 5mm steps. In the circular field, the cylinder covers 1229 positions in total and the triangular prism covers 749 positions. The object stays at each position for 20 frames (one frame represents one measurement round for all sensing coils) to obtain a stable measurement. We take the tenth frame as the measured data for that location. To obtain enough data, we repeat the above operations three to four rounds. Note that the data collected under different batches are affected by environmental noise and mechanical instability, and therefore they are not exactly the same. The label of each position is generated by the known conductivity, the size and the shape of the object and the like through codes. The cylinder and prism have 1229 and 749 positions, respectively, with three measurements at each position.

TABLE 1

In said step S1.2, the data set comprises a total of 3112 samples of 3cm cylinders and 4916 samples of 3.5cm cylinders, and 2247 samples of triangular prisms. The training set and the test set are taken at every other position, 2460 training set samples and 2456 test set samples are totally taken from a 3.5cm cylinder, 1557 training set samples and 1555 test set samples are totally taken from the 3cm cylinder, and 1125 training set samples and 1122 test set samples are totally taken from a triangular prism.

In said step S2.1, the voltage sequence input to the complex-valued network contains 512 values, i.e. 256 pairs of real and imaginary values, and although the measurement system detects complex-valued data, which has rich expressiveness, we only store the imaginary value in real numbers, so it needs to convert the real value data to complex-valued representation at the beginning of the network, as shown in fig. 3.

Complex number represents: assuming we have a complex number c ═ a + bi, where a is the real part and bi is the imaginary part, we should receive them using 2 real-valued channels. For example, assume that the input has N_inA plurality of cores of size m × m, the output having N_outAn eigenmap, we have a complex tensor T whose Size is defined as Size_T＝N_in×N_out×m×m×2。

Further, to process the complex-valued tensor, we need to define a complex-valued convolution. The complex-valued convolution and filter is determined by its weight matrix, which is represented in the same way as the complex tensor T, i.e. using two real-valued channels to receive the real and imaginary parts. A complex-valued weight matrix is defined, as follows:

W＝A+iB (6)

where A and B are real matrices. Assuming that the input is a complex tensor h ═ x + iy and is a convolution operator, in order for the complex convolution to equal a real-valued two-dimensional convolution, there is

W*h＝(A*x-B*y)+i(B*x+A*y) (7)

In the above equation, the real part and the imaginary part of the output tensor are calculated on 2 channels, respectively, according to a complex operation rule. The size of the output tensor follows the definition in the complex representation.

Similarly, all activation functions in the network are also given in complex-valued form, in the complex-valued neural network of the present invention, modReLU is used:

where Z represents a complex-valued feature of the input activation function, b is the bias (bias), a parameter that will continually update values as the neural network is trained, and e is the base of the natural logarithm, see euler's equation.

θ_zIs the phase of z and is,

are parameters of learning. ReLU inhibits neurons that output less than 0. In the complex-valued domain, modReLU uses modulo values instead. If z is within a circle of radius b from origin 0, it is set to 0, otherwise it will remain. Therefore, the phase θ as an important feature can be retained_z。

Further, with existing complex-valued CNN components and U-net classical network structures, we have designed their own complex-valued networks, we use the skipConnection structure to merge low-level features and high-level features in the same proportion, and then up-sample the extracted features. The last layer converts the complex value to a real value. Finally, we use dense fully-connected layers to obtain real-valued 1 × 512 vectors that match the triangulation units.

In step S2.2, the model is trained using a binary cross-entropy loss function (BCE), which is shown below:

where o is the output vector, t is the actual measured true vector, and w is the tag weight. In our setup, it is assumed that the conductivity of the object and surrounding area is uniform.

In step S2.3, since the output of the network corresponds to the discretized subdivision triangles, the value of each triangular region is averaged with the values of the adjacent triangular regions using the following formula to smooth the data.

Where m is the number of surrounding triangular cells, σ_iIs the conductivity value. And saving the generated image as a counterproductive network trainingAnd (5) training data.

In said step S3.1, we use the condition GAN in order to reconstruct the field image. It adds extra information y to penalize the output of the generator beyond the given information. The additional information y may be a tag or any other limitation. We set y to the result of the complex value CNN, forcing the GAN output to be more accurate. In practice, y is fed into the arbiter and generator as an additional input layer. The objective function can then be rewritten as:

L_cGAN(G，D)＝E_x，y[logD(x|y)]+E_x，y[log(1-D(G(z|y)))] (10)

in addition, we also use the annotation data to penalize the output L2 distance, with the arbiter remaining unchanged. After adding the penalty, the objective function becomes:

L^*＝argmin_Gmax_DL_cGAN(G，D)+λL_l2(G) (11)

our generator only takes the image as input and does not apply random noise. In this work, we also adopted an encoder-decoder structure.

In step S3.2, the arbiter adopts the design of PatchGAN. PatchGAN outputs an N matrix whose elements indicate whether the input image block is false. This is achieved by sending cascaded image pairs into a series of convolutional layers. An image block is a small portion of an input image. The image blocks represent different perspective fields of the discriminator, which are sensitive to image details under different structures. The PatchGAN discriminator models the input image as a Markov random field, assuming that there is no dependency between non-adjacent image blocks. In the MIT problem, this loss penalty makes the output of the generator more distinguishable between different conductivity objects. Further, the discriminator penalty corresponds to the high frequency part of the input image. For the low frequency part, we use the L1 penalty to limit the generated image.

In step S4, each test set is first input into a complex-valued deep neural network to obtain a preliminary conductivity distribution; and inputting the generated image into a generator in a generation countermeasure network to obtain a final conductivity distribution map, and converting the output RGB image into a binary image for convenience of image quality evaluation.

The imaging quality of the model, we measure the intersection ratio (IoU) and the Centroid Distance (CD).

The cross-over ratio is a general indicator for evaluating a reconstructed image and is defined as:

wherein R is_objIs the object in the reconstructed image, and G_objAre objects in the annotation graph. When in use

IoU is equal to 1, indicating that the reconstructed image is identical to the annotation situation.

Another indicator, known as Centroid Distance (CD), reflects the accuracy with which objects are located. The centroid represents the center of the geometric object. The centroid distance is the euclidean distance between the centroid of the annotated image and the centroid of the reconstructed image. The definition is as follows.

Where x, y are the centroid of the annotation and x, y are the centroid of the reconstructed image. In the equation, x and y are calculated using the following formula:

to examine the performance of the model, the model (MITNet) was compared with Newton-Raphson (NR), optimized fully-connected network (FCN), and stacked self-encoder (SAE).

The model was trained on a Tesla V100, Intel Xeon 2.30GHz CPU server with a pyrrch. All networks used an Adam optimizer with a learning rate of 0.001, training an epoch of 200, and a batch size set to 16.

Fig. 3 shows the reconstructed image of all three data, from which we can see that MITNet is the most true in all cases. It can most accurately recover the shape and position from the measured voltage signal. The reason is that our MITNet model acquires all the information of the complex-valued signal.

To better understand the nature of the algorithm of the present invention, the output of the NR, FCN and SAE algorithms is enhanced using the same GAN technique. The results are shown in table 2 below. After enhancement, all methods showed improvement for different data. Overall, MITNet is the best algorithm across all data, averaging IoU 82.25.25% and CD 3.31.

TABLE 2

A GAN enhanced magnetic induction tomography system based on complex value CNN comprises a data processing module, a complex value training module, an image enhancement module and an output module;

the data processing module is used for cleaning the acquired voltage sequence data, eliminating interference data and storing the 10 th frame of the data in every 20 frames of data; and simultaneously, making a corresponding label for each piece of data, and dividing all the data into a training set and a test set.

The complex value training module inputs the voltage sequence data into a complex value neural network for training, and specifically comprises the following steps:

S2.2: and calculating a loss function, updating the model parameters and repeating the steps. The last layer of the complex-valued neural network outputs values between [0, 1] through a sigmoid function, and then the loss is calculated according to a binary cross entropy loss function (BCE):

s2.3: the output vector of 1x512 is reduced to a conductivity distribution and smoothed. The smoothing process is performed according to the following formula:

the image enhancement module inputs the picture output by the complex value network into the confrontation generation network for training, and finally completes the training to a generator for image enhancement, which specifically comprises the following steps:

S3.2: training the discriminators in the countermeasure generation network.

S3.3: and S3.1-S3.2 are alternately carried out until the model is stable. Wherein the objective function is:

L_cGAN(G，D)＝E_x，y[logD(x|y)]+E_x，y[log(1-D(G(z|y)))] (10)

L^*＝argmin_Gmax_DL_cGAN(G，D)+λL_l2(G) (11)

and the output module is used for inputting the test set into the complex neural network trained in the S2 to obtain a preliminary conductivity distribution image, and inputting the output image into the generator trained in the S3 to perform image enhancement to obtain a conductivity distribution map with higher precision.

The invention provides a complex value neural network for extracting the characteristics of voltage sequence data and reconstructing conductivity distribution. Different from the common neural network structure, the convolution layer, the activation function and the like used in the network are all subjected to complex value reconstruction, and have the characteristics of complex value representation, complex value operation rule compliance and the like. By doing so, the information contained in the voltage series data can be utilized to the maximum, because the voltage series data without any processing contains a real part and an imaginary part, from which information such as amplitude, phase and the like can be extracted, and the expression capability is abundant. The introduction of complex-valued structures is a targeted improvement to the solution of the MIT inverse problem, not just the migration of deep learning methods. Meanwhile, on the basis of a complex value structure, the method uses a skip-connection cascade structure, the structure can fuse low-level features and high-level features, and as shown in fig. 3, in our network, the low-level features and the high-level features on the 8x8 and 16x16 scales are fused respectively. Meanwhile, real-value and complex-value conversion structures are designed at the beginning and the end of the network respectively, so that data represented by complex values are input into the network, and 512 conductivity real values are output from the network.

The invention designs a two-stage structure of a complex value CNN for reconstructing conductivity distribution and a GAN for image enhancement. When the MIT inverse problem is solved, a finite element method is often used for dividing a field to be measured into a finite number of subdivision areas, so that a reconstructed conductivity distribution image is coarse-grained, and the two-stage structure of complex values CNN and GAN ensures that the finally reconstructed conductivity distribution image has high precision and high resolution, thereby greatly improving the imaging quality.

The above-described embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements of the technical solutions of the present invention can be made by those skilled in the art without departing from the spirit of the present invention, and the technical solutions of the present invention are within the scope of the present invention defined by the claims.

Claims

1. A GAN enhanced magnetic induction imaging method based on complex value convolution is characterized by comprising the following steps:

2. The method according to claim 1, wherein the step S1 of acquiring the voltage sequence data comprises: and positioning a target object through a stepping motor, acquiring initial data, and then eliminating interference data to obtain the voltage sequence data.

3. The complex-valued convolution-based GAN enhanced magnetic induction imaging method of claim 1 wherein the step S1 of inputting the voltage sequence data into the complex-valued neural network model comprises:

4. The method according to claim 3, wherein the smoothing process in step S1.3 is to average the value of each triangular region with the value of the adjacent triangular region to obtain smoothed data;

the formula of the smoothing process is as follows:

5. The method of GAN enhanced magnetic induction imaging based on complex valued convolution of claim 1,

6. The method of GAN enhanced magnetic induction imaging based on complex valued convolution of claim 5,

step S2 of inputting the preliminary conductivity distribution image into the countermeasure generation network model for training includes:

s2.1: training the generator;

s2.2: training the discriminator;

7. The method of GAN enhanced magnetic induction imaging based on complex valued convolution of claim 1,

the S3 further includes performing a quality evaluation on the high-precision target conductivity distribution map, wherein the quality evaluation is measured according to the intersection ratio and the centroid distance by converting the high-precision target conductivity distribution map into a binary map;

the formula of the intersection ratio is as follows:

the centroid distance is given by the formula:

8. a system for implementing the complex-valued convolution based GAN enhanced magnetic induction imaging method of any one of claims 1 to 7, comprising: