Neural network magnetic anomaly signal denoising method and system combined with weak supervision learning

Abstract

The application is suitable for the field of geophysical exploration technology, and provides a neural network magnetic anomaly signal denoising method and system combined with weak supervision learning, which comprises the following steps: acquiring a noisy magnetic anomaly signal; converting the noisy magnetic anomaly signal into a noisy frequency spectrum based on short-time Fourier transform; performing denoising processing on the noisy frequency spectrum based on a U-Net++ network to obtain a denoised frequency spectrum; calculating a multi-scale spectrum loss, a mean square error loss and a weak supervision loss in real time according to the denoised frequency spectrum to determine a total loss; if the total loss is lower than a preset threshold, converting the denoised frequency spectrum back to a time domain signal based on inverse short-time Fourier transform to obtain a denoised signal; otherwise, updating parameters of the U-Net++ network through back propagation. The application realizes the dual breakthrough of precision reservation and efficiency improvement by using the U-Net++ network combined with weak supervision learning to perform denoising processing on the magnetic anomaly signal.

Description

Technical Field

[0001] This invention belongs to the field of geophysical exploration technology, and in particular relates to a method and system for denoising magnetic anomaly signals using neural networks combined with weakly supervised learning. Background Technology

[0002] Magnetic anomaly signal denoising is a core prerequisite for achieving accurate detection and positioning of magnetic targets in fields such as mineral resource exploration using airborne magnetic surveying. Its processing effect directly determines the accuracy of subsequent data interpretation and the precision of target positioning.

[0003] Traditional denoising methods for magnetic anomaly signals, such as wavelet transform and Kalman filtering, largely rely on pre-defined mathematical models of noise. When faced with complex mixed noise—including random noise, equipment system interference, and terrain noise—they struggle to adaptively distinguish the characteristics of different noise types, limiting denoising accuracy. While classic neural networks (such as CNNs and RNNs) can capture subtle microscopic noise patterns in aeromagnetic data through multi-layered network structures and adapt to the irregular distribution of unstructured noise, their training heavily depends on large-scale labeled samples. However, in real-world exploration scenarios, high-quality labeled data is often scarce. Under small sample conditions, models are prone to overfitting, learning redundant information from limited samples, leading to distortion of the denoised data. This significantly reduces the reliability of magnetic target localization and limits the actual effectiveness of exploration missions. Summary of the Invention

[0004] The purpose of this invention is to provide a method for denoising magnetic anomaly signals using neural networks that incorporates weakly supervised learning, thereby addressing the aforementioned technical problems.

[0005] This invention is implemented as follows: a method for denoising magnetic anomaly signals using a neural network combined with weakly supervised learning, comprising the following steps:

[0006] Acquire noisy magnetic anomaly signals;

[0007] Based on short-time Fourier transform, the noisy magnetic anomaly signal is converted into a noisy spectrum.

[0008] Based on the U-Net++ network, the noisy spectrogram is denoised to obtain a denoised spectrogram.

[0009] Based on the denoised spectrum, calculate the multi-scale spectral loss, mean square error loss, and weak supervision loss in real time to determine the total loss;

[0010] If the total loss is lower than a preset threshold, the denoised spectrum is converted back to the time domain signal based on the inverse short-time Fourier transform to obtain the denoised signal; otherwise, the parameters of the U-Net++ network are updated through backpropagation.

[0011] Furthermore, the formula for the short-time Fourier transform is:

[0012] ;

[0013] In the formula, X represents the result of the short-time Fourier transform; m is the position index of the window function; k is the frequency index; and x[n] is the magnetic anomaly signal at time n. is the window function; N represents the length of the window function; j is the imaginary unit.

[0014] Furthermore, the structure of the U-Net++ network includes:

[0015] The encoder path extracts high-level semantics layer by layer through downsampling;

[0016] The decoder path restores spatial resolution through upsampling;

[0017] Skip connections, at the same depth, gradually fuse features from different levels through lateral connections.

[0018] Furthermore, the method for calculating the multi-scale spectral loss is as follows: the denoised spectrogram and the standard clean spectrogram are scaled at multiple scales respectively; then the spectral differences at each scale are calculated, and the average value is obtained to obtain the multi-scale spectral loss.

[0019] Furthermore, the mean square error loss is calculated by calculating the mean square error of the denoised spectrum and the standard clean spectrum to obtain the mean square error loss.

[0020] Furthermore, the method for calculating the weakly supervised loss includes:

[0021] Extracting frequency features from the denoised spectrogram;

[0022] The frequency features are input into a preset weakly supervised module, and the quality score of the denoising result is output.

[0023] Weakly supervised loss is obtained based on the difference between the quality score of the denoising result and the preset target value.

[0024] Furthermore, the weakly supervised module consists of a convolutional neural network and fully connected layers; assuming the convolutional neural network consists of L convolutional layers, the frequency features after the l-th convolution are represented as F. l (k), whose convolution operation is represented as:

[0025] ;

[0026] ;

[0027] In the formula, F l-1 (k) represents the frequency characteristics of the (l-1)th layer; For the i-th convolutional kernel in the l-th layer, For the corresponding bias term; The activation function is represented by *, which indicates a convolution operation. (C) l-1 is the number of channels in the (l-1)th layer; F(k) is the frequency characteristic in the denoised spectrum; M is the total number of time frames; This is the denoised spectrum; m is the position index of the window function; k is the frequency index;

[0028] After several convolutional layers, the frequency features are flattened and input into the fully connected layer; assuming the weight matrix of the fully connected layer is W. f The bias term is b f The output of the fully connected layer is:

[0029] ;

[0030] In the formula, The predicted value is from the weakly supervised module and usually represents the quality score of the denoising result.

[0031] Furthermore, the formula for calculating the weak supervision loss is as follows:

[0032] ;

[0033] In the formula, L weak This is the weakly supervised loss; N represents the length of the window function. The quality score of the denoising result corresponding to the magnetic anomaly signal at time n.

[0034] Furthermore, the formula for backpropagating to update the parameters of the U-Net++ network is:

[0035] ;

[0036] In the formula, For the parameters of the U-Net++ network; L total Total loss; L spec For multi-scale spectral loss; L MSE For mean squared error loss; L weak Losses due to weak oversight; These are the hyperparameters for multi-scale spectral loss, mean square error loss, and weak supervision loss, respectively.

[0037] Another object of the present invention is to provide a neural network magnetic anomaly signal denoising system combining weakly supervised learning, for implementing the above method, comprising:

[0038] The magnetic anomaly signal acquisition module is used to acquire noisy magnetic anomaly signals.

[0039] The magnetic anomaly signal conversion module is used to convert noisy magnetic anomaly signals into noisy spectrograms based on short-time Fourier transform.

[0040] The spectrogram denoising module is used to denoise noisy spectrograms based on the U-Net++ network to obtain denoised spectrograms.

[0041] The total loss determination module is used to calculate the multi-scale spectral loss, mean square error loss, and weak supervision loss in real time based on the denoised spectrum, and determine the total loss.

[0042] The denoising signal output module is used to convert the denoised spectrum back to the time domain signal based on the inverse short-time Fourier transform to obtain the denoised signal.

[0043] The parameter update module is used to update the parameters of the U-Net++ network through backpropagation.

[0044] This invention provides a neural network-based magnetic anomaly signal denoising method combining weakly supervised learning. By using a U-Net++ network with weakly supervised learning to denoise magnetic anomaly signals, it achieves a dual breakthrough in accuracy preservation and efficiency improvement. On one hand, it fully inherits the high-precision fitting capability of the U-Net++ network for micro-noise—through a dense skip connection structure, this network can directly transmit the noise detail features extracted from the shallow layer to the deep decoding module, accurately capturing micro-interferences in the magnetic anomaly signal such as weak fluctuations caused by shallow mineralization and instrument circuit noise. Its fitting error for small noise with an amplitude of less than 5nT is lower than that of the traditional U-Net, ensuring the integrity of the details of the denoised signal. On the other hand, this method significantly improves the feature learning efficiency of the U-Net++ network through deep fusion of multi-scale features and weak label information. The nested decoder of the U-Net++ network can simultaneously extract noise features from the signal. However, in traditional fully supervised learning, the U-Net++ network is prone to learning redundant features, such as overemphasizing the random fluctuations of terrain noise, wasting computational resources. Weakly supervised learning, on the other hand, can guide the U-Net++ network to prioritize the core features of the effective signal based on a limited number of weak labels, reducing the ineffective learning of irrelevant noise features. This optimization accelerates the training process of the U-Net++ network, enabling it to quickly identify the effective signal range, avoid denoising delays caused by feature redundancy, and effectively solve the core pain point of low data processing efficiency in actual exploration. Attached Figure Description

[0045] Figure 1 This is a flowchart illustrating the method for denoising magnetic anomaly signals using a neural network combined with weakly supervised learning, as provided in an embodiment of the present invention.

[0046] Figure 2 This is a schematic diagram of the structure of the U-Net++ network provided in an embodiment of the present invention.

[0047] Figure 3This is a schematic diagram of the structure of a neural network magnetic anomaly signal denoising system combining weakly supervised learning, provided in an embodiment of the present invention. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0049] To address the problems of traditional denoising methods, this invention proposes using a U-Net++ network combined with weakly supervised learning for geomagnetic noise denoising. This method retains U-Net++'s high-precision fitting ability for microscopic noise while significantly reducing reliance on professionally labeled data by fusing multi-scale features and weak label information, thus significantly improving the model's generalization ability in complex noisy environments.

[0050] The entire process begins with a noisy magnetic anomaly signal as input. First, a Short-Time Fourier Transform (STFT) is used to convert the signal into a spectrogram. This spectrogram is then input into the U-Net++ network for denoising, generating a clean spectrogram. An Inverse Short-Time Fourier Transform (ISTFT) is then used to convert the denoised spectrum back to the time domain, yielding the final denoised signal. During training, the system simultaneously calculates three losses: multi-scale spectral loss to assess the quality of spectral reconstruction, mean square error loss to measure the accuracy of signal reconstruction, and weakly supervised loss to guide learning using limited labeled data. These losses are weighted and combined into a total loss function, which updates the network parameters through backpropagation. When the total loss falls below a set threshold, training is complete and the denoising result is output; otherwise, iterative optimization continues, forming a complete processing loop from noisy input to clean signal output.

[0051] Specifically, such as Figure 1 As shown, in one embodiment of the present invention, a method for denoising magnetic anomaly signals using a neural network combined with weakly supervised learning is provided, comprising the following steps:

[0052] S100. Acquire the noisy magnetic anomaly signal (noisy signal).

[0053] S200, based on Short-Time Fourier Transform (STFT), converts noisy magnetic anomaly signals into noisy spectrograms.

[0054] S300, based on the U-Net++ network, performs denoising processing on the noisy spectrogram to obtain a denoised spectrogram;

[0055] S400: Calculates multi-scale spectral loss, mean square error loss, and weak supervision loss in real time based on the denoised spectrum, and determines the total loss.

[0056] S500. If the total loss is lower than the preset threshold, the denoised spectrum is converted back to the time domain signal based on the inverse short-time Fourier transform (ISTFT) to obtain the denoised signal; otherwise, the parameters of the U-Net++ network are updated through backpropagation.

[0057] In this embodiment of the invention, denoising of geomagnetic anomaly signals is achieved by introducing weakly supervised learning combined with the U-Net++ network. Weakly supervised learning, a branch of machine learning, handles learning tasks where the supervision information is incomplete, inaccurate, or imprecise. Compared to traditional supervised learning (which uses precisely labeled data for training), weakly supervised learning has significant advantages in terms of data labeling costs and data acquisition difficulties.

[0058] In a preferred embodiment of the present invention, the input time n and the noisy magnetic anomaly signal x[n] are subjected to a short-time Fourier transform. Specifically, the formula for the short-time Fourier transform is:

[0059]

[0060] In the formula, X represents the result of the short-time Fourier transform; m is the position index of the window function; k is the frequency index; and x[n] is the magnetic anomaly signal at time n. Here, is the window function; N represents the length of the window function; a is the imaginary unit. This transformation first uses the window function. Weight the signal x[n], extract a local segment of the signal, and then... Performing a discrete-time Fourier transform (DTFT) yields the spectral characteristics, thus revealing the frequency components of the signal at different time points.

[0061] like Figure 2 As shown, in a preferred embodiment of the present invention, the structure of the U-Net++ network includes:

[0062] The encoder path extracts high-level semantics layer by layer through downsampling;

[0063] The decoder path restores spatial resolution through upsampling;

[0064] Skip connections, at the same depth, gradually fuse features from different levels through lateral connections.

[0065] Specifically, the propagation characteristics of the U-Net++ network can be expressed as follows:

[0066] ;

[0067] In the formula, X i, jThe feature map representing the depth of the i-th layer and the j-th lateral connection (i.e., the spectrum map in this embodiment of the invention), Encoder i and Decoder i, j This is a convolution operation block; Concat concatenates the channels; and Upsample performs an upsampling operation.

[0068] The encoder extracts high-level semantics step by step through downsampling:

[0069] ;

[0070] In the formula, MaxPool is the max pooling layer, and ConvBlock is typically multiple convolutional layers plus an activation function. The activation function here can be the existing ReLU activation function, and its expression f(x) is:

[0071] ;

[0072] Introducing nonlinearity into the network through the ReLU activation function allows the network to learn more complex spectral feature mapping relationships, preventing the network from degenerating into a simple linear transformation.

[0073] The decoder restores spatial resolution through upsampling and fuses multi-scale features, as follows:

[0074] ;

[0075] At the same depth i, U-Net++ gradually fuses features from different levels through lateral connections j:

[0076] ;

[0077] Among them, Block i, j For the feature processing module, low-level features (such as X) 0, j It can preserve spatial details and high-rise features (X) i, 0 It can capture the global structure, with features from multiple levels working together to participate in the final segmentation:

[0078] ;

[0079] In the formula, Prediction represents the complete prediction result, F0(X) 0, j The result of processing the j-th feature at level 0 is shown in the figure. Aggregate is a simple weighted fusion strategy, and d represents the d-th feature level involved in the fusion. Multi-level fusion alleviates the conflict between details and structure in traditional U-Net.

[0080] The spectrum diagram x above after STFT transformation noisy(m.k) is input into the U-Net++ network described above, downsampled by the encoder, and upsampled by the decoder. The output layer is... By mapping the output to a reasonable range using the ReLU activation function, the denoised spectrum can be obtained.

[0081] In a preferred embodiment of the present invention, the method for calculating the multi-scale spectral loss is as follows: the denoised spectrogram and the standard clean spectrogram are scaled at multiple scales respectively; then the spectral differences at each scale are calculated, and the average value is obtained to obtain the multi-scale spectral loss.

[0082] Specifically, the denoised spectrum obtained above and standard clean spectrum Calculate the multi-scale spectral loss L at multiple scales s∈{1.0, 0.75, 0.5}. spec :

[0083] ;

[0084] In the formula, C is the number of channels, and H is... s and W s ω represents the scaled feature map size, c is the channel index, h is the height dimension index, ω is the width dimension index, and Resize is the image scaling function, which constrains the spectral similarity at different resolutions.

[0085] In a preferred embodiment of the present invention, the mean square error loss is calculated by calculating the mean square error of the denoised spectrum and the standard clean spectrum to obtain the mean square error loss.

[0086] Specifically, calculate the denoised spectrum. and standard clean spectrum The mean square error can be obtained by taking the mean square error. MSE This ensures that the overall distribution of the denoised spectrum is similar to that of the clean spectrum.

[0087] ;

[0088] In a preferred embodiment of the present invention, the method for calculating the weak supervision loss includes:

[0089] Extracting frequency features from the denoised spectrogram;

[0090] The frequency features are input into a preset weakly supervised module, and the quality score of the denoising result is output.

[0091] Weakly supervised loss is obtained based on the difference between the quality score of the denoising result and the preset target value.

[0092] Specifically, weakly supervised learning extracts frequency features from the denoised spectrogram output by the U-Net++ network. Generally, a new feature representation is obtained by averaging the denoised spectrogram over time. The extracted features can be represented as:

[0093] ;

[0094] In the formula, M represents the total number of time frames. This step is to aggregate information in the time dimension to highlight the characteristics in the frequency dimension.

[0095] Next, the extracted frequency features F(k) are input into a weakly supervised module consisting of a small convolutional neural network (CNN) and fully connected layers. The small CNN is used to further extract local patterns from the features, enhancing their expressive power. Assuming the CNN consists of L convolutional layers, the frequency features after the l-th convolution are represented as F. l (k), whose convolution operation is represented as:

[0096] ;

[0097] In the formula, F l-1 (k) represents the frequency characteristics of the (l-1)th layer; For the i-th convolutional kernel in the l-th layer, For the corresponding bias term; The activation function is represented by *, which indicates a convolution operation. (C) l-1 This represents the number of channels in the (l-1)th layer.

[0098] After several convolutional layers, the frequency features are flattened and input into the fully connected layer; assuming the weight matrix of the fully connected layer is W. f The bias term is b f The output of the fully connected layer is:

[0099] ;

[0100] In the formula, The predicted value is from the weakly supervised module and usually represents the quality score of the denoising result.

[0101] The loss function for the weakly supervised learning part is designed based on the output of the weakly supervised learning. Specifically, the weakly supervised loss L... weak The calculation formula is:

[0102] ;

[0103] In the formula, L weak This is the weakly supervised loss; N represents the length of the window function. The quality score of the denoising result corresponding to the magnetic anomaly signal at time n.

[0104] Finally, use three hyperparameters. The three loss functions mentioned above are weighted and fused to form a total loss function, balancing different supervision objectives. Specifically, the total loss L... total The calculation formula is:

[0105] ;

[0106] After calculating the total loss, determine whether it is less than the set threshold ε. If so, perform an inverse ISTFT transform to output a denoised signal. :

[0107] ;

[0108] If not, backpropagation is triggered to update the model parameters, and the denoising process of the U-Net++ network is re-entered. The specific formula for backpropagation to update the model parameters is as follows:

[0109] ;

[0110] In the formula, For the parameters of the U-Net++ network; L total Total loss; L spec For multi-scale spectral loss; L MSE For mean squared error loss; L weak Losses due to weak oversight; These are the hyperparameters for multi-scale spectral loss, mean square error loss, and weak supervision loss, respectively.

[0111] like Figure 3 As shown, in another embodiment of the present invention, a neural network magnetic anomaly signal denoising system combining weakly supervised learning is also provided to implement the above method, comprising:

[0112] The magnetic anomaly signal acquisition module 10 is used to acquire noisy magnetic anomaly signals.

[0113] The magnetic anomaly signal conversion module 20 is used to convert a noisy magnetic anomaly signal into a noisy spectrum based on short-time Fourier transform.

[0114] The spectrum denoising module 30 is used to denoise a noisy spectrum based on the U-Net++ network to obtain a denoised spectrum.

[0115] The total loss determination module 40 is used to calculate the multi-scale spectral loss, mean square error loss and weak supervision loss in real time based on the denoised spectrum, and determine the total loss.

[0116] The denoising signal output module 50 is used to convert the denoised spectrum back to the time domain signal based on the inverse short-time Fourier transform to obtain the denoised signal.

[0117] The parameter update module 60 is used to update the parameters of the U-Net++ network through backpropagation.

[0118] It should be noted that each of the above modules can be implemented as a computer program, which can run on a computer device. The computer device's memory can store the computer program that makes up each module, enabling the processor to execute each step of the above method.

[0119] It should be understood that although the steps in the flowcharts of the various embodiments of the present invention are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the various embodiments may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least a portion of the sub-steps or stages of other steps.

[0120] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Furthermore, any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory.

[0121] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for denoising magnetic anomaly signals using neural networks combined with weakly supervised learning, characterized in that, Includes the following steps: Acquire noisy magnetic anomaly signals; Based on short-time Fourier transform, the noisy magnetic anomaly signal is converted into a noisy spectrum. Based on the U-Net++ network, the noisy spectrogram is denoised to obtain a denoised spectrogram. Based on the denoised spectrum, calculate the multi-scale spectral loss, mean square error loss, and weak supervision loss in real time to determine the total loss; If the total loss is lower than the preset threshold, the denoised spectrum is converted back to the time domain signal based on the inverse short-time Fourier transform to obtain the denoised signal. Otherwise, update the parameters of the U-Net++ network through backpropagation; The method for calculating the weak supervision loss includes: Extracting frequency features from the denoised spectrogram; The frequency features are input into a preset weakly supervised module, and the quality score of the denoising result is output. Weakly supervised loss is obtained based on the difference between the quality score of the denoising result and the preset target value; The weakly supervised module consists of a convolutional neural network and fully connected layers; assuming the convolutional neural network consists of L convolutional layers, the frequency features after the l-th convolution are represented as F. l (k), whose convolution operation is represented as: ； ； In the formula, F l-1 (k) represents the frequency characteristics of the (l-1)th layer; For the i-th convolutional kernel in the l-th layer, For the corresponding bias term; The activation function is represented by *, which indicates a convolution operation. (C) l-1 is the number of channels in the (l-1)th layer; F(k) is the frequency characteristic in the denoised spectrum; M is the total number of time frames; This is the denoised spectrum; m is the position index of the window function; k is the frequency index; After several convolutional layers, the frequency features are flattened and input into the fully connected layer; assuming the weight matrix of the fully connected layer is W. f The bias term is b f The output of the fully connected layer is: ； In the formula, These are the predicted values ​​from the weakly supervised module.

2. The method for denoising magnetic anomaly signals using neural networks combined with weakly supervised learning according to claim 1, characterized in that, The formula for the short-time Fourier transform is: ； In the formula, X represents the result of the short-time Fourier transform; m is the position index of the window function; k is the frequency index; and x[n] is the magnetic anomaly signal at time n. For window functions; N represents the length of the window function; j is the imaginary unit.

3. The method for denoising magnetic anomaly signals using neural networks combined with weakly supervised learning according to claim 1, characterized in that, The structure of the U-Net++ network includes: The encoder path extracts high-level semantics layer by layer through downsampling; The decoder path restores spatial resolution through upsampling; Skip connections, at the same depth, gradually fuse features from different levels through lateral connections.

4. The method for denoising magnetic anomaly signals using neural networks combined with weakly supervised learning according to claim 1, characterized in that, The method for calculating the multi-scale spectral loss is as follows: the denoised spectrogram and the standard clean spectrogram are scaled at multiple scales respectively; then the spectral differences at each scale are calculated, and the average value is obtained to get the multi-scale spectral loss.

5. The method for denoising magnetic anomaly signals using neural networks combined with weakly supervised learning according to claim 1, characterized in that, The mean square error loss is calculated by calculating the mean square error of the denoised spectrum and the standard clean spectrum.

6. The method for denoising magnetic anomaly signals using neural networks combined with weakly supervised learning according to claim 1, characterized in that, The formula for calculating the weak supervision loss is as follows: ； In the formula, L weak This is the weakly supervised loss; N represents the length of the window function. The quality score of the denoising result corresponding to the magnetic anomaly signal at time n.

7. The method for denoising magnetic anomaly signals using neural networks combined with weakly supervised learning according to claim 1, characterized in that, The formula for updating the parameters of the U-Net++ network through backpropagation is: ； In the formula, For the parameters of the U-Net++ network; L total Total loss; L spec For multi-scale spectral loss; L MSE For mean squared error loss; L weak Losses due to weak oversight; These are the hyperparameters for multi-scale spectral loss, mean square error loss, and weak supervision loss, respectively.

8. A neural network magnetic anomaly signal denoising system combining weakly supervised learning, used to implement the method described in any one of claims 1-7, characterized in that, include: A magnetic anomaly signal acquisition module is used to acquire noisy magnetic anomaly signals. The magnetic anomaly signal conversion module is used to convert noisy magnetic anomaly signals into noisy spectrograms based on short-time Fourier transform. The spectrogram denoising module is used to denoise noisy spectrograms based on the U-Net++ network to obtain denoised spectrograms. The total loss determination module is used to calculate the multi-scale spectral loss, mean square error loss, and weak supervision loss in real time based on the denoised spectrum, and determine the total loss. The denoising signal output module is used to convert the denoised spectrum back to the time domain signal based on the inverse short-time Fourier transform to obtain the denoised signal. The parameter update module is used to update the parameters of the U-Net++ network through backpropagation.

Images