A GAN-enhanced magnetic induction imaging method and system based on complex-valued convolution

Abstract

The present invention discloses a GAN enhanced magnetic induction imaging method and system based on complex-valued convolution, comprising: S1, collecting voltage sequence data, constructing a complex-valued neural network model, inputting the voltage sequence data into the complex-valued neural network model for training, and obtaining a preliminary conductivity distribution image; S2, constructing a generative adversarial network model, inputting the preliminary conductivity distribution image into the generative adversarial network model for training, and obtaining a generator for image enhancement; S3, inputting the preliminary conductivity distribution image into the generator, and obtaining a high-precision target conductivity distribution map. The present invention uses the generative adversarial network model as an image optimization module to perform image enhancement on the output of the complex-valued convolutional network, making full use of the complex-valued characteristics of the voltage sequence data, improving the training efficiency of the neural network and the accuracy of conductivity reconstruction, and thus improving the resolution and accuracy of the final image.

Description

Technical Field

[0001] The present invention relates to the fields of biomedical imaging and deep learning, and mainly to a GAN-enhanced magnetic induction imaging method and system based on complex-valued convolution. Background Art

[0002] The imaging technologies currently used for clinical diagnosis include ultrasound imaging, X-ray computer-tomography (X-CT), magnetic resonance imaging (MRI), positron emission tomography (PET), etc. While these detection technologies have brought great impetus to human medicine, they still have various limitations. For example, they are expensive, inconvenient to operate, generate radiation, and cannot be monitored in real time. Especially with the development of the economy, the aging of the population in my country is becoming increasingly serious, and diseases such as cerebral hemorrhage and cerebral infarction are threatening the elderly. Real-time image monitoring of these diseases is of great significance for diagnosing the cause and observing the development of the disease, but existing imaging technologies cannot achieve real-time dynamic monitoring. Electrical impedance tomography (EIT) and magnetic induction tomography (MIT) technologies are expected to solve this problem.

[0003] Electrical impedance tomography is an imaging technology that estimates the internal electrical properties of an object by measuring the surface of the object. Usually, the current is injected into the surface of the object through electrodes and the resulting electrode voltage is measured. The current and voltage information obtained are then used through a reconstruction algorithm to solve the inverse problem and calculate the conductivity and dielectric constant distribution in the object. It is a non-invasive, radiation-free, fast-response, and low-cost imaging method. At present, electrical impedance tomography has been widely used in industrial process imaging, biomedical imaging, and geological exploration due to its advantages.

[0004] Magnetic induction tomography is a non-contact, non-destructive electrical impedance tomography technology that uses the conductivity distribution of the human body as the imaging target. For reference, see (Griffith H. Magnetic Induction Tomography [J]. Meas Sci Tech, 2001, 12 (8): 1126-1131.). The basic principle of MIT is the eddy current detection principle based on Faraday's electromagnetic induction theory. It detects the conductivity distribution and its changes of the target without contacting the target.

[0005] MIT is very similar to EIT, and both aim to reconstruct the conductivity distribution in the field. However, the difference is that the electrode array in EIT needs to be in contact with the human body, which is extremely inconvenient when encountering allergies, trauma, etc. MIT avoids this series of problems, has better convenience, and can reduce the measurement errors caused by contact with the human body. In addition, compared with EIT, MIT's magnetic field excitation method is easier to penetrate tissues with low conductivity such as the human skull. Therefore, MIT has great potential and is a research hotspot in the medical field.

[0006] For MIT, in the process of studying traditional reconstruction algorithms, it is necessary to consider the direct problem and the inverse problem. The essence of the direct problem is to solve a boundary value problem of a time-harmonic open-domain quasi-static eddy current field, that is, to find the voltage value in the detection coil from the known conductivity distribution inside the measured object and the excitation current distribution in the excitation coil outside the conductor, as well as information such as dielectric constant and magnetic permeability. The inverse problem is to restore the conductivity distribution in the field from the measured boundary voltage sequence through the reconstruction algorithm. Its essence is to solve a second-order partial differential equation, which is nonlinear and pathological. The so-called pathological means that a small error in the data will cause a huge change in the solution, which makes many solution methods unstable, and ultimately leads to inaccurate reconstructed conductivity distribution images, large artifacts, and low imaging quality.

[0007] In recent years, with the continuous development of deep learning, researchers have gradually tried to use deep neural networks to study reconstruction algorithms.

[0008] An article titled "A Novel Algorithm for High-Resolution Magnetic Induction Tomography Based on Stacked Auto-Encoder for Biological Tissue Imaging" published in IEEE Access in 2019 proposed a stacked autoencoder neural network to solve the MIT problem. The article compared the location and reconstruction accuracy of abnormalities based on SAE and back projection, and simulated hemorrhagic stroke to verify the practicality of the proposed algorithm. The results show that the relative error of reconstruction based on the SAE network algorithm reached 0.29%, which improved the accuracy of abnormal reconstruction and reduced the prediction time to 0.02s. The proposed SAE neural network reconstruction algorithm can autonomously learn the nonlinear relationship between input and output, and can solve the problems of serious artifacts and complex calculations in traditional reconstruction algorithms.

[0009] The method proposed in this article shows good performance in simulation experiments, but it has not been proven to be superior in real data sets. Compared with simulation data, the data collected in reality is often more complex because there are noises in various scenarios such as temperature and electromagnetic interference in the real world. This results in different or even very different data even if the experimental object does not change. Therefore, pursuing high performance on real data sets is obviously more challenging and more able to solve problems in practical applications.

[0010] Patent CN112001977A (An electrical impedance tomography image reconstruction method based on residual network) proposes a residual network to solve the inverse problem. This method attempts to use deep learning methods to replace traditional algorithms to improve the quality of imaging. The patent includes the following steps: using MIT equipment to make human skull models and heterogeneous objects, and designing different frequencies for data collection. The MIT device has a total of 16 electrodes, which can work in excitation and detection states respectively. Therefore, in the case of single excitation and single reception, 256 data are collected at each frequency, and a total of 512 voltage data are collected. At the same time, the circular collection field is evenly divided into 512 triangles, and the relative conductivity distribution in the field is constructed by combining different position coordinates and the actual resistance value of the target object. The residual network is a mapping of 512 voltage sequences to 512 conductivity distribution values; the collected one-dimensional voltage sequence is converted into a multi-channel matrix form similar to the image, one frequency is one channel, and considering the influence between frequencies, the third channel matrix H3 is introduced, which is calculated by the first two channels according to the formula H3=H2-f2*H1 / f1, where f2 and f1 are two excitation frequencies respectively; in view of the particularity of the imaging problem, the residual network structure is modified, and the loss function is customized for training; the training results are used to generate data for image processing and optimization.

[0011] This invention applies the residual network in deep learning to solve the inverse problem of MIT, but it does not make full use of the information contained in the voltage sequence. Each voltage value collected by the MIT device contains two parts, the real part and the imaginary part, which contain phase information, while this invention only takes the voltage amplitude as useful information and inputs it into the neural network, which loses some of its information. At the same time, this invention divides the field into 512 subdivided triangles, which has a low resolution and there will be many edges and corners around the image, so the final reconstructed image needs to continue to perform morphological opening operations, which is a rough processing method. Summary of the invention

[0012] The present invention aims to overcome the above-mentioned shortcomings of the prior art and provide a GAN enhanced magnetic induction imaging method and system based on complex-valued convolution.

[0013] The inverse problem of MIT, namely image reconstruction, is to reconstruct the conductivity distribution in the object field area and visualize it with the known voltage signal in the detection coil. It is both nonlinear and pathological. The nonlinearity mainly refers to the nonlinear relationship between the conductivity distribution in the object field and the voltage signal in the detection coil. What MIT needs to solve is the inverse problem of a second-order partial differential equation. The pathological nature is mainly manifested in that a small error in its data will lead to a huge change in the solution, which makes traditional solution methods such as the Newton-Raphson method and the least squares method unstable, ultimately resulting in inaccurate reconstructed conductivity distribution images, large artifacts, low resolution, and low image quality. The deep learning algorithm proposed in the present invention solves the common problems of traditional algorithms and has better performance than existing deep learning algorithms.

[0014] Although the existing deep learning methods in the MIT field are more complex than traditional algorithms and have improved the image reconstruction quality to a certain extent, they have not proposed a targeted network structure based on the specificity of MIT data, which leads to insufficient data utilization and affects the final imaging quality. The present invention introduces a more reasonable complex-valued convolutional neural network, and the parameter calculations between neurons follow the complex-valued operation rules, making full use of the complex-valued characteristics of voltage sequence data, thereby improving the training efficiency of the neural network and the accuracy of conductivity reconstruction.

[0015] Whether it is a traditional method or a deep learning method, when solving the MIT inverse problem, i.e. reconstructing the conductivity distribution, the imaging area is often divided into a finite number of units by the finite element method, and a single conductivity value is used to represent the entire divided unit. Therefore, the reconstructed conductivity is often low-resolution and coarse-grained. The present invention adopts a two-step structure, uses the adversarial generative network model as an image optimization module to enhance the output of the complex-valued convolutional network, and improves the resolution and accuracy of the final image.

[0016] To achieve the above object, the present invention provides the following solution: The present invention provides a GAN enhanced magnetic induction imaging method based on complex-valued convolution, comprising the following steps:

[0017] S1, collecting voltage sequence data, constructing a complex-valued neural network model, inputting the voltage sequence data into the complex-valued neural network model for training, and obtaining a preliminary conductivity distribution image;

[0018] S2, constructing a generative adversarial network model, inputting the preliminary conductivity distribution image into the generative adversarial network model for training, and obtaining a generator for image enhancement;

[0019] S3. Input the preliminary conductivity distribution image into the generator to obtain a high-precision target conductivity distribution map.

[0020] Preferably, the specific process of collecting the voltage sequence data in step S1 is: positioning the target object by a stepper motor, collecting initial data, removing interference data, and obtaining the voltage sequence data.

[0021] Preferably, step S1 of inputting the voltage sequence data into the complex-valued neural network model comprises:

[0022] S1.1, converting the voltage sequence data including the real part and the imaginary part into a complex value representation and then performing a complex value operation;

[0023] S1.2: Calculate the loss function, update the model parameters, and repeat this step;

[0024] S1.3: Restore the output 1x512 vector to conductivity distribution and perform smoothing.

[0025] Preferably, the smoothing process in step S1.3 is to average the value of each triangular area with the value of the adjacent triangular area to obtain smoothed data;

[0026] The formula for the smoothing process is:

[0027]

[0028] Where m is the number of surrounding triangle elements, σ i is the conductivity value.

[0029] Step S2: The adversarial generative network model includes at least a generator and a discriminator. GAN (G, D) = E x [logD(x)]+E x [log(1-D(G(z)))], where D is maximized as logD(x), G is minimized as log(1-D(G(z))), x is the label image, and z is random noise;

[0030] The generator output G(z) is a candidate image with a probability distribution of x, which is mapped from a previous distribution of z;

[0031] The discriminator outputs D(x) or D(G(z)), which is used to perform a scalar score on the proximity of the input.

[0032] Preferably, step S2 of inputting the preliminary conductivity distribution image into the generative adversarial network model for training comprises:

[0033] S2.1: Train the generator.

[0034] S2.2: Train the discriminator.

[0035] S2.3: Steps S2.1-S2.2 are performed alternately until the adversarial generative network model is stable.

[0036] Preferably, step S3 further comprises performing a quality assessment on the high-precision target conductivity distribution map, wherein the quality assessment is performed by converting the high-precision target conductivity distribution map into a binary map and measuring the quality according to the intersection-over-union ratio and the centroid distance;

[0037] The formula of the intersection-over-union ratio is:

[0038]

[0039] Among them, R obj To reconstruct the object in the image, G obj For objects in the labeled image, when IoU is equal to 1, it means that the reconstructed image is consistent with the labeled image;

[0040] The formula for the centroid distance is:

[0041]

[0042] Among them, x* and y* are the x-axis and y-axis coordinates of the annotated image, and x and y are calculated by the following formula:

[0043]

[0044] The present invention also provides a GAN enhanced magnetic induction tomography system based on complex-valued CNN, comprising:

[0045] Data processing module, complex value training module, image enhancement module, output module;

[0046] The data processing module is connected to the image enhancement module through the complex value training module, and is used to collect voltage sequence data;

[0047] The complex-valued training module is connected to the output module through the image enhancement module, and is used to input the voltage sequence data into a complex-valued neural network model for training;

[0048] The image enhancement module is used to input the preliminary conductivity distribution image into the adversarial generative network model for training to obtain a generator for image enhancement;

[0049] The output module is used to input the voltage sequence data into the complex-valued neural network model to obtain the preliminary conductivity distribution image, and then input the preliminary conductivity distribution image into the generator for image enhancement to obtain the high-precision target conductivity distribution map.

[0050] The present invention uses the generative adversarial network model as an image optimization module to perform image enhancement on the output of the complex-valued convolutional network, making full use of the complex-valued characteristics of the voltage sequence data, improving the training efficiency of the neural network and the accuracy of conductivity reconstruction, thereby improving the resolution and accuracy of the final image.

[0051] The advantages of the present invention are:

[0052] Many existing theoretical results are completed on simulated data, that is, MIT problems are simulated by simulation software, and experiments are conducted on the obtained data. Such an experimental environment is an ideal noise-free environment. The conclusions obtained by experimental verification illustrate the theoretical effects and have low reference value for practical applications. In view of this, all data of this method are collected from actual equipment, and the model finally trained is also based on actual data, which is more meaningful for practical applications.

[0053] This method uses a complex-valued neural network to extract the features of voltage sequence data. Complex-valued neural networks are different from current neural networks in that they have the characteristics of complex-valued representation and compliance with complex-valued operation rules. The convolutional layers and activation functions used in this method are all reconstructed with complex values, which can maximize the use of the information contained in the voltage sequence data, because the voltage sequence data without any processing contains real and imaginary parts, from which information such as amplitude and phase can be extracted, and it has rich expressive power. The introduction of complex-valued structures is a targeted improvement in solving the MIT inverse problem, not just a migration of deep learning methods. At the same time, based on the complex-valued structure, this method uses a skip-connection cascade structure, which can fuse low-level features and high-level features, enabling the network to learn multi-scale features.

[0054] This method adopts a two-step approach. After reconstructing the conductivity distribution through a complex-valued neural network, the generator trained by GAN is input for image enhancement, so that the final image has higher resolution and accuracy. When solving the MIT inverse problem, the finite element method is often used to divide the field to be measured into a finite number of subdivision regions, which makes the reconstructed conductivity distribution image coarse-grained. The introduction of GAN makes up for this deficiency. Through the alternating training of the generator and the discriminator, the final generator can map the coarse-grained conductivity distribution image to an image with higher accuracy and resolution. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0056] Figure 1 is a flow chart of the MIT imaging method of the present invention;

[0057] Figure 2 It is a complex-valued CNN structure diagram of the present invention;

[0058] Figure 3 It is a comparison diagram of the final effects of the embodiments of the present invention. DETAILED DESCRIPTION

[0059] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0060] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0061] Reference Figure 1 As shown, this embodiment provides a GAN enhanced magnetic induction imaging method based on complex-valued convolution, comprising the following steps:

[0062] S1: Collect real data and create datasets. We use the MIT system to collect real-world datasets. The system uses a circular domain as the imaging area and plastic cylinders filled with salt water of different conductivity as experimental objects.

[0063] S1.1: Collect experimental data by using a mechanical device with a stepper motor.

[0064] S1.2: Eliminate interference data and divide the data into training set and test set.

[0065] S2: Input the voltage sequence data into the complex-valued neural network training. The training process is as follows.

[0066] S2.1: Convert the voltage sequence data including the real part and the imaginary part into a complex value representation and then perform complex value operation.

[0067] S2.2: Calculate the loss function, update the model parameters, and repeat this step.

[0068] S2.3: Restore the output 1x512 vector to conductivity distribution and perform smoothing.

[0069] S3: Train a Generative Adversarial Network (GAN) using the images generated in step S2. GAN consists of a generator and a discriminator, described by the following objective function.

[0070] LGAN (G,D)=E x [logD(x)]+E x [log(1-D(G(z)))] (5)

[0071] Among them, D is the discriminator in GAN, and G is the generator in GAN. The discriminator is used to improve its recognition accuracy, while the generator is used to improve the quality of its generated data so that the discriminator cannot recognize it. The two are mutually adversarial training. D maximizes D(x) to make it tend to 1, while G minimizes D(G(z)) to make it tend to 0. x is the label image and z is 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 discriminator output D(x) or D(G(z)) is a scalar score for the closeness of the input, which is defined as the possibility that the input belongs to x.

[0072] S3.1: Training the generator in a generative adversarial network.

[0073] S3.2: Training the discriminator in a generative adversarial network.

[0074] S3.3: Steps S3.1-S3.2 are performed alternately until the model is stable.

[0075] S4: Input the test set data into the model to verify the model effect.

[0076] In step S1.1, a plastic cylinder filled with saline is fixed on a slide rail using three rigid rods, the center of the circular field is set as the origin, and a stepper motor is used to accurately move and position the object. We used two cylinders with diameters of 3 cm and 3.5 cm and a triangular prism, as shown in Table 1 below, and the height of all plastic cylinders is 8 cm. Move the two cylinders and record the results in steps of 4 mm, while the triangular prism moves in steps of 5 mm. In the circular field, the cylinders cover a total of 1229 positions and the triangular prism covers 749 positions. The object stays at each position for 20 frames (one frame represents a round of measurement of all sensing coils) to obtain stable measurements. We take the tenth frame as the measured data at that position. In order to obtain enough data, we repeat the above operation for three to four rounds. Please note that the data collected in different batches are affected by environmental noise and mechanical instability, so they are not exactly the same. The label for each position is generated by code from known information such as conductivity, object size and shape. There are 1229 and 749 positions for cylinders and prisms, respectively, with three measurements at each position.

[0077] Table 1

[0078]

[0079] In step S1.2, the data set contains a total of 3112 samples of 3 cm cylinders and 4916 samples of 3.5 cm cylinders, as well as 2247 samples of triangular prisms. The training set and test set are taken at every other position. There are a total of 2460 training set samples and 2456 test set samples for 3.5 cm cylinders, 1557 training set samples and 1555 test set samples for 3 cm cylinders, and 1125 training set samples and 1122 test set samples for triangular prisms.

[0080] In step S2.1, the voltage sequence input to the complex-valued network contains 512 values, i.e., 256 pairs of real and imaginary values. Although the measurement system detects complex-valued data with rich expressiveness, we only save the imaginary values ​​as real numbers. Therefore, it is necessary to convert the real-valued data into complex-valued representation at the beginning of the network, as shown in Figure 3 shown.

[0081] Complex number representation: Suppose we have a complex number c = a + bi, where a is the real part and bi is the imaginary part, we should use 2 real-valued channels to receive them. For example, suppose the input has N in complex numbers, the kernel size is m×m, and the output has N out feature maps, then we have a complex tensor T whose size is defined as Size T =N in ×N out ×m×m×2.

[0082] Furthermore, in order to process complex-valued tensors, we need to define complex-valued convolution. Complex-valued convolution and filters are determined by their weight matrices, which are represented in the same way as complex tensors T, that is, using two real-valued channels to receive the real and imaginary parts. Define a complex-valued weight matrix as follows:

[0083] W=A+iB (6)

[0084] Where A and B are real matrices. Assuming the input is a complex tensor h = x + iy, and * is the convolution operator, in order to make the complex convolution equal to a real-valued two-dimensional convolution, we have

[0085] W*h=(A*xB*y)+i(B*x+A*y) (7)

[0086] In the above formula, the real and imaginary parts of the output tensor are calculated on two channels respectively according to the complex number operation rules. The size of the output tensor follows the definition in the complex number representation.

[0087] Similarly, all activation functions in the network are given in complex value form. In the complex-valued neural network of the present invention, modReLU is used:

[0088]

[0089] Among them, Z represents a complex-valued feature of the input activation function, b is the bias, which is a parameter that will be continuously updated as the neural network is trained, and e is the base of the natural logarithm, see Euler's formula. θ z is the phase of z, is a learned parameter. ReLU prohibits neurons whose output is less than 0. In the complex-valued domain, modReLU uses the modulus value instead. If z is within the circle with radius b at the origin 0, it is set to 0, otherwise it is retained. Therefore, the phase θ, which is an important feature, can be retained z .

[0090] Furthermore, we designed our own complex-valued network using the existing complex-valued CNN components and the U-net classic network structure. We used the skipConnection structure to merge low-level features and high-level features in the same proportion, and then upsampled the extracted features. The last layer converts the complex values ​​into real values. Finally, we use a dense fully connected layer to obtain a real-valued 1×512 vector that matches the triangulation unit.

[0091] In step S2.2, a binary cross entropy loss function (BCE) is used to train the model, and the loss function is as follows:

[0092]

[0093] where o is the output vector, t is the actual measured true vector, and w is the label weight. In our setting, the conductivity of the object and the surrounding area is assumed to be uniform.

[0094] In step S2.3, because the output of the network corresponds to the discretized subdivided triangles, the value of each triangular area is averaged with the value of the adjacent triangular area using the following formula to make the data smooth.

[0095]

[0096] where m is the number of surrounding triangle elements, σ i is the conductivity value. And save the generated image as the data for training the adversarial generation network.

[0097] In step S3.1, to reconstruct the field image, we use conditional GAN. It adds extra information y to penalize the generator output that exceeds the given information. The extra information y can be a label or any other restriction. We set y to the result of the complex-valued CNN, thus forcing the GAN output to be more accurate. In fact, y is fed into the discriminator and generator as an additional input layer. The objective function can then be rewritten as:

[0098] L cGAN (G, D) = E x，y [logD(x|y)]+E x，y [log(1-D(G(z|y)))] (10)

[0099] In addition, while the discriminator remains unchanged, we also use the labeled data to penalize the L2 distance of the output. After adding the penalty, the objective function becomes:

[0100] L * =argmin G max D L cGAN (G, D)+λL l2 (G) (11)

[0101] Our generator only takes images as input and does not apply random noise. In this work, we also adopt an encoder-decoder structure.

[0102] In step S3.2, the discriminator adopts the design of PatchGAN. PatchGAN outputs an N×N matrix whose elements indicate whether the input image patch is fake. It is achieved by sending cascaded image pairs to a series of convolutional layers. An image patch is a small part of the input image. The image patch represents different perspective fields of the discriminator, which is 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 patches. In the MIT problem, this loss penalty makes the output of the generator easier to distinguish between objects of different conductivity. In addition, the discriminator loss corresponds to the high-frequency part of the input image. For the low-frequency part, we use L1 loss to limit the generated image.

[0103] In step S4, each test set is first input into a complex-valued deep neural network to obtain a preliminary conductivity distribution; the generated image is then input into a generator in a generative adversarial network to obtain a final conductivity distribution map. In order to facilitate image quality assessment, the output RGB image is converted into a binary image.

[0104] We use the intersection over union (IoU) and centroid distance (CD) to measure the imaging quality of the model.

[0105] The intersection-over-union ratio is a common metric for evaluating reconstructed images and is defined as:

[0106]

[0107] Where R obj is the object in the reconstructed image, and G obj is an object in the labeled graph.

[0108] When IoU is equal to 1, it means that the reconstructed image is exactly the same as the annotation.

[0109] Another metric is called Centroid Distance (CD), which reflects the accuracy of locating objects. The centroid represents the center of a geometric object. The Centroid Distance is the Euclidean distance between the centroid of the annotated image and the centroid of the reconstructed image. It is defined as follows.

[0110]

[0111] Where x*, y* are the centroids of the annotations and x, y are the centroids of the reconstructed image. In the equation, x and y are calculated using the following formulas:

[0112]

[0113] In order to test the performance of the model, the model (MITNet) is compared with Newton-Raphson (NR), optimized fully connected network (FCN) and stacked autoencoder (SAE).

[0114] The models were trained on a Tesla V100, Intel Xeon 2.30GHz CPU server with pytorch. All networks used the Adam optimizer with a learning rate of 0.001, trained for 200 epochs, and the batch size was set to 16.

[0115] Figure 3 The reconstructed images for all three data are shown, from which we can see that MITNet matches the ground truth best in all cases. It can most accurately recover the shape and position from the measured voltage signal. The reason is that our MITNet model captures the full information of the complex-valued signal.

[0116] In order to better understand the properties of the proposed algorithm, the outputs of the NR, FCN, and SAE algorithms were enhanced using the same GAN technique. The results are shown in Table 2 below. After enhancement, all methods showed improvements on different data. Overall, MITNet is the best algorithm on all data, achieving an IoU of 82.25% and a CD of 3.31 on average.

[0117] Table 2

[0118]

[0119] A GAN enhanced magnetic induction tomography system based on complex-valued CNN, comprising a data processing module, a complex-valued training module, an image enhancement module, and an output module;

[0120] The data processing module cleans the collected voltage sequence data, removes interference data, and saves the 10th frame out of every 20 frames of data; at the same time, it creates a corresponding label for each piece of data and divides all the data into a training set and a test set.

[0121] The complex value training module inputs the voltage sequence data into the complex value neural network for training, which specifically includes:

[0122] S2.1: Convert the voltage sequence data including the real part and the imaginary part into a complex value representation and then perform complex value operation.

[0123] S2.2: Calculate the loss function, update the model parameters, and repeat this step. The last layer of the complex-valued neural network outputs a value between [0, 1] through the sigmoid function, and then calculates the loss according to the binary cross entropy loss function (BCE):

[0124]

[0125] S2.3: The output 1x512 vector is restored to the conductivity distribution and smoothed. The smoothing is performed according to the following formula:

[0126]

[0127] The image enhancement module inputs the image output by the complex-valued network into the adversarial generative network for training, and finally trains a generator for image enhancement, including:

[0128] S3.1: Training the generator in a generative adversarial network.

[0129] S3.2: Training the discriminator in a generative adversarial network.

[0130] S3.3: Steps S3.1 to S3.2 are performed alternately until the model is stable. The objective function is:

[0131] L cGAN (G, D) = E x，y [logD(x|y)]+E x，y [log(1-D(G(z|y)))] (10)

[0132] L * =argmin G max D L cGAN (G, D)+λL l2 (G) (11)

[0133] The output module inputs the test set into the complex-valued neural network trained in S2 to obtain a preliminary conductivity distribution image, and then inputs the output image into the generator trained in S3 for image enhancement to obtain a higher-precision conductivity distribution map.

[0134] The present invention proposes a complex-valued neural network for extracting features of voltage series data and reconstructing conductivity distribution. Different from ordinary neural network structures, the convolutional layers, activation functions, etc. used in this network are all reconstructed with complex values, and have the characteristics of complex-valued representation and compliance with complex-valued operation rules. Doing so can maximize the use of the information contained in the voltage series data, because the voltage series data without any processing contains real and imaginary parts, from which information such as amplitude and phase can be extracted, and it has rich expressive power. The introduction of complex-valued structures is a targeted improvement to the solution of the MIT inverse problem, not just a migration of deep learning methods. At the same time, based on the complex-valued structure, this method uses a skip-connection cascade structure, which can fuse low-level features and high-level features, such as Figure 3 As shown in the figure, in our network, low-level features and high-level features at 8x8 and 16x16 scales are fused respectively. At the same time, real-valued and complex-valued conversion structures are designed at the beginning and end of the network respectively to ensure that the data input to the network is complex-valued and the data output from the network is 512 conductivity real values.

[0135] The present invention designs a two-level structure of complex-valued CNN for reconstructing conductivity distribution and GAN for image enhancement. When solving the MIT inverse problem, the field to be measured is often divided into a finite number of subdivision regions using the finite element method, which makes the reconstructed conductivity distribution image coarse-grained, and the two-level structure of complex-valued CNN and GAN ensures that the final reconstructed conductivity distribution image has high precision and high resolution, thereby greatly improving the quality of imaging.

[0136] The embodiments described above are only descriptions of the preferred modes of the present invention, and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A GAN enhanced magnetic induction imaging method based on complex-valued convolution, characterized in that: The steps include: S1, collecting voltage sequence data, constructing a complex-valued neural network model, inputting the voltage sequence data into the complex-valued neural network model for training, and obtaining a preliminary conductivity distribution image; Inputting the voltage sequence data into the complex-valued neural network model comprises: S1.1, converting the voltage sequence data including the real part and the imaginary part into a complex value representation and then performing a complex value operation; S1.2: Calculate the loss function, update the model parameters, and repeat this step; S1.3: Restore the output 1x512 vector to conductivity distribution and perform smoothing; S2, constructing a generative adversarial network model, inputting the preliminary conductivity distribution image into the generative adversarial network model for training, and obtaining a generator for image enhancement; the generative adversarial network model at least includes a generator and a discriminator, and the function L GAN (G, D) = E x [logD(x)]+E x [log(1-D(G(z)))], where D is maximized as logD(x), G is minimized as log(1-D(G(z))), x is the label image, and z is random noise; The generator output G(z) is a candidate image with a probability distribution of x, which is mapped from a previous distribution of z; The discriminator outputs D(x) or D(G(z)) for scalar scoring of the proximity of the input; S3. Input the preliminary conductivity distribution image into the generator to obtain a high-precision target conductivity distribution map.

2. The GAN enhanced magnetic induction imaging method based on complex-valued convolution according to claim 1, characterized in that: The specific process of collecting voltage sequence data described in step S1 is: positioning the target object by a stepper motor, collecting initial data, eliminating interference data, and obtaining the voltage sequence data.

3. The GAN enhanced magnetic induction imaging method based on complex-valued convolution according to claim 1, characterized in that: The smoothing process in step S1.3 is to average the value of each triangular area with the value of the adjacent triangular area to obtain smooth data; The formula for the smoothing process is: Where m is the number of surrounding triangle elements, σ i is the conductivity value.

4. The GAN enhanced magnetic induction imaging method based on complex-valued convolution according to claim 1, characterized in that: Step S2: inputting the preliminary conductivity distribution image into the adversarial generative network model for training comprises: S2.1: training the generator; S2.2: training the discriminator; S2.3: Steps S2.1-S2.2 are performed alternately until the adversarial generative network model is stable.

5. The GAN enhanced magnetic induction imaging method based on complex-valued convolution according to claim 1, characterized in that: The S3 further includes performing a quality assessment on the high-precision target conductivity distribution map, wherein the quality assessment is performed by converting the high-precision target conductivity distribution map into a binary map and measuring the quality according to the intersection-over-union ratio and the centroid distance; The formula of the intersection-over-union ratio is: Among them, R obj To reconstruct the object in the image, G obj For objects in the labeled image, when IoU is equal to 1, it means that the reconstructed image is consistent with the labeled image; The formula for the centroid distance is: Among them, x* and y* are the x-axis and y-axis coordinates of the annotated image, and x and y are calculated by the following formula:

6. A system for implementing the GAN enhanced magnetic induction imaging method based on complex-valued convolution according to any one of claims 1 to 5, characterized in that: include: Data processing module, complex value training module, image enhancement module, output module; The data processing module is connected to the image enhancement module through the complex value training module, and is used to collect voltage sequence data; The complex-valued training module is connected to the output module through the image enhancement module, and is used to input the voltage sequence data into a complex-valued neural network model for training; The image enhancement module is used to input the preliminary conductivity distribution image into the adversarial generative network model for training to obtain a generator for image enhancement; The output module is used to input the voltage sequence data into the complex-valued neural network model to obtain the preliminary conductivity distribution image, and then input the preliminary conductivity distribution image into the generator for image enhancement to obtain the high-precision target conductivity distribution map.

Images