A method for magnetic resonance powerline harmonic noise suppression based on deep residual network

Abstract

The present application relates to the field of magnetic resonance signal processing, and is a kind of magnetic resonance power harmonic noise suppression method based on deep residual network. First, the noise signal mixed with power harmonic noise and the power harmonic noise are used as the input and output of the deep residual network, the error is calculated by forward propagation and back propagation, and the identity mapping is established by introducing the residual block. The loss function is reduced to the expected value by repeated training, and the denoising model is determined. The noise is extracted by the model and subtracted from the noisy signal to obtain the signal without power noise. Compared with the traditional method, the trained model is used for prediction, and the network parameters do not need to be adjusted. Compared with the convolution network, the residual network solves the degradation problem at high depth, has higher accuracy, better model effect and more power saving.

Description

Technical Field

[0001] This invention belongs to the field of magnetic resonance sounding (MRS) signal noise suppression methods, and in particular to a method for suppressing power frequency harmonic noise in magnetic resonance groundwater detection based on deep residual network (DRN). Background Technology

[0002] Nuclear magnetic resonance (NMR) technology is currently the only direct geophysical method for groundwater detection. Compared with traditional geophysical detection methods, it has advantages such as high resolution, high efficiency, rich information content, and unique solutions. The quality of the NMR signal is crucial to the detection results. The accuracy of signal parameter estimation depends on the electromagnetic noise level at the measurement site. Because the amplitude of the NMR signal received by the receiving coil is extremely small, only in the nV range, environmental noise is sufficient to overwhelm it. The two types of noise that most seriously affect signal quality are power frequency harmonic noise and spike noise. Power frequency and its harmonic noise originate from power lines, generators, and transformers, with frequencies fixed at integer multiples of 50Hz or 60Hz. Power frequency harmonic noise has the most serious impact on the received signal, and power frequency interference near the Larmor frequency is particularly prominent. The presence of power frequency harmonics can cause the signal conditioning module in the receiving device to reach saturation prematurely, affecting the subsequent data inversion effect and thus reducing the accuracy of the NMR detection results.

[0003] Legchenko, A et al., in their paper "Removal of power-line harmonics from proton magnetic resonance measurements" published in the Journal of Applied Geophyics [2003, 53(2-3), 103-120], conducted research on power-line harmonic noise reduction based on NUMIS, using data processing methods such as block cancellation to eliminate power-line harmonic interference. Larsen, J et al., in their paper "Noise cancelling of MRS signals combining model-based removal of powerline harmonics and multichannel Wiener filtering" published in Geophysical Journal International [2014, 196(2), 828-836], proposed a method for power-line harmonic noise suppression based on a combination of power-line harmonic modeling and multichannel Wiener filtering. In her paper "Research on Power-line Harmonic Noise Reduction and Full-wave Signal Extraction Method of Ground Magnetic Resonance" published in December 2022, Li Yue proposed a new method for power-line harmonic noise processing, proposing a frequency-domain symmetric algorithm to address the problem of severe and densely distributed power-line harmonic noise interference. By utilizing the imaginary part spectrum generated from power frequency harmonic noise through Fourier transform and demodulation processes, the real part spectrum superimposed on the MRS signal is estimated, thereby eliminating noise. Patent CN111860273A discloses a "Noise Suppression Method for Magnetic Resonance Groundwater Detection Based on Convolutional Neural Networks," which utilizes the learning ability of convolutional neural networks, using simulated training datasets to optimize model parameters. Once the model is trained, it can be used for denoising measured data.

[0004] The traditional methods described above require manual adjustment of filtering parameters, which is inconvenient for non-technical personnel. While convolutional neural network-based noise reduction methods are generally applicable, their effectiveness in filtering power frequency noise is limited, and they fail to achieve the desired results in environments with strong power frequency noise. Summary of the Invention

[0005] The technical problem this invention aims to solve is to provide a method for suppressing power frequency harmonic noise in magnetic resonance imaging (MRI) based on deep residual networks. This method utilizes the learning ability of deep residual networks to train a well-established model for eliminating power frequency harmonic noise. When an MRS signal containing power frequency harmonic noise is input into the model, the model automatically extracts and eliminates the noise. Compared with traditional methods, this invention allows for very short prediction times using the trained model and eliminates the need for network parameter adjustments.

[0006] This invention is implemented as follows:

[0007] A method for suppressing power frequency harmonic noise in magnetic resonance based on deep residual networks, the method comprising:

[0008] Dataset formation: Establish a magnetic resonance signal dataset X(n) collected by a simulated magnetic resonance groundwater detector, add power frequency and its harmonic noise N(n) of various frequencies to obtain a magnetic resonance signal Y(n) containing power frequency harmonic noise, forming a training dataset, where the length of each signal is N, and the number of signals in each dataset is M;

[0009] Network construction: Design the structure of the residual network, determine the network depth and residual block types, and initialize the network parameters;

[0010] Training the model: Input the training dataset, calculate the error during forward propagation, update the network parameters using gradient descent during back propagation, and establish the mapping relationship between the noisy signal and the noise using the residual learning mechanism, so that the loss function is gradually optimized to the minimum;

[0011] Test model: Construct a test dataset based on actual measurement data, and use the trained model for noise reduction.

[0012] Furthermore, the residual network includes:

[0013] Convolution operations are used to extract features from the input data. The first layer of convolution operations adjusts the size of the input noisy signal for pooling.

[0014] Pooling layers are used to extract feature information from data and filter out redundant information.

[0015] Residual blocks are used to prevent neural network degradation in deep networks, enabling the network to achieve higher accuracy as the depth increases.

[0016] A fully connected layer is placed at the end of the residual network to make the output the same size as the input.

[0017] Furthermore, the specific steps for constructing the residual network are as follows: Step a: Select the type of residual block, determine the number of layers L, the number of residual blocks n, and the type and parameters of each hidden layer in the residual network structure, and define the kernel size K, padding size P, and stride S;

[0018] Step b: Initialize the network parameters θ = {W, b}, learning rate β, and stopping iteration threshold ε, where W and b represent the linear relationship coefficient matrix and bias vector between the hidden layer and the output layer within each residual block, respectively.

[0019] Furthermore, the specific steps for training the model include:

[0020] Using the magnetic resonance signal Y(n) containing power frequency harmonic noise as the input of the residual network and the power frequency harmonic noise N(n) as the output of the residual network, a residual network model with power frequency harmonic noise removed is constructed:

[0021] x = y - RN(y; θ)

[0022] Wherein, RN represents the constructed residual network, and θ={W,b} are the network parameters. The network parameters will be continuously updated during back propagation. The simulated nuclear magnetic resonance signal Y(n) containing power frequency harmonic noise is input into the residual network. The noisy magnetic resonance signal data y is output as power frequency harmonic noise data RN(y;θ) through the network forward propagation algorithm. Subtracting the noise data RN(y;θ) from y yields the clean signal x.

[0023] The forward propagation algorithm uses noisy data as input to the residual network, introducing residual blocks. Each residual block consists of multiple convolutional layers plus an identity mapping. Let F be the residual function, h be the identity mapping, and x... n For the input of the nth residual block, y n W is the output of the nth residual block. n Let be the internal relation matrix of the nth residual block, then we have:

[0024] x n+1 =y n =h(x n )+F(x n W n );

[0025] Let the input tensor of a single convolutional layer be a, and the corresponding internal coefficient matrix be W. l The bias vector is b l Then the input tensor, internal coefficient matrix, and bias vector of the Lth layer of the convolutional layer are respectively a L W l L and The input tensor of the (L+1)th layer network is obtained after convolution and activation operations:

[0026]

[0027] Here, ReLU(x) = max(0,x) represents the activation function, and * represents the convolution operation. Within a single convolutional layer, the convolution operation and the activation operation are batch normalized using the BN algorithm to accelerate network training.

[0028] Furthermore, the residual block has two layers, if a L Let a be the input tensor of the nth two-layer residual block. L =x n According to the residual block structure, we have

[0029]

[0030] F(x n W n )=x n+1 =a L+2

[0031] Forward propagation is performed on a residual block basis:

[0032]

[0033]

[0034] Establish loss function The smaller J(θ) is, the closer the predicted noise output is to the actual noise.

[0035] Perform backpropagation algorithm: Introduce residual δ into the residual network, and use the loss function J(θ) to calculate the residual of the nth residual block:

[0036]

[0037] Then we get

[0038]

[0039] Where b n For the bias vector corresponding to the nth residual block, update the network parameters using gradient descent:

[0040] (W k )'←W k -β·x k δ k+1

[0041] (b k )'←b k -β·δ k+1 k = 1, 2, ..., n-1, θ = {W, b}, β is the learning rate;

[0042] When the linear relationship coefficient matrix W and the bias vector b between each hidden layer and the output layer are less than the threshold ε for stopping updates, the gradient descent method is stopped and W and b are output, where W and b represent the linear relationship coefficient matrix and bias vector between the hidden layer and the output layer within each residual block, respectively.

[0043] Furthermore, the specific steps for constructing the training dataset are as follows:

[0044] Step a: Construct a simulated magnetic resonance signal using MATLAB, expressed as follows: Where t is time, E0 is the initial amplitude, and T2 is the initial amplitude.* It is the relaxation time, f L It is the Lamour frequency. Given the initial phase, we obtain X1(n). Repeating this process m times yields a dataset of NMR signals with M signals and a data length of N, X(n) = [X0(n), X1(n), X2(n), ..., X...]. M-1 (n)];

[0045] Step b: Use MATLAB to construct a simulated power frequency harmonic signal, the expression of which is: Where k is the order of the power frequency harmonic, f N This is the fundamental frequency, which is 50±0.1 or 60±0.1 Hz, E k and The initial amplitude and phase of the k-th harmonic are given. Changing the harmonic order k allows for the creation of power frequency harmonic noise of different frequencies and amplitudes. N(n) = [N0(n), N1(n), N2(n), ..., N...]. M-1 [(n)], the number of signals is M, and the length of the collected data is N;

[0046] Step c: Based on Y(n)=X(n)+N(n), construct multiple sets of nuclear magnetic resonance signal datasets X(n) and power frequency harmonic noise signals N(n) by changing the initial amplitude, initial phase and harmonic order, and obtain the noisy magnetic resonance signal Y(n).

[0047] Compared with existing technologies, the advantages of this invention are as follows: After model training, this invention can directly eliminate power frequency harmonic noise without adjusting filter parameters, and it also has a good denoising effect on untrained power frequency harmonic noise. Compared with traditional denoising methods that rely on manual experience and have low processing efficiency, this invention greatly improves the efficiency of eliminating power frequency harmonic noise, effectively eliminating power frequency harmonic noise in magnetic resonance signals and achieving ideal denoising results. This invention can effectively suppress interference caused by power frequency harmonic noise, and has better anti-interference ability than traditional denoising methods, improving reliability and ensuring that the magnetic resonance groundwater detection method can be used in environments with strong power frequency harmonic noise interference. Furthermore, compared with convolutional neural networks, this invention introduces residual blocks, effectively avoiding the degradation problem of neural networks and achieving higher accuracy against power frequency noise. Attached Figure Description

[0048] Figure 1 The flowchart shows a magnetic resonance power frequency harmonic noise suppression method based on deep residual networks.

[0049] Figure 2 This is a diagram of the deep residual network structure.

[0050] Figure 3This is a diagram of the two-layer residual block structure used in deep residual networks. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0052] See Figure 1 As shown, a magnetic resonance power frequency harmonic noise suppression method based on deep residual networks includes the following steps:

[0053] a. Forming a dataset: Establish a dataset X(n) of magnetic resonance signals collected by a simulated magnetic resonance groundwater detector, add power frequency and harmonic noise of various frequencies N(n) to obtain magnetic resonance signals Y(n) containing power frequency harmonic noise, forming a training dataset, where the length of each signal is N, and the number of signals in each dataset is M.

[0054] b. Building a network: such as Figure 2 The deep residual network structure shown is used to determine the network depth and residual block types, and the network parameters are initialized.

[0055] c. Training the model: Input the training dataset, calculate the error during forward propagation, update the network parameters using gradient descent during back propagation, and establish the mapping relationship between the noisy signal and the noise using the residual learning mechanism, so that the loss function is gradually optimized to the minimum.

[0056] d. Test model: Construct a test dataset based on actual measurement data and use the trained model for noise reduction.

[0057] The basic steps for forming the dataset in step a are as follows:

[0058] Step a1: Constructing a simulated magnetic resonance signal Where t = (0:N-1) / fs, fs is the sampling rate, N = 2000, and E0 ∈ (10, 4000)nV. f L ∈(1300,3700)Hz, Obtain X0(n), repeat 1000 times, and obtain a nuclear magnetic resonance signal dataset X(n) = [X0(n), X1(n), X2(n), ..., X...] with M = 1000 signals and N = 2000 data points. 999 (n)];

[0059] Step a2: Construct the simulated power frequency harmonic signal, whose expression is: Where t0 = (0:N-1) / fs, fs is the sampling rate, N = 2000, and the signal is the superposition of the 45th and 47th harmonics of power frequency noise, with its frequency just near the Larmor frequency. The initial amplitude of the 45th harmonic is 50 nV, and the initial phase is... The initial amplitude of the 47th harmonic is 40 nV, and the initial phase is... Repeating this process 1000 times yields a power frequency harmonic noise signal dataset N(n) = [N0(n), N1(n), N2(n), ..., N...]. The dataset consists of M = 1000 signals and N = 2000 data points. 999 (n)].

[0060] Step a3: Based on Y(n)=X(n)+N(n), construct multiple sets of nuclear magnetic resonance signal datasets X(n) and power frequency harmonic noise signals N(n) by changing parameters such as initial amplitude, initial phase, and harmonic order, and obtain the noisy magnetic resonance signal Y(n).

[0061] The specific steps for constructing the residual network in step b are as follows:

[0062] Step b1: Select Figure 3 The double-layer residual block shown determines the number of layers L of the residual network structure and the type and parameters of each hidden layer, and defines the kernel size K, padding size P, and stride S.

[0063] Step b2: Initialize network parameters θ = {W, b}, learning rate β = 0.05, and stopping iteration threshold ε = 50 nV.

[0064] The specific steps for training the model in step c are as follows:

[0065] Step c1: Using the magnetic resonance signal Y(n) containing power frequency harmonic noise as the input of the residual network and the power frequency harmonic noise N(n) as the output of the residual network, construct a residual network model with power frequency harmonic noise removed.

[0066] x = y - RN(y; θ)

[0067] Where RN represents the constructed residual network, and θ = {W, b} are the network parameters.

[0068] A forward propagation algorithm is used, with the noisy data as input to the residual network. Let F be the residual function, h be the identity mapping, and x... n For the input of the nth residual block, y n W is the output of the nth residual block. n Let be the internal relation matrix of the nth residual block, then we have

[0069] x n+1 =y n =h(xn )+F(x n W n );

[0070] Forward propagation is performed on a residual block basis:

[0071]

[0072] Step c2: Establish the loss function The smaller J(θ) is, the closer the predicted noise output is to the actual noise.

[0073] Step c3: Perform backpropagation algorithm: Update network parameters using gradient descent.

[0074] (W k )'←W k -β·x k δ k+1

[0075] (b k )'←b k -β·δ k+1 k = 1, 2, ..., n-1, θ = {W, b}, β is the learning rate;

[0076] When the linear relationship coefficient matrix W and the bias vector b between each hidden layer and the output layer are less than the threshold ε for stopping updates, the gradient descent method is stopped and W and b are output.

[0077] The specific implementation process of step d is as follows:

[0078] Data set Y was obtained by collecting actual data at a certain MRS detection point. test (n), the Larmor frequency at this location should be similar to the Larmor frequency used during network training. Y test (n) is input into the trained residual network RN(y; θ) to obtain the predicted power frequency harmonic noise output as N. test (n), using Y test (n)-N test (n)=X test (n), to obtain the signal X after eliminating power frequency harmonic noise. test (n).

Claims

1. A method for suppressing power frequency harmonic noise in magnetic resonance based on deep residual networks, characterized in that, The method includes: Dataset formation: Establish a magnetic resonance signal dataset X(n) collected by a simulated magnetic resonance groundwater detector, add power frequency and its harmonic noise N(n) of various frequencies to obtain a magnetic resonance signal Y(n) containing power frequency harmonic noise, forming a training dataset, where the length of each signal is N, and the number of signals in each dataset is M; Network construction: Design the structure of the residual network, determine the network depth and residual block types, and initialize the network parameters; Training the model involves inputting a training dataset, calculating the error during forward propagation, updating the network parameters using gradient descent during backpropagation, and establishing a mapping relationship between the noisy signal and noise using a residual learning mechanism to gradually optimize the loss function to its minimum. The specific steps for training the model include: Using the magnetic resonance signal Y(n) containing power frequency harmonic noise as the input of the residual network and the power frequency harmonic noise N(n) as the output of the residual network, a residual network model with power frequency harmonic noise removed is constructed: ， Wherein, RN represents the constructed residual network. The network parameters are continuously updated during backpropagation. The simulated nuclear magnetic resonance signal Y(n) containing power frequency harmonic noise is input into the residual network, and the noisy magnetic resonance signal data y is output as power frequency harmonic noise data through the network's forward propagation algorithm. ,Will Subtract noise data Get a clean signal ; The forward propagation algorithm uses noisy data as input to the residual network, introducing residual blocks. Each residual block consists of multiple convolutional layers plus an identity mapping. Let F be the residual function and h be the identity mapping. This is the input for the nth residual block. This is the output of the nth residual block. Let be the internal relation matrix of the nth residual block, then we have: ； Let the input tensor of a single convolutional layer be a, and the corresponding internal coefficient matrix be W. l The bias vector is b l Then the input tensor, internal coefficient matrix, and bias vector of the Lth layer of the convolutional layer are respectively , and After convolution and activation operations, the input tensor of the (L+1)th layer network is obtained: ， in, The symbol represents the activation function, and * represents the convolution operation. Within a single convolutional layer, the convolution operation and the activation operation are batch normalized using the BN algorithm to accelerate network training. The residual block has two layers. Let be the input tensor of the nth two-layer residual block. According to the residual block structure, we have ， ， Forward propagation is performed on a residual block basis: ， ， ， Establish loss function ,J( The smaller the value, the closer the predicted noise output is to the actual noise. Perform backpropagation algorithm: Introduce residuals into the residual network Using the loss function J( Calculate the residual of the nth residual block: ， Then we get: ， ， in For the bias vector corresponding to the nth residual block, update the network parameters using gradient descent: ， , =1,2,...,n-1, β is the learning rate; When the linear relationship coefficient matrix W and the bias vector b between each hidden layer and the output layer are less than the threshold ε for stopping updates, the gradient descent method is stopped and W and b are output, where W and b represent the linear relationship coefficient matrix and bias vector between the hidden layer and the output layer within each residual block, respectively. Test model: Construct a test dataset based on actual measurement data, and use the trained model for noise reduction.

2. The method according to claim 1, characterized in that, Residual networks include: Convolution operations are used to extract features from the input data. The first layer of convolution operations adjusts the size of the input noisy signal for pooling. Pooling layers are used to extract feature information from data and filter out redundant information. Residual blocks are used to prevent neural network degradation in deep networks, enabling the network to achieve higher accuracy as the depth increases. A fully connected layer is placed at the end of the residual network to make the output the same size as the input.

3. The method according to claim 2, characterized in that, The specific steps for constructing a residual network are as follows: Step a: Select the type of residual block, determine the number of layers L, the number of residual blocks n, and the type and parameters of each hidden layer in the residual network structure, and define the kernel size K, padding size P, and stride S; Step b: Initialize network parameters The learning rate β and the stopping iteration threshold ε are given, where W and b represent the linear relationship coefficient matrix and bias vector between the hidden layer and the output layer within each residual block, respectively.

4. The method according to claim 1, characterized in that, The specific steps for constructing the training dataset are as follows: Step a: Construct a simulated magnetic resonance signal using MATLAB, expressed as follows: Where t is time, E0 is the initial amplitude, and T2 is the amplitude. * It is the relaxation time, f L It is the Lamour frequency. The initial phase is X1(n). This is repeated m times to obtain a nuclear magnetic resonance signal dataset X(n) = [X0(n), X1(n), X2(n), ..., X...]. M-1 (n)]; Step b: Use MATLAB to construct a simulated power frequency harmonic signal, the expression of which is: Where k is the order of the power frequency harmonic, f N This is the fundamental frequency, which is 50±0.1 or 60±0.1 Hz. and The initial amplitude and phase of the k-th harmonic are given. Changing the harmonic order k allows for the creation of power frequency harmonic noise of different frequencies and amplitudes. N(n) = [N0(n), N1(n), N2(n), ..., N...]. M-1 [(n)], the number of signals is M, and the length of the collected data is N; Step c: Based on Y(n)=X(n)+N(n), construct multiple sets of nuclear magnetic resonance signal datasets X(n) and power frequency harmonic noise signals N(n) by changing the initial amplitude, initial phase and harmonic order, and obtain the noisy magnetic resonance signal Y(n).

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