A noise suppression method for terrestrial nuclear magnetic resonance signals based on generative adversarial networks

Abstract

The present invention discloses a ground nuclear magnetic resonance (NMR) signal noise suppression method based on a generative adversarial network, comprising: using a group of observed MRS signals X1(t) with known Larmor frequencies collected by a nuclear magnetic resonance sounder; performing Hilbert transform on the collected observed MRS signals X1(t) to transform the full-wave signal into a complex envelope signal X2(t); preprocessing the MRS complex envelope signal using a short-time Fourier transform method to convert the one-dimensional signal into two-dimensional time-frequency image information as input data for training a generative adversarial network; cropping a two-dimensional image of size 65×85, performing min-max normalization processing to achieve mapping of all data in the interval [0,1]; constructing a WGAN-GP generative adversarial network structure for MRS denoising to achieve removal of three different types of noise: random noise, power frequency harmonic noise, and spike noise; and performing an inverse short-time Fourier transform on the denoised data to restore the two-dimensional image information into an MRS complex envelope signal, thereby achieving noise removal and parameter extraction of the MRS signal.

Description

Technical Field

[0001] The present invention belongs to the field of Magnetic Resonance Sounding (MRS) signal noise filtering, and specifically is a ground nuclear magnetic resonance signal noise suppression method based on a generative adversarial network. Background Art

[0002] Magnetic resonance sounding (MRS) is a non-invasive method for groundwater resource detection. It can directly measure groundwater content, depth, and thickness by counting hydrogen protons, and has recently attracted widespread attention. However, because MRS signals are in the nanovolt range, they are highly sensitive to environmental noise, including spike noise, power frequency noise, and random noise. In the presence of interference, the extraction of characteristic parameters of the MR signal can produce significant errors, leading to unreliable inversion interpretation results. Therefore, eliminating noise from the acquired signal has become a core task in MR signal processing.

[0003] In response to the above problems, experts and scholars at home and abroad have carried out a lot of research work. Regarding the filtering of power frequency harmonics: Larsen et al. proposed a model-based harmonic noise removal method in the paper "Noise cancelling of MRS signals combining model-based removal of powerline harmonics and multichannel Wiener filtering" (Geophysical Journal International, Vol. 196, No. 2, 2014: pp. 828-836). This method determines the model parameters of the harmonic noise by least squares fitting, and then subtracts the modeled noise from the noisy signal, but the performance of this method depends on the noise distribution at the specific measurement location. Li Fan et al. proposed a frame denoising method based on frequency domain multi-channel Wiener filtering in the paper "Cancellation of varying harmonic noise in magnetic resonance sounding signals" (Journal of Applied Geophysics, Vol. 177, 2020), considering that the harmonic noise changes in the main coil and reference coil may be asynchronous, which further improved the noise reduction effect. However, when the Larmor frequency is close to the power frequency, this method may cause the NMR signal to be incorrectly filtered out.

[0004] Regarding random noise removal: In 2018, Lin Tingting et al. proposed a time-frequency peak filtering (STFPF) method for random noise suppression in the paper "Suppressing Random Noise in Full-Wave Magnetic Resonance Signals Using Segmented Time-Frequency Peak Filtering" (Chinese Journal of Geophysics, Vol. 61, No. 9, 2018, pp. 3812-3824). This method divides the full-wave MRI signal into several segments, encoding them as the instantaneous frequency of the analytical signal. By extracting the peaks of the time-frequency distribution, an unbiased estimate of the signal is obtained, achieving the goal of suppressing random noise in the full-wave MRI signal. However, the suppression effect is poor when the signal-to-noise ratio is very low. In 2021, Lin Tingting et al. proposed using improved short-time Fourier transform to suppress random noise in the paper "Magnetic resonance random noise reduction method based on improved short-time Fourier transform" ("Acta Physica Sinica", Vol. 70, No. 16, 2021: pp. 134-146). They used analytical signals to replace the real-valued signals in conventional short-time Fourier transform to obtain high-precision time-frequency distribution of MRS signals, and then extracted the time-frequency domain peak amplitude and peak phase to reconstruct the signal to eliminate random noise, achieving good results.

[0005] Regarding spike noise in MRS signals: In 2016, Wan Ling et al. proposed an energy calculation method in their paper "Energy-based spike noise suppression in magnetic resonance signals" (Chinese Journal of Geophysics, Vol. 59, No. 6, 2016: pp. 2290-2301). By calculating signal energy, this method effectively detects spike noise and highlights small, difficult-to-identify spikes. The method then uses a median-based absolute deviation method to determine a threshold and remove the spike noise. Compared to traditional statistical superposition methods, this method effectively detects and removes small spike noise that occurs during measurement. In the same year, to better eliminate spike noise in power grids, LARSEN proposed modeling spike noise as the unit impulse response of two cascaded second-order bandpass filters, then subtracting the noise from the noisy data to achieve noise filtering. However, this method still has the defects of overfitting and signal distortion.

[0006] CN107957566A discloses a "magnetic resonance sounding signal extraction method based on frequency-selective singular spectrum analysis". This method reconstructs the MRS signal by selecting the singular spectrum corresponding to the Larmor frequency of the MRS signal, and can effectively filter out random noise, spike noise and power frequency harmonic interference in the noisy signal; CN109828318A discloses a "magnetic resonance sounding signal noise filtering method based on variational mode decomposition", and proposes a "three-VMD" decomposition method for processing power frequency harmonic noise and random white noise in the magnetic resonance sounding signal; CN109885906A discloses a "magnetic resonance sounding signal sparse denoising method based on particle swarm optimization", and proposes to construct an oscillating atom library targeting the characteristics of MRS signals and power frequency harmonic noise, and use the particle swarm algorithm to reconstruct the signal to remove power frequency harmonic interference and random white noise in the magnetic resonance signal.

[0007] The above MRS noise removal methods have achieved good results under certain conditions, but they also have their own limitations. Due to the diversity of noise contained in MRS signals, it is difficult to use one method to simultaneously eliminate multiple complex noises in MRS signals. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide a method and system for suppressing noise in terrestrial nuclear magnetic resonance signals. Due to the diversity of noise contained in MRS signals and the limitations of existing algorithms, it is difficult to use one method to simultaneously eliminate multiple complex noises in MRS signals.

[0009] The present invention is achieved in this way:

[0010] A method for suppressing noise in terrestrial nuclear magnetic resonance signals based on a generative adversarial network, the method comprising the following steps:

[0011] Step 1: Observe the MRS signal X1(t) with known Larmor frequency collected by the nuclear magnetic resonance sounder;

[0012] Step 2: Perform Hilbert transform on the collected observation MRS signal X1(t) to transform the full-wave signal into the complex envelope signal X2(t);

[0013] Step 3: Use the short-time Fourier transform method to preprocess the MRS complex envelope signal and convert the one-dimensional signal into a two-dimensional time-frequency image information as the input data X3 for generative adversarial network training;

[0014] Step 4: Crop the data X2 to obtain a two-dimensional image X4 of size 65×85, and perform min-max normalization on the cropped data to map all data to the interval [0,1].

[0015] Step 5: Construct a WGAN-GP generative adversarial network structure for MRS denoising to remove three different types of noise: random noise, power frequency harmonic noise, and spike noise;

[0016] Step 6: Use short-time inverse Fourier transform on the noise-removed data to restore the two-dimensional image information to the MRS complex envelope signal to achieve noise removal and parameter extraction of the MRS signal.

[0017] Further,

[0018] In step 2, the collected observation MRS signal X1(t) is transformed into a complex envelope signal X2(t) by Hilbert transform. The specific steps are as follows:

[0019] The observed MRS signal X1(t) is analyzed as follows:

[0020]

[0021] Hilbert transform of the imaginary part X1(t) The MRS complex envelope signal is obtained from the analytical signal:

[0022]

[0023] f T represents the center frequency of X1(t). For MRS signal, f T That is the transmission frequency.

[0024] Further,

[0025] In step 3, the MRS complex envelope signal is preprocessed using the short-time Fourier transform method, which specifically includes:

[0026] The signal undergoes continuous short-time Fourier transform:

[0027]

[0028] s(t) is the time domain signal to be transformed, g(t) is the window function, * indicates taking the conjugate, and the one-dimensional signal is converted into two-dimensional image information through the short-time Fourier transform method.

[0029] Further,

[0030] In step 4, the data X3 is cropped and min-max normalized, which includes:

[0031] The time-frequency two-dimensional image information obtained by short-time Fourier transform is cropped to obtain a two-dimensional image input data X4 with a size of 65×85;

[0032] Perform min-max normalization on the data X4 used for WGAN-GP network training:

[0033]

[0034] X min and X max Represent the minimum and maximum values ​​of the training set respectively; map all data X4 to the interval [0,1];

[0035] The imaginary and real part information of the image are stored separately to obtain image data X5 of size 65×85×2, where 65 represents the frequency scale, 85 represents the time scale, and 2 represents the two different dimensions of information contained in the imaginary and real parts of the MRS signal.

[0036] Further,

[0037] In step 5, the WGAN-GP generative adversarial network structure includes a generator and a discriminator. The noisy MRS 2D time-frequency image after STFT processing is input into the generator. The denoised MRS 2D time-frequency image generated by the generator and the real MRS 2D time-frequency image are input into the discriminator. The discriminator determines whether the input image is real or fake and feeds the result back to the generator. Specifically:

[0038] The generator's network structure consists of transposed convolutional layers and activation layers. It includes four transposed convolutional layers, specifying a 5×5 filter, a stride of 1, and setting the padding to same. The number of filters in each layer is 256, 128, 64, and 2, respectively. The first three transposed convolutional layers are followed by a ReLU activation layer. For the final transposed convolutional layer, the number of filters is specified to be 2 to achieve an output image of the same size as the input. At the end of the network structure, a tanh layer is included to map the output image data to [-1, 1].

[0039] The network structure of the discriminator includes convolutional layers, activation layers and LN layers. The entire discriminator contains 5 convolutional layers. The first 4 convolutional layers specify 3×3 filters with a step size of 2 and set the padding mode to same. The number of filters in each layer is 64, 128, 256, and 512 respectively; the last convolutional layer specifies a 5×6 filter with a step size of 1 and no padding, which is used to output a value of 1×1×1. The network structure of the discriminator uses LeakyReLU as the activation function. At the end of the network structure of the discriminator, a Sigmoid layer is used to output a value in the range of [0,1] to represent the true or false probability.

[0040] Further,

[0041] The learning rate of the generator network is 0.001, the learning rate of the discriminator network is 0.0002, and the iteration ratio of the generator and discriminator is set to 1:5. The loss functions of the generator and discriminator networks of the WGAN-GP generative adversarial network structure are:

[0042]

[0043]

[0044] P r Represents the probability distribution of real data, P z Represents the prior distribution of random noise z, D(x) represents the probability that the discriminator judges that the input x comes from the real data distribution, x~P r Indicates that x obeys P r The distribution of gradient penalty is the distribution P r "Push" to another distribution P z Find the relationship between the gradient and the constant K on the optimal path, λ represents the degree of gradient penalty, After sampling the generated data and the training sample data, random interpolation sampling is performed again on the line connecting the two points, which is defined as x r and x g Random interpolation sampling on the connection line satisfies the formula:

[0045]

[0046] x r is the sampled training sample data, x g is the sampled generated data, and ε is a random parameter from the real domain, which ranges from 0 to 1.

[0047] Compared with existing technologies, the present invention offers the following advantages: The method utilizes generative adversarial networks to learn the characteristics of MRS signals and thereby achieve noise removal. Compared to other traditional methods, this method eliminates interference from harmonic noise, random noise, and spike noise by training the WGAN-GP network when parameters such as the initial amplitude and average relaxation time of the MRS signal vary, achieving effective extraction of the MRS signal. This method has the advantage of being able to quickly and efficiently remove multiple noises simultaneously, with excellent generalization, and is of great significance for solving the problem of extracting effective magnetic resonance sounding signals in complex environmental noise interference.

[0048] Compared to traditional GAN ​​networks, the WGAN-GP network introduces a W distance and gradient penalty. The network structure is adjusted to suit different objectives. The network structure described in this article is based on the characteristics of MRS signals, including the architecture of the generator and discriminator, and the short-time Fourier transform cropping size, all of which are suitable for MRS signal characteristics.

[0049] The present invention changes the input signal from one dimension to two dimensions, and it is necessary to grasp the precise correspondence between frequency and time to provide the local time-frequency characteristics of the signal. Compared with common transformation methods, including continuous wavelet transform, Hilbert-Huang transform and short-time Fourier transform used in this article, the time scale of the time-frequency diagram obtained by continuous wavelet transform is not suitable as the input of the neural network of this application, and the Hilbert-Huang transform is also based on the time scale of the signal itself for transformation, with a high time resolution, and is not suitable for preprocessing the network input image. The present invention uses short-time Fourier transform for MRS signals and can obtain a time-frequency diagram of appropriate size by setting appropriate parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 A flowchart of a method for suppressing noise in terrestrial nuclear magnetic resonance signals based on a generative adversarial network provided by an embodiment of the present invention;

[0051] Figure 2 STFT transformation results of different types of noise signals provided by the embodiments of the present invention;

[0052] Figure 3 The embodiment of the present invention provides a WGAN-GP network for constructing MRS to remove random noise;

[0053] Figure 4 The MRS full-wave signal and the MRS signal containing harmonic noise, random noise, and spike noise and their spectrum provided by the embodiment of the present invention are as follows: Figure 4 (a) is the time domain diagram of the MRS full-wave signal, Figure 4 (b) is the spectrum of the MRS full-wave signal. Figure 4 (c) is the time domain diagram of the MRS full-wave signal containing harmonic noise, random noise and spike noise. Figure 4 (d) is the spectrum of the MRS full-wave signal containing harmonic noise, random noise and spike noise;

[0054] Figure 5 WGAN-GP network score graph provided by an embodiment of the present invention;

[0055] Figure 6 The time-frequency domain comparison before and after removing different noises provided by the embodiment of the present invention is Figure 6 (a) is the time-frequency domain comparison before and after removing random noise. Figure 6 (b) is the time-frequency domain comparison before and after removing harmonic noise. Figure 6 (c) is the time-frequency domain comparison before and after removing the spike noise. Figure 6 (d) is the time-frequency domain comparison before and after removing the three types of noise;

[0056] Figure 7The time-frequency domain comparison of the measured data before and after denoising provided by the embodiment of the present invention, Figure 7 (a) is f L =2350HzE0=160nV Time-frequency domain comparison of measured data before and after denoising, Figure 7 (b) is f L =2360HzE0=125nV Time-frequency domain comparison of measured data before and after denoising. DETAILED DESCRIPTION

[0057] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0058] like Figure 1 As shown, the method for suppressing ground NMR signal noise based on the generative adversarial network includes the following steps:

[0059] Step 1: Use a nuclear magnetic resonance sounder to collect a set of observed MRS full-wave signals X1(t) with known Larmor frequencies;

[0060] Step 2: Perform Hilbert transform on the collected observation MRS signal X1(t) to transform the full-wave signal into the complex envelope signal X2(t);

[0061] Step 3: Use the short-time Fourier transform (STFT) method to preprocess the MRS complex envelope signal and convert the one-dimensional signal into a two-dimensional time-frequency image information as the input data X3 for generative adversarial network training;

[0062] Step 4: Cropping the data X3 appropriately to obtain a 2D image X4 of size 65×85, and performing min-max normalization on the cropped data to map all data to the interval [0,1].

[0063] Step 5: Construct a WGAN-GP generative adversarial network structure for MRS denoising to remove three different types of noise: random noise, power frequency harmonic noise, and spike noise;

[0064] Step 6: Apply inverse short-time Fourier transform to the noise-removed data to restore the two-dimensional image information to the MRS complex envelope signal, thereby achieving noise removal and parameter extraction of the MRS signal;

[0065] The observed MRS signal X1(t) is transformed into a complex envelope signal X2(t) by Hilbert transform. The specific steps are as follows:

[0066] The full-wave signal is transformed into a complex envelope signal through Hilbert transform, mainly to eliminate the redundant frequency band part and obtain an analytical signal containing only positive frequencies;

[0067] For the real signal X1(t), its analytical signal is:

[0068]

[0069] Hilbert transform of the imaginary part X1(t) Based on the analytical signal expression, its complex envelope signal is specifically defined as:

[0070]

[0071] f T represents the center frequency of x(t), for MRS signal f T is the transmitting frequency;

[0072] The short-time Fourier transform (STFT) method is used to preprocess the MRS complex envelope signal. The specific steps are as follows:

[0073] The continuous short-time Fourier transform expression of the signal is:

[0074]

[0075] s(t) is the time domain signal to be transformed, g(t) is the window function, * represents the conjugate, and the one-dimensional signal is converted into two-dimensional image information X3 through STFT;

[0076] The data is normalized by min-max. The specific steps are as follows:

[0077] like Figure 2 The time-frequency two-dimensional image information obtained by short-time Fourier transform of the MRS signal containing different noises is appropriately cropped to obtain two-dimensional image data X4 with a size of 65×85;

[0078] Secondly, the data X4 used for WGAN-GP network training needs to be normalized by min-max:

[0079]

[0080] X min and X max Represent the minimum and maximum values ​​of the training set respectively, and the data X4′ is the normalized data. In this way, all data X4 are mapped to data X4′ in the interval [0,1].

[0081] The imaginary and real parts of the image are stored separately to obtain image data X5 of size 65×85×2. Among them, 65 represents the frequency scale, 85 represents the time scale, and 2 represents the two different dimensions of information contained in the MRS signal, the imaginary and real parts.

[0082] The construction of WGAN-GP generative adversarial network includes the following methods:

[0083] After the above processing, for the generator, its direct input is the noisy MRS two-dimensional time-frequency image after STFT processing, and for the discriminator, its direct input is the real (clean and noise-free) MRS two-dimensional time-frequency image and the denoised MRS two-dimensional time-frequency image generated by the generator;

[0084] like Figure 3 The WGAN-GP network structure is designed to remove random noise from MRS. The generator network consists of transposed convolutional layers and activation layers. The image is upsampled and extracted through the transposed convolutional layers. The ReLU activation layer introduces nonlinearity to the network. Finally, the Tanh activation layer maps the output image data to the range [-1, 1]. The entire generator network structure includes four transposed convolutional layers, with a specified 5×5 filter, a stride of 1, and padding set to "same." The number of filters in each layer is 256, 128, 64, and 2, respectively. The first three transposed convolutional layers are followed by a ReLU activation layer. The final transposed convolutional layer is specified to have 2 filters, again to ensure that the output image is the same size as the input. A tanh layer is included at the end of the network to map the output image data to the range [-1, 1].

[0085] The network structure of the discriminator consists of convolutional layers, activation layers, and LN (Layer Normalization) layers. The image is downsampled through the convolutional layer to extract features, the LN layer speeds up and stabilizes the training process, the LeakyReLU activation layer introduces nonlinear elements to the network, and finally the Sigmoid activation layer outputs a probability value between 0 and 1. The entire discriminator contains 5 convolutional layers. The first 4 layers specify 3×3 filters with a step size of 2 and the padding method is set to the same. The number of filters in each layer is 64, 128, 256, and 512 respectively. The last convolutional layer specifies a 5×6 filter with a step size of 1 and no padding, in order to output a value of 1×1×1. The network uses LeakyReLU as the activation function. At the end of the discriminator network, a Sigmoid layer is used to output a value in the range of [0,1] to represent the probability of true or false.

[0086] In the actual process of training the network, the mini-batch size of each training iteration is set to 64, the learning rate of the generator network is specified to be 0.001, and the learning rate of the discriminator network is specified to be 0.0002. The iteration ratio of the generator and the discriminator is set to 1:5, that is, each time the generator performs a parameter update, the discriminator performs five updates. Affected by computer performance, the total number of noisy samples and clean samples is set to about 3000 respectively. A gradient penalty term is added to the discriminator network loss function of the WGAN-GP network. Here, the constant K is taken as 1, which means that the L2 norm of the gradient relative to the original input is constrained to be around 1, and the parameter λ representing the degree of gradient penalty is taken as 10; the generator and discriminator network loss functions of the WGAN-GP generative adversarial network structure are:

[0087]

[0088]

[0089] P r Represents the probability distribution of real data, P z Represents the prior distribution of random noise z. D(x) represents the probability that the discriminator judges that the input x comes from the real data distribution, x~P r Indicates that x obeys P r The distribution of

[0090] Gradient penalty This means that the distribution P r "Push" to another distribution P z Find the relationship between the gradient and the constant K on the optimal path. K is a constant, usually 1, and λ represents the degree of gradient penalty. After sampling the generated data and the training sample data, random interpolation sampling is performed again on the line connecting the two points, which is defined as x r and x g Random interpolation sampling on the connection line satisfies the formula

[0091] x r is the sampled training sample data, x g is the sampled generated data, and ε is a random parameter from the real domain, which ranges from 0 to 1.

[0092] The MRS noisy data is fed into the generator network for training. After a series of transposed convolutional layers, the goal is for the generator to generate denoised data. The generator data and real (clean and noise-free) data are then fed into the discriminator network for training.

[0093] The discriminator determines whether the input image is real or fake and feeds the result back to the generator. The above steps are repeated continuously until the discriminator cannot distinguish between the generated data and the real noise-free data, indicating that the generator has generated the ideal denoised data.

[0094] Example 1

[0095] This embodiment is a simulation experiment of the method of the present invention carried out in the MATLAB 2020a programming environment. Based on the generative adversarial network as a method for suppressing the noise of the ground nuclear magnetic resonance signal, refer to Figure 1 , including the following steps:

[0096] Step (1): Based on Construct Larmor frequency f L is 2330Hz, the amplitude E0 is 100nV, and the relaxation time 0.25s, phase for The pure MRS signal, such as Figure 4 (a) and Figure 4 As shown in (b). Based on this signal, 24 groups of noisy signals are simulated. Among them, the 1-6 groups of signals are added with randomly generated random noises of SNR = 0.46, 5.61, 10.85, 15.66, 20.25, 25.13dB; the 7-12 groups of signals are added with randomly generated harmonic noises of SNR = 0.46, 5.61, 10.85, 15.66, 20.25, 25.13dB; the 13-18 groups of signals are added with randomly generated spike noises of SNR = 0.46, 5.61, 10.85, 15.66, 20.25, 25.13dB. Take three groups as shown in Figure 4 (c) and Figure 4 (d) The 19-24 groups of signals are added with three randomly generated noises of SNR = 0.46, 5.61, 10.85, 15.66, 20.25, and 25.13 dB;

[0097] Step (2): The two-dimensional time-frequency diagram obtained by STFT transformation of the above simulation signal is the input of subsequent network training;

[0098] Step (3): Use the WGAN-GP structure to train the network to remove three different types of noise: random noise, power frequency harmonic noise, and spike noise. In the actual network training process, the mini-batch size of each training iteration is set to 64, the generator network learning rate is specified to be 0.001, and the discriminator network learning rate is specified to be 0.0002. The iteration ratio of the generator and the discriminator is set to 1:5, that is, the generator performs a parameter update once, and the discriminator performs five updates. Similarly, due to the influence of computer performance, the total number of noisy samples and clean samples is set to 3000 respectively. Compared with the original GAN ​​network, the WGAN-GP network loss function adds a gradient penalty term. Here, the constant K is taken as 1, which means that the L2 norm of the gradient relative to the original input is constrained to be around 1, and the parameter λ representing the degree of gradient penalty is taken as 10. Taking the network training of data containing random noise as an example, the maximum number of iterations of the generator is set to 10000, and the network score graph obtained is as follows: Figure 5 As shown, from Figure 5 As can be seen from the figure, with the iteration of training times, the scores of the two networks gradually stabilize at the middle value.

[0099] The results are as follows Figure 6 (a)(b)(c)(d);

[0100] In order to verify the practicability of the method of the present invention, the signal-to-noise ratio (SNR) of the denoised MRS signal was estimated.

[0101] After calculation, the SNR of groups 1-6 is 21.55, 28.16, 28.37, 24.52, 30.29, 27.19dB, the SNR of groups 7-12 is 17.83, 27.61, 28.01, 28.34, 31.53, 29.22dB, the SNR of groups 13-18 is 24.61, 28.49, 26.24, 24.80, 27.82, 28.31dB, and the SNR of groups 19-24 is 23.69, 22.82, 26.29, 29.31, 25.70, 30.86dB. After denoising, the SNR of the MRS signal is generally improved to more than 20dB, and can be increased to 30dB at the highest, achieving good denoising effect. Then the envelope extraction and data fitting of the denoised signal were performed to obtain the key parameters of the separation signal, the initial amplitude E0 and the relaxation time. Calculations show that the fitting errors of all initial amplitudes are within 5%, the fitting errors of all average relaxation times are within 10%, and the average error of the test data is within 2%, and the average error is within 5%, which meets the application requirements.

[0102] Example 2

[0103] In this embodiment, the MRS signals collected from the Changchun Cultural Square are used as the processing objects of the method of the present invention.

[0104] Based on the generative adversarial network as a method to suppress the noise of ground MRI signals, refer to Figure 1 , including the following steps:

[0105] Step (1): Calculate the signal-to-noise ratio, initial amplitude E0 and relaxation time of the six sets of MRS signals collected by the nuclear magnetic resonance sounder (MRS) water detector.

[0106] Step (2): The two-dimensional time-frequency diagram obtained by STFT transformation of the above-mentioned collected signal is the input of subsequent network training;

[0107] Step (3): Use WGAN-GP structure training to remove the noise. In the actual network training process, set the mini-batch size of each training iteration to 64, specify the generator network learning rate to 0.001, and the discriminator network learning rate to 0.0002. Set the iteration ratio of the generator to the discriminator to 1:5, that is, each time the generator performs a parameter update, the discriminator performs five updates. Similarly, due to the influence of computer performance, the total number of noisy samples and clean samples is set to 3000 respectively. Compared with the original GAN ​​network, the WGAN-GP network loss function adds a gradient penalty term. Here, the constant K is taken as 1, which means that the L2 norm of the gradient relative to the original input is constrained to be around 1, and the parameter λ representing the degree of gradient penalty is taken as 10. Taking the network training of data containing random noise as an example, the maximum number of iterations of the generator is set to 10000, and the network score graph obtained is as follows Figure 5 As shown in Figure 3, with the increase in the number of training iterations, the scores of the two networks gradually stabilize at an intermediate value.

[0108] Figure 7 (a) Figure 7 (b) shows the time-frequency domain comparison of the two sets of measured data before and after denoising.

[0109] In order to verify the practicability of the method of the present invention, the signal-to-noise ratio (SNR) of the denoised MRS signal was estimated.

[0110] Calculations show that the signal-to-noise ratio (SNR) of the processed signal improved by approximately 30dB. The fitting error of the initial amplitude was within ±5%, and the fitting error of the average relaxation time was within ±6%. The average fitting error of the test data was 2.68%, and the average fitting error was 2.98%. Therefore, the GAN-based MRS signal denoising method has certain practicality and effectiveness.

[0111] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for suppressing noise in terrestrial nuclear magnetic resonance signals based on a generative adversarial network, characterized in that: The method comprises the following steps: Step 1: Observe the MRS signal of known Larmor frequency collected by the NMR sounder ; Step 2: Observe the collected MRS signal Perform Hilbert transform to transform the full-wave signal into a complex envelope signal ; Step 3: Use the short-time Fourier transform method to preprocess the MRS complex envelope signal and convert the one-dimensional signal into a two-dimensional image of time-frequency information as the input data for generative adversarial network training. ; Step 4: Data Cropping to obtain a 2D image of size 65×85 , and perform min-max normalization on the cropped data to map all data to the interval [0,1]; Step 5: Construct a WGAN-GP generative adversarial network structure for MRS denoising to remove three different types of noise: random noise, power frequency harmonic noise, and spike noise; Step 6: Apply inverse short-time Fourier transform to the noise-removed data to restore the two-dimensional image information to the MRS complex envelope signal, thereby achieving noise removal and parameter extraction of the MRS signal; Among them, the WGAN-GP generative adversarial network structure in step 5 includes a generator and a discriminator. The noisy MRS two-dimensional time-frequency image after STFT processing is input into the generator. The denoised MRS two-dimensional time-frequency image generated by the generator and the real MRS two-dimensional time-frequency image are input into the discriminator. The discriminator judges the authenticity of the input image and feeds the result back to the generator. Specifically: The generator's network structure consists of transposed convolutional layers and activation layers. It includes four transposed convolutional layers, specifying a 5×5 filter, a stride of 1, and setting the padding to same. The number of filters in each layer is 256, 128, 64, and 2, respectively. The first three transposed convolutional layers are followed by a ReLU activation layer. For the final transposed convolutional layer, the number of filters is specified to be 2 to achieve an output image of the same size as the input. At the end of the network structure, a tanh layer is included to map the output image data to [-1, 1]. The network structure of the discriminator includes convolutional layers, activation layers and LN layers. The entire discriminator contains 5 convolutional layers. The first 4 convolutional layers specify 3×3 filters with a step size of 2 and set the padding mode to same. The number of filters in each layer is 64, 128, 256, and 512 respectively; the last convolutional layer specifies a 5×6 filter with a step size of 1 and no padding, which is used to output a value of 1×1×1. The network structure of the discriminator uses LeakyReLU as the activation function. At the end of the network structure of the discriminator, a Sigmoid layer is used to output a value in the range of [0,1] to represent the true or false probability.

2. The method for suppressing noise in terrestrial nuclear magnetic resonance signals based on a generative adversarial network according to claim 1, wherein: In step 2, the collected observation MRS signal Transform the full-wave signal into a complex envelope signal through Hilbert transform , the specific steps are: For observing MRS signals Parses as: （1）， The imaginary part is Hilbert transform , the MRS complex envelope signal is obtained from the analytical signal: （2）， express The center frequency of the MRS signal, That is the transmission frequency.

3. The method for suppressing noise in terrestrial nuclear magnetic resonance signals based on a generative adversarial network according to claim 1, wherein: In step 3, the MRS complex envelope signal is preprocessed using the short-time Fourier transform method, which specifically includes: The signal undergoes continuous short-time Fourier transform: （3）， is the time domain signal to be transformed, is the window function, * represents the conjugate, and the one-dimensional signal is converted into two-dimensional image information through the short-time Fourier transform method.

4. The method for suppressing noise in terrestrial nuclear magnetic resonance signals based on a generative adversarial network according to claim 1, wherein: In step 4, the data Cropping and min-max normalization processing, including: The time-frequency two-dimensional image information obtained by short-time Fourier transform is cropped to obtain a two-dimensional image input data of size 65×85 ; The data used for WGAN-GP network training Perform min-max normalization: （4）， and Represent the minimum and maximum values ​​of the training set respectively; put all the data Mapped to the interval [0,1]; The imaginary part information and real part information of the image are stored separately to obtain image data of size 65×85×2 , where 65 represents the frequency scale, 85 represents the time scale, and 2 represents the two different dimensions of information contained in the MRS signal, the imaginary part and the real part.

5. The method for suppressing noise in terrestrial nuclear magnetic resonance signals based on a generative adversarial network according to claim 1, wherein: The learning rate of the generator network is 0.001, the learning rate of the discriminator network is 0.0002, and the iteration ratio of the generator and discriminator is set to 1:

5. The loss functions of the generator and discriminator networks of the WGAN-GP generative adversarial network structure are: （5）， （6）， represents the probability distribution of real data, represents the prior distribution of random noise z, Characterizes the discriminator's judgment input Probability from the true data distribution, express obey The distribution of gradient penalty , is the distribution "Push to" another distribution Find the relationship between the gradient and the constant K on the optimal path, Represents the degree of gradient penalty, After sampling the generated data and the training sample data, random interpolation sampling is performed again on the line connecting the two points, which is defined as and Random interpolation sampling on the connection line satisfies the formula: ， is the sampled training sample data, is the sampled generated data, and ε is a random parameter from the real domain, which ranges from 0 to 1.

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