A dual-domain magnetic resonance groundwater detection same-frequency harmonic noise processing method and system

Abstract

The application relates to the field of magnetic resonance sounding technology, in particular to a dual-domain magnetic resonance groundwater detection same-frequency harmonic noise processing method and system, which comprises the following steps: decomposing obtained noisy magnetic resonance signals to obtain frequency weight coefficients of the strength of the noisy magnetic resonance signals at different components, generating a frequency strength matrix from the multiple frequency weight coefficients; adjusting the frequency strength matrix to obtain a frequency weight matrix, multiplying the frequency weight matrix and an input data set channel by channel, retaining signal components near the Larmor frequency to obtain a preliminary de-noised signal; establishing a time domain mapping relationship between the preliminary de-noised signal and a pure magnetic resonance signal, and performing network training to obtain a trained time domain mapping relationship, and adjusting the frequency strength matrix according to the result of each round of training; and constructing a de-noised signal according to the trained time domain mapping relationship, so that the same-frequency harmonic noise in the magnetic resonance signal can be well eliminated, and an ideal de-noising effect can be achieved.

Description

Technical Field

[0001] This application relates to the field of magnetic resonance sounding (MRS) technology, specifically to a method and system for processing harmonic noise in dual-domain magnetic resonance groundwater detection. Background Technology

[0002] Magnetic resonance groundwater detection technology, as the only geophysical method currently capable of non-invasive direct water discovery, is widely used in groundwater resource exploration, prediction of water-related geological hazards, and groundwater pollution monitoring. However, limited by the strength of the natural geomagnetic field, the MRS signal received by the magnetic resonance groundwater detector is only at the nanovolt level and is subject to strong environmental noise interference. Power frequency harmonic noise is one of the most serious types of noise affecting signal quality, originating from power lines, generators, and transformers, with the frequencies of each harmonic component fixed as integer multiples of 50Hz or 60Hz. When the Larmor frequency at the detection site is close to or coincides with the frequency of a certain power frequency harmonic component, the MRS signal is interfered with by the same-frequency harmonic noise. Existing methods struggle to fully preserve the effective signal while removing the same-frequency noise interference, reducing the accuracy of magnetic resonance detection results. Therefore, it is essential to study methods for denoising the same-frequency noise in magnetic resonance groundwater detection signals.

[0003] Chinese Patent Publication No. CN116561515A discloses a method for suppressing power frequency noise in magnetic resonance signals based on recurrent neural networks. This method constructs a network model using recurrent and bilinear layers. The noisy magnetic resonance signal is segmented and input to the network bidirectionally, while the simulated signal is used as the ideal output. The input segment of the noisy magnetic resonance signal is then preprocessed to initialize the recurrent layer's state parameters. Next, each segment is bidirectionally extended at its endpoints, and redundant nodes are used for recurrent layer calculations. The global parameters are then updated using backpropagation until the loss function stabilizes, resulting in a noise reduction model. By constructing a complex mapping relationship between the noisy magnetic resonance signal and power frequency noise, noise reduction is achieved. This method, combined with recurrent neural networks, achieves rapid and efficient suppression of magnetic resonance power frequency harmonic noise. However, when the noise and the magnetic resonance signal have the same frequency, it cannot simultaneously preserve the complete effective signal while eliminating noise at the same frequency. Summary of the Invention

[0004] This application provides a method for processing harmonic noise in dual-domain magnetic resonance groundwater detection, which solves the problem of difficulty in removing interference from the same frequency noise while fully preserving the effective signal.

[0005] Another aspect of this application provides a dual-domain magnetic resonance groundwater detection system for processing harmonic noise of the same frequency.

[0006] A method for processing harmonic noise in dual-domain magnetic resonance groundwater detection according to an embodiment of this application includes:

[0007] The acquired noisy magnetic resonance signal is decomposed to obtain the frequency weighting coefficients of the intensity of the noisy magnetic resonance signal at different components, and the multiple frequency weighting coefficients are used to generate a frequency intensity matrix.

[0008] The frequency intensity matrix is ​​adjusted to obtain the frequency weight matrix. The frequency weight matrix is ​​then multiplied with the input dataset channel by channel to retain the signal components near the Larmor frequency, thus obtaining the preliminary denoised signal.

[0009] A time-domain mapping relationship between the initial denoised signal and the pure magnetic resonance signal is established, and the network is trained to obtain the trained time-domain mapping relationship. The frequency intensity matrix is ​​adjusted according to the results of each training round.

[0010] The denoised signal is constructed based on the time-domain mapping relationship after training.

[0011] Furthermore, the acquired noisy magnetic resonance signal is decomposed to obtain frequency weighting coefficients of the intensity of the noisy magnetic resonance signal at different components, including:

[0012] By downsampling the noisy magnetic resonance signal, the noisy magnetic resonance signal after downsampling is obtained;

[0013] The downsampled noisy magnetic resonance signal is decomposed by frequency to obtain frequency intensity coefficients, which represent the frequency intensity coefficients of the first-order magnetic resonance signal. A signal at a certain frequency component The frequency intensity coefficient at that location.

[0014] Furthermore, the frequency weight matrix is ​​multiplied channel by channel with the input noisy magnetic resonance signal to retain the signal components near the Larmor frequency, resulting in a preliminary denoised signal. This includes assigning high weights to the effective magnetic resonance signal at the Larmor frequency and low weights to harmonic noise interference at other frequencies.

[0015] Furthermore, the downsampled noisy magnetic resonance signal is decomposed by frequency to obtain the frequency intensity coefficients, expressed by the following formula:

[0016] , As the normalization factor, we obtain the expression that can represent the first... A signal at a certain frequency component Frequency intensity coefficient at , , ,in For a certain data point, , This represents the data length.

[0017] Furthermore, the frequency intensity matrix is ​​adjusted based on the results of each training session, including: calculating the error between the denoised signal and the clean magnetic resonance signal output after each training round, updating the network parameters using the error backpropagation method, and adjusting the frequency intensity matrix based on the network parameters.

[0018] A dual-domain magnetic resonance groundwater detection harmonic noise processing system according to another embodiment of this application includes:

[0019] Frequency domain decomposition network: The user decomposes the acquired noisy magnetic resonance signal to obtain the frequency weighting coefficients of the intensity of the noisy magnetic resonance signal at different components, and generates a frequency intensity matrix based on the frequency weighting coefficients;

[0020] The frequency intensity matrix is ​​adjusted according to the frequency domain characteristics of the signal to obtain the frequency weight matrix. The frequency weight matrix is ​​then multiplied with the input dataset channel by channel to retain the signal components near the Larmor frequency, thus obtaining the preliminary denoised signal.

[0021] A time-domain reconstruction network is used to establish a time-domain mapping relationship between the initial denoised signal and the clean magnetic resonance signal; the denoised signal is then constructed based on the time-domain mapping relationship.

[0022] Furthermore, the frequency domain decomposition network includes: a global average pooling layer, a weight calculation layer, a first fully connected layer, and a first activation layer, wherein:

[0023] The global flat pooling layer obtains the downsampled noisy magnetic resonance signal by downsampling the noisy magnetic resonance signal;

[0024] The weighting layer decomposes the downsampled noisy magnetic resonance signal according to frequency to obtain frequency intensity coefficients, which represent the frequency intensity coefficients of the first-order magnetic resonance signal. A signal at a certain frequency component The frequency intensity coefficient at a given location; a frequency intensity matrix is ​​generated based on the frequency intensity coefficient;

[0025] The first fully connected layer and the first activation layer adjust the frequency intensity matrix to obtain the frequency weight matrix. The frequency weight matrix is ​​then multiplied with the input noisy magnetic resonance signal channel by channel, giving high weight to the effective magnetic resonance signal at the Larmor frequency and low weight to the harmonic noise interference at other frequencies.

[0026] Furthermore, the temporal reconstruction network includes two convolutional layers and a second fully connected layer. Each convolutional layer is followed by a second activation layer, and the output is obtained through the second fully connected layer, wherein:

[0027] Two convolutional layers with identical input and output channels are used to establish a temporal mapping relationship between the initial denoised signal and the clean magnetic resonance signal;

[0028] The second fully connected layer is used to reshape the feature map shape of the initial denoised signal, making the initial denoised signal consistent with the dimension of the clean magnetic resonance signal dataset.

[0029] Furthermore, the frequency domain decomposition network and the time domain reconstruction network are trained, and the error between the denoised signal and the pure magnetic resonance signal output after each training round is calculated. The network parameters are updated using the error backpropagation method, and the frequency intensity matrix is ​​adjusted using the updated network parameters in the first fully connected layer and the first activation layer.

[0030] Furthermore, the weight calculation layer decomposes the downsampled noisy magnetic resonance signal according to frequency to obtain frequency intensity coefficients, expressed by the following formula:

[0031] , As the normalization factor, we obtain the expression that can represent the first... A signal at a certain frequency component Frequency intensity coefficient at , , ,in For a certain data point, , This represents the data length.

[0032] The embodiments of this application have at least the following advantages and beneficial effects:

[0033] Compared with existing magnetic resonance harmonic noise suppression techniques, this application significantly improves the efficiency of eliminating harmonic noise, effectively eliminating it from magnetic resonance signals and achieving ideal denoising results. This application effectively suppresses interference caused by harmonic noise and exhibits better adaptability than traditional denoising methods, requiring no parameter adjustment and thus improving reliability. Furthermore, compared to convolutional neural networks, this application utilizes a frequency decomposition network to learn the frequency domain features of the signal, effectively avoiding the limitation of neural networks that can only acquire time-domain information, and significantly enhancing the denoising effect. Attached Figure Description

[0034] Figure 1 This is a schematic diagram of the network structure of a dual-domain magnetic resonance groundwater detection harmonic noise processing system provided in an embodiment of this application;

[0035] Figure 2 This is a flowchart of a method for processing harmonic noise in dual-domain magnetic resonance groundwater detection, provided in an embodiment of this application.

[0036] Figure 3These are frequency domain diagrams and time domain diagrams of the denoising process provided in the embodiments of this application, wherein (a) is a time domain diagram of the noisy magnetic resonance signal, (b) is a frequency domain diagram of the noisy magnetic resonance signal, (c) is a time domain diagram of the preliminary denoised signal, (d) is a frequency domain diagram of the preliminary denoised signal, (e) is a time domain diagram of the denoised signal, and (f) is a frequency domain diagram of the denoised signal.

[0037] Figure 4 These are time-domain (a) and frequency-domain (b) diagrams of a noisy signal provided in an embodiment of this application.

[0038] Figure 5 These are time-domain (a) and frequency-domain (b) diagrams of a denoised signal provided in an embodiment of this application. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0040] This application constructs a denoising network that includes a frequency domain decomposition network and a time domain reconstruction network. The frequency domain decomposition network is used to suppress most of the noise signal while preserving the frequency components of the signal. The time domain reconstruction network is combined to capture the detailed features of the signal. Through training, the network parameters are updated using the backpropagation method to learn the relationship between the noisy magnetic resonance signal input to the network and the clean magnetic resonance signal.

[0041] See Figure 1 As shown, a dual-domain magnetic resonance groundwater detection harmonic noise processing system includes: a frequency domain decomposition network, in which the user decomposes the acquired noisy magnetic resonance signal to obtain frequency weighting coefficients of the intensity of the noisy magnetic resonance signal at different components, and generates a frequency intensity matrix based on the frequency weighting coefficients.

[0042] The frequency intensity matrix is ​​adjusted according to the frequency domain characteristics of the signal to obtain the frequency weight matrix. The frequency weight matrix is ​​then multiplied with the input dataset channel by channel to retain the signal components near the Larmor frequency, thus obtaining the preliminary denoised signal.

[0043] A time-domain reconstruction network is used to establish a time-domain mapping relationship between the initial denoised signal and the clean magnetic resonance signal; the denoised signal is then constructed based on the time-domain mapping relationship.

[0044] In one embodiment, the frequency domain decomposition network includes: a global average pooling layer, a weight calculation layer, a first fully connected layer, and a first activation layer, wherein:

[0045] The global flat pooling layer obtains the downsampled noisy magnetic resonance signal by downsampling the noisy magnetic resonance signal;

[0046] The weighting layer decomposes the downsampled noisy magnetic resonance signal according to frequency to obtain frequency intensity coefficients, which represent the frequency intensity coefficients of the first-order magnetic resonance signal. A signal at a certain frequency component The frequency intensity coefficient at a given location; a frequency intensity matrix is ​​generated based on the frequency intensity coefficient;

[0047] The first fully connected layer and the first activation layer adjust the frequency intensity matrix to obtain the frequency weight matrix. The frequency weight matrix is ​​then multiplied with the input noisy magnetic resonance signal channel by channel, giving high weight to the effective magnetic resonance signal at the Larmor frequency and low weight to the harmonic noise interference at other frequencies.

[0048] Specifically, the signal is obtained using a frequency domain decomposition network. The calculation process is as follows:

[0049] First, the global average pooling layer handles the noisy input magnetic resonance signal. Downsampling is performed, and the data length of the noisy magnetic resonance signal is reduced from... Reduce to The downsampled noisy magnetic resonance signal was obtained. ,in ;

[0050] Secondly, the weight calculation layer will calculate the downsampled noisy magnetic resonance signal. Decomposition by frequency:

[0051] , to obtain the ability to represent the first A signal at a certain frequency component Frequency intensity coefficient at , Normalization factor Defined as: ,in For a certain data point, ;

[0052] According to the A signal at a certain frequency component Frequency intensity coefficient at Generate frequency intensity matrix : ; The total number of signals in the dataset. .

[0053] The frequency domain features of the signal are learned using the first fully connected layer and the first activation layer, and the frequency intensity matrix is ​​adjusted. To obtain the required frequency weight matrix Learning the frequency domain features of a signal refers to the real-time updating of network parameters in the fully connected and activation layers during backpropagation. If the frequency intensity matrix is ​​directly used as the frequency weight matrix, the frequency weights cannot be updated according to the learning process. The first fully connected layer and the first activation layer are essentially multiplying the frequency intensity matrix by a variable-parameter matrix. Therefore, changes in the network parameters of the first fully connected layer and the first activation layer update and adjust the frequency weight matrix, allowing the weight information to be continuously adjusted and optimized during network training, thus transforming the frequency weight matrix... With the input noisy magnetic resonance signal Channel-by-channel multiplication is performed, using high weights to fully preserve the effective magnetic resonance signal at the Larmor frequency, while assigning lower weights to harmonic noise interference at other frequencies, resulting in a preliminarily denoised signal:

[0054]

[0055] Refers to the frequency weight matrix The transposed matrix is ​​the frequency domain weight matrix obtained here. The dimension is The input noisy magnetic resonance signal Since the dimensions are I*N, they cannot be directly multiplied. Therefore, the frequency domain weight matrix needs to be transposed first. This is the initial noise reduction signal;

[0056] This refers to the signal after initial noise reduction. The I-th signal in the initial noise reduction signal It is a matrix of dimension I*I (number of signals * data length of each signal), composed of I signals, where the data length of each signal is I. .

[0057] In one embodiment, the temporal reconstruction network includes two convolutional layers and a second fully connected layer, with each convolutional layer followed by a second activation layer, and the output is obtained through the second fully connected layer, wherein:

[0058] Two convolutional layers with identical input and output channels are used to establish a temporal mapping relationship between the initial denoised signal and the clean magnetic resonance signal;

[0059] The second activation layer is used to introduce more nonlinear relationships while effectively suppressing overfitting.

[0060] The second fully connected layer is used to reshape the feature map shape of the initial denoised signal, making the initial denoised signal consistent with the dimension of the clean magnetic resonance signal dataset.

[0061] The two second activation layers in the temporal reconstruction network use Parametric Rectified Linear Units (PReLUs) for each input data point. Perform the following operations: , among which, when hour, ( (for learnable parameters); when hour, . This represents the improved activation function.

[0062] The training sets for the frequency domain decomposition network and the time domain reconstruction network described above are constructed in the following manner:

[0063] First, a dataset containing harmonic noise interference of the same frequency is constructed: In the frequency domain, the energy of the magnetic resonance signal is concentrated in the Larmor frequency. At the frequency, while power frequency harmonic interference is caused by multiple center frequencies. The fundamental frequency The energy of the magnetic resonance signal is discretely distributed at various center frequencies, obtained by superimposing cosine signals that are integer multiples of each other. When the Larmor frequency of the magnetic resonance signal... The center frequency of interference with a certain power frequency harmonic noise When signals are close to or identical in frequency, magnetic resonance signals are subject to interference from harmonic noise of the same frequency. By combining frequency and time domain information to learn the nonlinear mapping relationship between noisy and clean magnetic resonance signals, it is possible to effectively remove noise of the same frequency and improve signal quality.

[0064] According to the power frequency interference formula: The parameter range is set as follows: noise level Fundamental frequency phase Simulation generation The length of the data is Power frequency harmonic noise Building a Noise Dataset , of which The power frequency harmonic noise signal is represented as follows: , , .

[0065] According to the magnetic resonance signal formula: The parameter range is set as follows: initial amplitude Mean lateral relaxation time Lamoer frequency initial phase Simulation generation The length of the data is pure magnetic resonance signal Constructing a pure magnetic resonance signal dataset , of which A pure magnetic resonance signal is represented as , , .

[0066] In the generated noisy magnetic resonance signal dataset, for a pure magnetic resonance signal with a Larmor frequency of 2350 Hz, due to its Larmor frequency... The fundamental frequency interfering with the 47th harmonic They are similar, both affected by noise at the same frequency.

[0067] The noise dataset and the clean magnetic resonance signal dataset are superimposed on each sample to obtain the result. The length of the signal is Noisy magnetic resonance signal datasets affected by harmonic noise of the same frequency , of which A noisy magnetic resonance signal is represented as , , .

[0068] Noisy magnetic resonance signal dataset As the network training set, the error between the denoised signal and the noisy magnetic resonance signal output after each training round is calculated. The network parameters are then updated using the error backpropagation method to learn the input noisy magnetic resonance signal. To pure magnetic resonance signal The mapping relationship can also be used to mitigate losses through early stopping strategies. Terminate training and save the current network model if the wheel does not descend;

[0069] The trained network model is used to denoise magnetic resonance signals containing harmonic noise of the same frequency, and the output signal is the denoised signal.

[0070] After training is completed, a simulation experiment is conducted to test the noise reduction effect of the network model.

[0071] First, a Larmor frequency of 2350 Hz, an initial amplitude of 100 nV, an average transverse relaxation time of 0.15 s, and an initial phase of [missing information] were generated through simulation. A clean magnetic resonance signal was obtained. The signal sampling frequency was 25000Hz, and the number of sampling points was 6000. Random noise was generated in the simulation, with an amplitude of 10nV, to simulate small-amplitude interference encountered in actual signal acquisition. Power frequency harmonic noise was generated in the simulation, with a fundamental frequency ranging from 49.95 to 50.05Hz, 20 harmonics, and a noise level of 600nV. After mixing the above noise with the clean signal, a noisy magnetic resonance signal with a signal-to-noise ratio of -16.09dB was obtained. Its time-domain and frequency-domain images are shown below. Figure 3 (a) and Figure 3 The signal containing harmonic noise of the same frequency shown in (b) is obtained as the preliminary noise-reduced signal. Figure 3 (c) and Figure 3 As shown in (d) above, the time-domain and frequency-domain plots of the obtained denoised signal are as follows: Figure 3 (e) and Figure 3 As shown in (f), the signal-to-noise ratio is 25.36 dB, which is 41.45 dB higher after denoising than before.

[0072] On the other hand, see Figure 2 As shown in the embodiment of this application, a method for processing harmonic noise in dual-domain magnetic resonance groundwater detection is provided. The method includes:

[0073] The acquired noisy magnetic resonance signal is decomposed to obtain the frequency weighting coefficients of the intensity of the noisy magnetic resonance signal at different components, and the multiple frequency weighting coefficients are used to generate a frequency intensity matrix.

[0074] The frequency intensity matrix is ​​adjusted to obtain the frequency weight matrix. The frequency weight matrix is ​​then multiplied with the input dataset channel by channel to retain the signal components near the Larmor frequency, thus obtaining the preliminary denoised signal.

[0075] A time-domain mapping relationship between the initial denoised signal and the pure magnetic resonance signal is established, and the network is trained to obtain the trained time-domain mapping relationship. The frequency intensity matrix is ​​adjusted according to the results of each training round.

[0076] The denoised signal is constructed based on the time-domain mapping relationship after training.

[0077] In one embodiment, the acquired noisy magnetic resonance signal is decomposed to obtain frequency weighting coefficients of the intensity of the noisy magnetic resonance signal at different components, including:

[0078] By downsampling the noisy magnetic resonance signal, the noisy magnetic resonance signal after downsampling is obtained;

[0079] The downsampled noisy magnetic resonance signal is decomposed by frequency to obtain frequency intensity coefficients, which represent the frequency intensity coefficients of the first-order magnetic resonance signal. A signal at a certain frequency component The frequency intensity coefficient at that location.

[0080] In one embodiment, the frequency weighting matrix is ​​multiplied channel by channel with the input noisy magnetic resonance signal to retain the signal components near the Larmor frequency, thereby obtaining a preliminary denoised signal. This includes assigning high weights to the effective magnetic resonance signal at the Larmor frequency and low weights to harmonic noise interference at other frequencies.

[0081] In one embodiment, the downsampled noisy magnetic resonance signal is decomposed by frequency to obtain the frequency intensity coefficients, expressed by the following formula:

[0082] , As the normalization factor, we obtain the expression that can represent the first... A signal at a certain frequency component Frequency intensity coefficient at , , ,in For a certain data point, , This represents the data length.

[0083] In one embodiment, adjusting the frequency intensity matrix based on the results of each training iteration includes: calculating the error between the denoised signal and the clean magnetic resonance signal output after each training round, updating the network parameters using the error backpropagation method, and adjusting the frequency intensity matrix based on the network parameters.

[0084] This application uses magnetic resonance signals collected on-site at Changchun Cultural Square as the processing object of the method. A signal generator is used to generate a Larmor frequency of 2350Hz, an initial amplitude of 150nV, an average transverse relaxation time of 0.20s, and an initial phase of... The pure magnetic resonance signal is obtained by simultaneously acquiring ambient noise and the pure magnetic resonance signal generated by the signal generator using a receiving coil, resulting in a noisy magnetic resonance signal containing harmonic noise interference. For example... Figure 4 As shown, Figure 4 (a) and Figure 4 (b) in the figure represents the time domain and frequency domain plots of the noisy magnetic resonance signal, respectively, and its signal-to-noise ratio is calculated to be -23.47dB.

[0085] The obtained denoised signal is as follows Figure 5 As shown, Figure 5 (a) and Figure 5(b) shows the time-domain and frequency-domain plots of the denoised signal, respectively. The signal-to-noise ratio is calculated to be 8.90 dB, which is 32.47 dB higher than that before processing. Parameter fitting of the denoised signal yields an initial amplitude of 157.93 nV and an average transverse relaxation time of 0.19 s. The obtained key parameters meet the application requirements.

[0086] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for processing harmonic noise in dual-domain magnetic resonance groundwater detection, characterized in that, The method includes: The acquired noisy magnetic resonance signal is decomposed to obtain frequency intensity coefficients of the intensity of the noisy magnetic resonance signal at different components, and multiple frequency intensity coefficients are used to generate a frequency intensity matrix; including: By downsampling the noisy magnetic resonance signal, the noisy magnetic resonance signal after downsampling is obtained; The downsampled noisy magnetic resonance signal is decomposed by frequency to obtain frequency intensity coefficients, which represent the frequency intensity coefficients of the first-order magnetic resonance signal. A signal at a certain frequency component Frequency intensity coefficient at that location; The downsampled noisy magnetic resonance signal is decomposed by frequency to obtain the frequency intensity coefficients, expressed by the following formula: , As the normalization factor, we obtain the expression that can represent the first... A signal at a certain frequency component Frequency intensity coefficient at , , ,in For a certain data point, , For data length, It is the downsampled, noisy magnetic resonance signal; The frequency intensity matrix is ​​adjusted to obtain the frequency weight matrix. The frequency weight matrix is ​​then multiplied with the input dataset channel by channel to retain the signal components near the Larmor frequency, thus obtaining the preliminary denoised signal. A time-domain mapping relationship between the initial denoised signal and the pure magnetic resonance signal is established, and the network is trained to obtain the trained time-domain mapping relationship. The frequency intensity matrix is ​​adjusted according to the results of each training round. The denoised signal is constructed based on the time-domain mapping relationship after training.

2. The method for processing harmonic noise in dual-domain magnetic resonance groundwater detection according to claim 1, characterized in that, The frequency weighting matrix is ​​multiplied channel by channel with the input noisy magnetic resonance signal to retain the signal components near the Larmor frequency, resulting in a preliminary denoised signal. This includes assigning high weights to the effective magnetic resonance signal at the Larmor frequency and low weights to harmonic noise interference at other frequencies.

3. The method for processing harmonic noise in dual-domain magnetic resonance groundwater detection according to claim 1, characterized in that, The frequency intensity matrix is ​​adjusted based on the results of each training session, including: calculating the error between the denoised signal and the clean magnetic resonance signal output after each training round, updating the network parameters using the error backpropagation method, and adjusting the frequency intensity matrix based on the network parameters.

4. A dual-domain magnetic resonance groundwater detection harmonic noise processing system, characterized in that, include: The frequency domain decomposition network allows users to decompose the acquired noisy magnetic resonance signal to obtain the frequency intensity coefficients of the intensity of the noisy magnetic resonance signal at different components, and generate a frequency intensity matrix based on the frequency intensity coefficients. The frequency domain decomposition network includes: a global average pooling layer, a weight calculation layer, a first fully connected layer, and a first activation layer, wherein: The global flat pooling layer obtains the downsampled noisy magnetic resonance signal by downsampling the noisy magnetic resonance signal; The weighting layer decomposes the downsampled noisy magnetic resonance signal according to frequency to obtain frequency intensity coefficients, which represent the frequency intensity coefficients of the first-order magnetic resonance signal. A signal at a certain frequency component The frequency intensity coefficient at a given location; a frequency intensity matrix is ​​generated based on the frequency intensity coefficient; The first fully connected layer and the first activation layer adjust the frequency intensity matrix to obtain the frequency weight matrix. The frequency weight matrix is ​​then multiplied with the input noisy magnetic resonance signal channel by channel to assign high weight to the effective magnetic resonance signal at the Larmor frequency and low weight to the harmonic noise interference at other frequencies. The weighting calculation layer decomposes the downsampled noisy magnetic resonance signal according to frequency to obtain the frequency intensity coefficient, which is expressed by the following formula: , As the normalization factor, we obtain the expression that can represent the first... A signal at a certain frequency component Frequency intensity coefficient at , , ,in For a certain data point, , For data length, It is the downsampled, noisy magnetic resonance signal; The frequency intensity matrix is ​​adjusted according to the frequency domain characteristics of the signal to obtain the frequency weight matrix. The frequency weight matrix is ​​then multiplied with the input dataset channel by channel to retain the signal components near the Larmor frequency, thus obtaining the preliminary denoised signal. A time-domain reconstruction network is used to establish a time-domain mapping relationship between the initial denoised signal and the clean magnetic resonance signal; the denoised signal is then constructed based on the time-domain mapping relationship.

5. The dual-domain magnetic resonance groundwater detection harmonic noise processing system according to claim 4, characterized in that, The temporal reconstruction network includes two convolutional layers and a second fully connected layer. Each convolutional layer is followed by a second activation layer, and the output is obtained through the second fully connected layer. Two convolutional layers with identical input and output channels are used to establish a temporal mapping relationship between the initial denoised signal and the clean magnetic resonance signal; The second fully connected layer is used to reshape the feature map shape of the initial denoised signal, making the initial denoised signal consistent with the dimension of the clean magnetic resonance signal dataset.

6. The dual-domain magnetic resonance groundwater detection harmonic noise processing system according to claim 5, characterized in that, The frequency domain decomposition network and the time domain reconstruction network are trained. The error between the denoised signal and the clean magnetic resonance signal after each training round is calculated. The network parameters are updated using the error backpropagation method. The frequency intensity matrix is ​​adjusted using the updated network parameters in the first fully connected layer and the first activation layer.

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