CN115670421A - Electrical impedance depth imaging method based on denoising autoencoder - Google Patents
Electrical impedance depth imaging method based on denoising autoencoder Download PDFInfo
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Abstract
The invention discloses an electrical impedance depth imaging method based on a denoising self-encoder, which combines a traditional method and a denoising self-encoder. Firstly, numerical simulation is carried out on the two-dimensional circular-domain electrical impedance imaging problem by adopting a finite element method, and an impedance distribution image of a two-dimensional circular domain and a boundary voltage of the circular domain are obtained. Then, a coarse image was obtained using the Split Bregman Method (SBM) algorithm. And finally, training the denoising self-encoder network by taking the rough imaging as input and the real impedance distribution image as output. The denoised self-encoder network may be used for electrical impedance imaging. Simulation and actual measurement results show that aiming at a circular target, the provided method can remove artifacts with higher precision and realize accurate shape reconstruction.
Description
Technical Field
The invention belongs to the technical field of electrical impedance imaging, and particularly relates to an electrical impedance depth imaging method based on a denoising autoencoder.
Background
Electrical Impedance Tomography (EIT) technology is a new generation of non-invasive medical imaging technology that has emerged over the last two decades. The EIT technology injects alternating signal current into an object through electrodes arranged on the surface of the object to be measured, measures voltage values on other electrodes at the same time, and obtains electrical impedance distribution in the object to be measured through a certain reconstruction algorithm by using obtained voltage information so as to obtain an impedance image. The inverse problem is a highly ill-posed ill-conditioned non-linearity problem and the resulting reconstructed image artifacts are large.
Several EIT image reconstruction algorithms have been developed, including The Back-Projection Algorithm (BP), the Gaussian-Newton Algorithm (GN), the iterative Tikhonov Algorithm, and so on. The traditional method has the disadvantages of small calculated amount, low configuration requirement on a computer and poor imaging effect. Modern methods are represented by deep learning, such as: the method is characterized by comprising a simulated annealing algorithm (SA), a Convolutional Neural Network (CNN), a U2-Net and the like, and is characterized by large calculation amount, high requirement on computer configuration and good imaging effect.
The denoise auto-encoder (DAE) is an auto-encoder which takes damaged data as input and takes non-damaged data as output, and is essentially a process of abstracting features layer by layer, and features do not need to be labeled for training data, so that a great deal of time and energy can be saved.
Disclosure of Invention
The invention aims to provide an electrical impedance depth imaging method based on a denoising autoencoder, and aims to solve the problems of poor imaging effect, large calculation amount and high requirement on computer configuration in the prior art. In order to obtain a clearer reconstructed image, a depth imaging method combining a traditional method and a denoising self-encoder is provided.
The invention adopts the following technical scheme for solving the technical problems: an electrical impedance depth imaging method based on a denoising autoencoder comprises the steps of firstly, carrying out numerical simulation on a two-dimensional circular-domain electrical impedance imaging problem by adopting a finite element method to obtain an impedance distribution image of a two-dimensional circular domain and a boundary voltage of the circular domain; then, a coarse image is obtained using the Split Bregman Method (SBM) algorithm; and finally, taking the rough imaging as input and the real impedance distribution image as output, and training the denoising self-encoder network. The method specifically comprises the following steps:
s1, taking a triangle as a partitioning unit for a background area, partitioning by using a finite element, simulating and generating simulated circular target objects with different radiuses in the background area, and setting impedance distribution data of the target objects;
s2, obtaining an impedance distribution image of a two-dimensional circular domain and a boundary voltage of the circular domain by using a finite element method according to the impedance distribution data obtained in the S1; obtaining a coarse image by using an SBM algorithm through the boundary voltage value;
s3, taking the rough image obtained in the S2 as input and the real impedance distribution image as output, training the denoising encoder, and continuously debugging all parameters of the denoising encoder until an optimal trained denoising encoder is obtained;
and S4, using the boundary voltage value of the object to be measured to be solved as input data, obtaining a coarse image by using an SBM algorithm, and inputting the coarse image into the denoising encoder trained in the S3 to obtain an impedance imaging graph of the object to be measured.
Further, in step S2, a coefficient matrix of each triangulation unit is obtained according to the impedance distribution data of the target object and the model data of the finite element, and then an overall coefficient matrix is obtained;
applying boundary conditions to obtain a finite element equation, and solving the finite element equation to finally obtain a boundary voltage value; the model data of the finite element refers to a grid on the image, and the boundary condition is an excitation current.
Further, in step S3, the training process of the denoising autoencoder includes encoding and decoding;
defining pixel values of a picture of a simulated object after noise is added into the picture by using an SBM algorithm as noisy data
Will take the data of making a noise
Encoding process f by an autoencoder θ Mapping to a low-dimensional hidden feature space y, decoding process g θ′ Decoding y to obtain pixel data z of the noise-free picture;
the encoding process is represented as:
the decoding process is represented as: z = g θ′ (y)＝s(w 2 y+b 2 ) (ii) a Wherein f is θ And g θ′ For a non-linear activation function, s (×) is the codec function; w is a 1 And w 2 Is a weight matrix, b 1 And b 2 Is a deviation vector, θ is { w 1 ,b 1 Is parameterized by θ' is w 2 ,b 2 Parameterization of { right before } a;
and minimizing the reconstruction error by using a back propagation algorithm during training, wherein an error function is expressed as:
wherein x represents the pixel value of the original picture of the simulation object; the debugging parameters in the training process comprise a learning rate, an excitation function and an error function L H And (x, z) obtaining the optimal parameters when the (x, z) is minimum, stopping training, and obtaining the denoising self-encoder network model with the minimum target function error.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
the electrical impedance depth imaging method based on the denoising autoencoder provided by the invention uses simulation data for training, and has good adaptability to measured data. The method combines the traditional method with the denoising self-encoder, and has the advantages of small calculated amount, low configuration requirement on a computer and good imaging effect.
The denoising encoder belongs to unsupervised feature learning, namely, features do not need to be labeled for training data, and a large amount of time and energy can be saved. Also, the input data passed through the encoder can create a compressed representation, which is the intermediate layer, after which the original input can be reconstructed by the decoder, making the calculation simpler.
The trained denoising encoder can effectively remove the artifacts in the background area, so that the imaged background area is more uniform, and the target object is clearer. Compared with the traditional algorithm, the method has stronger popularization capability and higher operation speed.
Drawings
FIG. 1 is a schematic flow diagram of an embodiment of the present invention;
FIG. 2 is a process of denoised self-encoder training in an embodiment of the invention;
FIG. 3 is a real image of agar as a test object in the example of the present invention;
FIG. 4 is an agar image generated by the method of the present invention.
Detailed Description
In order to make the purpose, technical effect and technical solution of the embodiments of the present invention clearer, the following describes the technical solution of the embodiments of the present invention clearly and completely with reference to the drawings in the embodiments of the present invention; it is to be understood that the described embodiments are only some of the embodiments of the present invention. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
The embodiment of the invention provides an electrical impedance depth imaging method based on a denoising self-encoder. And obtaining coarse imaging by using an SBM algorithm through the boundary voltage value, and respectively taking the coarse imaging and the real impedance distribution image as the input and the output of a denoising coder (DAE) to obtain a training data set of the denoising coder. And then, training the denoising encoder through a training data set, and continuously debugging each parameter of the denoising encoder until the optimal trained denoising encoder is obtained. And finally, taking the boundary voltage value of the object to be measured to be solved as input data, obtaining a coarse image by using an SBM algorithm, and inputting the coarse image into a trained denoising encoder to obtain an impedance imaging graph of the object to be measured. As shown in fig. 1, the method specifically comprises the following steps:
s1, a triangle is used as a subdivision unit for a background area, a finite element subdivision is used, simulated circular target objects with different radiuses are generated in a simulation mode in the background area, and impedance distribution data of the target objects are set.
Specifically, the number i of generated objects is randomly selected, i is 1-3, namely i points are randomly selected in a background area divided by finite elements, and then the circular target to be generated is sequentially selected. The diameter of the round target is set to be 4-8.
S2, obtaining an impedance distribution image of a two-dimensional circular domain and a boundary voltage of the circular domain by using a finite element method according to the impedance distribution data obtained in the S1; from the boundary voltage values, a coarse imaging is obtained using the SBM algorithm.
Specifically, impedance values are assigned to a unit where the object is located and a background unit respectively, impedance distribution of the target object is obtained, and then the finite element method is used for calculating and solving the EIT problem. The mathematical model of the EIT field is a partial differential equation.
The finite element method is characterized in that a problem to be solved is discretized, unit analysis is carried out, results of the unit analysis are combined to carry out comprehensive analysis on the whole, and the method specifically comprises the following steps: and selecting a limited point in the field domain, and substituting a finite difference equation for a partial differential equation in the EIT problem approximately to obtain the value of the field function at each discrete point.
The variational principle is the basis of finite element method, and the partial differential equation to be solved is converted into the corresponding variational problem, then the interpolation polynomial is introduced, and the variational problem is discretized into the problem of solving the extreme value by the ordinary multivariate function, and finally the problem is arranged into the problem of solving the multivariate function equation set. The boundary voltage value of the target object is determined.
Specifically, 16 electrode plates are sequentially pasted on a two-dimensional circle boundary at equal intervals, the conductivity of a background region is set to be 0.1S/m, the conductivity of a target region is set to be 0.01S/m, the EIDORS software package based on MATLAB is adopted for calculation, and an adjacent excitation-adjacent measurement mode is adopted, so that 208 (16 multiplied by 13) voltage values of the circle boundary are obtained.
Specifically, a coarse imaging picture is obtained and grayed by using an SBM algorithm through the boundary voltage value. In order to improve the resolution after imaging, the pixel value of each picture is then extracted, and each group of samples is made up of 10000 pixels.
And S3, taking the rough image obtained in the S2 as input and the real impedance distribution image as output, training the denoising encoder, and continuously debugging all parameters of the denoising encoder until an optimal trained denoising encoder is obtained, wherein the training process is shown in FIG. 2.
Specifically, the training process of the denoising autoencoder comprises encoding and decoding; defining pixel values of a picture of a simulated object after noise is added into the picture by using an SBM algorithm as noisy data
Will take the data of making a noise
Encoding process f by an auto-encoder θ Mapping to Low-dimensional hidden feature space y, decoding Process g θ′ And decoding the y to obtain pixel data z of the noise-free picture.
The encoding process is represented as:
the decoding process is represented as: z = g θ′ (y)＝s(w 2 y+b 2 ) (ii) a Wherein f is θ And g θ′ For a non-linear activation function, s (×) is the codec function; w is a 1 And w 2 Is a weight matrix, b 1 And b 2 Is a deviation vector, θ is { w 1 ,b 1 Is parameterized by θ' is w 2 ,b 2 Parameterization of.
And minimizing the reconstruction error by using a back propagation algorithm during training, wherein an error function is expressed as:
where x represents the pixel value of the original picture of the simulated object. Using training data to adjust individual parameters, e.g. learning rate, excitation function, error function L H And (x, z) obtaining the optimal parameters when the (x, z) is minimum, stopping training, and obtaining the denoising self-encoder network model with the minimum target function error.
Specifically, the DAE model learning rate is set to 0.001; the input and output numerical values are the same and are both the pixel value 10000 of the picture; the encoding excitation function is relu, and the decoding excitation function is sigmoid; the Adam (Adaptive motion optimization) optimizer is a combination of SGDM and RMSProp. Run 100epochs with a batch size of 128.
And S4, using the boundary voltage value of the object to be measured (such as the lung of an agar simulator) to be solved as input data, obtaining a coarse image by using an SBM algorithm, and inputting the coarse image into the denoising encoder trained in the S3 to obtain an impedance imaging image of the object to be measured. Fig. 3 is a real image of agar and fig. 4 is an image of agar generated according to the method of the present invention.
It should be noted that the above description of the embodiments is only for the purpose of assisting understanding of the method of the present application and the core idea thereof, and that those skilled in the art can make several improvements and modifications to the present application without departing from the principle of the present application, and these improvements and modifications are also within the protection scope of the claims of the present application.
Claims (3)
1. An electrical impedance depth imaging method based on a denoising autoencoder is characterized by comprising the following steps:
s1, taking a triangle as a subdivision unit for a background area, using a finite element to subdivide, simulating and generating simulated circular target objects with different radiuses in the background area, and setting impedance distribution data of the target objects;
s2, obtaining an impedance distribution image of a two-dimensional circular domain and a boundary voltage of the circular domain by using a finite element method according to the impedance distribution data obtained in the S1; obtaining coarse imaging by using an SBM algorithm through the boundary voltage value;
s3, taking the rough image obtained in the S2 as input and the real impedance distribution image as output, training the denoising encoder, and continuously debugging all parameters of the denoising encoder until an optimal trained denoising encoder is obtained;
and S4, using the boundary voltage value of the object to be measured to be solved as input data, obtaining a coarse image by using an SBM algorithm, and inputting the coarse image into the denoising encoder trained in the S3 to obtain an impedance imaging graph of the object to be measured.
2. The electrical impedance depth imaging method based on the denoising self-encoder as claimed in claim 1, wherein in step S2, the coefficient matrix of each triangulation unit is obtained according to the impedance distribution data of the target object and the model data of the finite element, and further the overall coefficient matrix is obtained;
applying boundary conditions to obtain a finite element equation, and solving the finite element equation to finally obtain a boundary voltage value; the model data of the finite element refers to a grid on the image, and the boundary condition is an excitation current.
3. The electrical impedance depth imaging method based on the denoising self-encoder as claimed in claim 1 or 2, wherein in step S3, the training process of the denoising self-encoder comprises encoding and decoding;
defining pixel values of a picture of a simulated object after noise is added into the picture by using an SBM algorithm as noisy data
Will take the data of making a noise
Encoding process f by an autoencoder θ Mapping to a low-dimensional hidden feature space y, decoding process g θ′ Decoding y to obtain pixel data z of the noise-free picture;
the encoding process is represented as:
the decoding process is represented as: z = g θ′ (y)＝s(w 2 y+b 2 ) (ii) a Wherein f is θ And g θ′ For a non-linear activation function, s (×) is the codec function; w is a 1 And w 2 Is a weight matrix, b 1 And b 2 Is a deviation vector, θ is { w 1 ,b 1 Is parameterized by θ' is w 2 ,b 2 Parameterization of { right before } a;
and minimizing the reconstruction error by using a back propagation algorithm during training, wherein an error function is expressed as:
wherein x represents the pixel value of the original picture of the simulation object; the debugging parameters in the training process comprise a learning rate, an excitation function and an error function L H And (x, z) obtaining the optimal parameters when the (x, z) is minimum, stopping training, and obtaining the denoising self-encoder network model with the minimum target function error.
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| CN117011673B (en) * | 2023-10-07 | 2024-03-26 | 之江实验室 | Electrical impedance tomography image reconstruction method and device based on noise diffusion learning |
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