Time-frequency joint denoising method and system for geomagnetic data under multi-scale mamba

Abstract

The application discloses a time-frequency joint geomagnetic data denoising method and system under a multiscale Mamba, belongs to the geomagnetic signal processing technical field based on deep learning, and aims to solve the problem that geomagnetic data is prone to signal distortion caused by environmental electromagnetic interference. The application restores pure signals gradually through the cooperation of two-level units of coarse granularity and fine granularity, and introduces the multiscale Mamba model into the field for the first time, ingeniously designs the network position of the multiscale Mamba module, and performs feature analysis of different scales through the multiscale Mamba module. Secondly, the technical scheme of the application further introduces a dual-frequency fusion module, uses low-frequency attention parameters to modulate high-frequency, and uses high-frequency attention parameters to modulate low-frequency, realizes cross information guidance, and the mechanism enables the high-frequency and low-frequency features to be mutually calibrated before feature extraction, finally realizes feature fusion through splicing, and significantly improves the denoising effect of the model.

Description

Technical Field

[0001] This invention belongs to the field of geomagnetic signal processing technology based on deep learning, and particularly relates to a method and system for denoising time-frequency joint geomagnetic data under multi-scale Mamba. Background Technology

[0002] Geomagnetic signals, as the core carrier of geophysical fields, contain crucial information about the Earth's internal structure and space environment. Geomagnetic signal analysis results can directly serve fields such as space weather early warning, geological resource exploration, and seismic activity monitoring. However, geomagnetic data is susceptible to environmental electromagnetic interference (such as industrial noise and high-voltage power transmission interference), instrument noise, and extreme space events (such as auroral interference), leading to signal distortion and severely limiting application accuracy. Therefore, developing efficient and robust geomagnetic signal processing technologies is of great significance for geophysical observation and space security.

[0003] Geomagnetic denoising requires removing interference while preserving the true characteristics of the data. With the rapid development of deep learning technology, its application in geophysical signal processing is becoming increasingly widespread. Deep learning possesses end-to-end automatic feature learning capabilities, efficiently extracting useful information from complex geophysical signals and overcoming the limitations of traditional methods in noise processing, fine signal classification, and pattern recognition. Zhang et al. used deep residual networks to achieve automatic noise identification and suppression, largely preserving the effective signal; however, this method is highly dependent on large-scale labeled, high-quality datasets, leading to significant model training difficulties. Xu et al. introduced a self-attention mechanism into convolutional neural networks, effectively improving data inversion accuracy; however, its model structure is complex, and the debugging process is time-consuming and laborious. Liu et al. proposed a deep learning network based on autoencoders, effectively reducing the distortion of induced polarization signals in geophysical exploration; however, it is currently mainly applied to analog signals, and its practical effectiveness needs further verification. Wang et al., in the analysis of controllable source signals, combined deep residual denoising convolutional neural networks and shift-invariant sparse coding techniques to effectively remove noise and restore signal quality; however, the model's generalization ability and interpretability have certain limitations. Li et al. proposed a method based on temporal convolutional networks to remove strong noise segments from data. This method outperforms traditional methods in noise removal while preserving the structural features and physical meaning of the signal. Dong et al. proposed a method based on multi-scale strategies and spatial attention networks for seismic data denoising, capable of handling different types and intensities of noise; however, this model requires significant computational resources. Li et al. proposed a denoising method combining deep convolutional networks and long short-term memory networks, which performed well in handling complex magnetotelluric noise but is prone to overfitting. Wang et al. built the TEM-NLnet deep denoising network using an encoder-decoder architecture, achieving significant results in handling complex noise and high-resolution data.

[0004] Therefore, it is evident that further in-depth exploration of the application of deep learning in this field, improving noise reduction effects and enhancing model performance remain research hotspots. Among these, joint noise reduction based on time-domain and frequency-domain characteristics is currently a research hotspot, but how to fully leverage the advantages of time-domain and frequency-domain features still needs further exploration. Summary of the Invention

[0005] This invention aims to specifically address the problem of geomagnetic data being susceptible to signal distortion due to environmental electromagnetic interference. Utilizing deep learning technology, it provides a novel technical approach for geomagnetic signal denoising. Specifically, this invention offers a time-frequency joint geomagnetic data denoising method under multi-scale Mamba. This method is the first to introduce a multi-scale Mamba model into the field of geomagnetic data denoising. It cleverly designs the embedding position of the multi-scale Mamba module in the overall network, using the multi-scale Mamba module at multiple network locations to perform feature analysis at different scales, significantly improving the denoising accuracy of geomagnetic data. Secondly, this invention differs from traditional techniques that process the time and frequency domains independently and then fuse them. This invention designs a dual-frequency fusion module, achieving low-frequency attention parameter modulation of high-frequency data, and high-frequency attention parameter modulation of low-frequency data, fully guiding cross-information. This mechanism allows high and low frequency features to be mutually calibrated before fusion, and finally, feature fusion is achieved through splicing. Compared to traditional methods, this significantly improves the denoising effect and specifically addresses the problem of geomagnetic data being susceptible to signal distortion due to environmental electromagnetic interference.

[0006] Therefore, the present invention provides the following technical solution:

[0007] On the one hand, the present invention provides a method for denoising time-frequency joint geomagnetic data under multi-scale Mamba, comprising the following steps:

[0008] S1: Coarse-grained denoising, inputting the noisy geomagnetic signal into the neural network-based coarse-grained denoising module for initial denoising;

[0009] S2: Fine-grained denoising, wherein the fine-grained denoising module is provided with a time-domain branch and a frequency-domain branch, which are used to split the signal after preliminary denoising through channel expansion to the time-domain branch and the frequency-domain branch. Finally, the output features of the time-domain branch and the frequency-domain branch are spliced ​​and fused together and then the residuals are summed with the input noisy geomagnetic signal to obtain the denoised geomagnetic signal.

[0010] The frequency domain branch is equipped with a wavelet transform (DWT), a dual-frequency fusion module, a multi-scale Mamba module, and an inverse wavelet transform (IDWT). The wavelet transform (DWT) divides the current signal into high-frequency and low-frequency signals. The high-frequency and low-frequency signals interact through the dual-frequency fusion module. After the interaction, the high-frequency and low-frequency signals are respectively processed by the multi-scale Mamba module for signal feature extraction, and then processed by the inverse wavelet transform (IDWT) to obtain the output features of the frequency domain branch. The time domain branch is equipped with a multi-scale Mamba module.

[0011] Specifically, a geomagnetic data sample set is constructed, and the network models of the coarse-grained denoising module and the fine-grained denoising module are trained based on the geomagnetic data sample set. Then, the geomagnetic signal to be denoised is input into the trained coarse-grained denoising module and the fine-grained denoising module to obtain the denoised geomagnetic signal.

[0012] Optionally, the dual-frequency fusion module adopts a U-Net architecture of encoder-bottleneck layer-decoder, wherein a bidirectional cross-attention mechanism targeting high and low frequency features is used to replace convolution operations in the bottleneck layer, specifically:

[0013] For feature data input to the bottleneck layer ,Will Segmented into low-frequency features along the channel dimension and high frequency characteristics , , These represent the number of channels and the data length, respectively.

[0014] Low frequency characteristics After global average pooling Obtain global feature information, that is, generate statistical feature sequences at the channel level. Then based on statistical characteristic sequences High-frequency features are modulated through linear transformation and a gating mechanism with a sigmoid activation function. Obtain the calibrated high-frequency components ;

[0015] High frequency components After group normalization Obtaining spatial-level statistical information Then based on statistical information Low-frequency components are modulated through linear transformation and a gating mechanism with a sigmoid activation function. Obtain the calibrated low-frequency component ;

[0016] Finally, for and By concatenating the data to make the number of output and input channels equal, the calibrated feature data is obtained. As the output of the bottleneck layer, Represents a real number.

[0017] Optionally, in the dual-frequency fusion module, the high-frequency signal and the low-frequency signal are spliced ​​along the channel dimension and then input into the encoder; the output feature map of the decoder is a feature sequence that matches the number of channels of the high-frequency signal and the low-frequency signal, and is spliced ​​interleaved with the low-frequency signal and the high-frequency signal respectively to obtain the high-frequency signal and the low-frequency signal after information interaction.

[0018] Furthermore, when the architecture is decoded to the original length L, it is not concatenated with the input again. That is, compared with the original architecture, there is one less concatenation of the original length data. This design allows the high and low frequencies to modulate each other to the best effect. If there is an extra layer of connection, additional noise will be mixed into the interactive information, reducing the denoising effect.

[0019] Optionally, the processing procedure of the multi-scale Mamba module is as follows:

[0020] First, the input data of the multi-scale Mamba module is input into the first residual module, and the residual connection is used to enhance the feature representation and maintain gradient propagation during model training.

[0021] Subsequently, the output of the first residual module is fed into the Mamba operation to achieve long sequence feature modeling, and then fed into the second residual module;

[0022] Furthermore, the output of the second residual module is divided into three branches. One branch does not perform any processing, while the other two branches perform downsampling operations at different scales. All of these are then processed through a dropout layer, Mamba operation, and upsampling to restore the features to the original scale.

[0023] Then, the output features of the three branches are concatenated and fused.

[0024] Finally, the fused features are sequentially processed by the third residual module and Mamba operations to obtain the output features of the multi-scale Mamba module.

[0025] In particular, the present invention preferably uses Mamba for long sequence modeling and analysis after data processing at different scales during the use of the multi-scale Mamba module.

[0026] Optionally, the two branches perform downsampling operations at different scales, respectively, by performing downsampling through convolutions with strides of 2 and 4.

[0027] Optionally, the noisy geomagnetic signal samples in the geomagnetic data sample set are obtained by adding square waves, pulses, Gaussian white noise, triangular wave noise and mixed noise of different amplitudes to high-quality samples, and all samples are normalized to remove minimum values.

[0028] Secondly, the present invention also provides a system based on the above-mentioned denoising method, comprising:

[0029] The coarse-grained denoising module is used to input noisy geomagnetic signals into the neural network-based coarse-grained denoising module for initial denoising.

[0030] The fine-grained denoising module is used to split the signal after preliminary denoising through channel expansion to the time domain branch and the frequency domain branch. Finally, the output features of the time domain branch and the frequency domain branch are spliced ​​and fused together and then summed with the residual of the input noisy geomagnetic signal to obtain the denoised geomagnetic signal.

[0031] The frequency domain branch includes a wavelet transform (DWT), a dual-frequency fusion module, a multi-scale Mamba module, and an inverse wavelet transform (IDWT). The wavelet transform (DWT) divides the current signal into high-frequency and low-frequency signals. The high-frequency and low-frequency signals interact through the dual-frequency fusion module. After interaction, the high-frequency and low-frequency signals undergo feature extraction by the multi-scale Mamba module, and then the output features of the frequency domain branch are obtained by the inverse wavelet transform (IDWT). The time domain branch includes a multi-scale Mamba module.

[0032] The sample set construction module is used to construct geomagnetic data sample sets;

[0033] The training module is used to train the network models of the coarse-grained denoising module and the fine-grained denoising module based on the geomagnetic data sample set.

[0034] In addition, the present invention provides a computer device, comprising: one or more processors and a memory storing one or more computer programs;

[0035] The processor invokes a computer program to achieve the following:

[0036] The steps of a time-frequency joint geomagnetic data denoising method under multi-scale Mamba.

[0037] Fourthly, the present invention also provides a computer-readable storage medium storing a computer program, which is invoked by a processor to implement the following:

[0038] The steps of a time-frequency joint geomagnetic data denoising method under multi-scale Mamba.

[0039] Compared with the prior art, the present invention achieves the following effects:

[0040] This invention is the first to propose introducing a multi-scale Mamba model into the field of geomagnetic data denoising. It cleverly designs the embedding position of the multi-scale Mamba module within the overall network, exploring the application of the multi-scale Mamba model in this field and providing a novel deep learning-based geomagnetic data denoising technique that significantly improves the denoising accuracy of geomagnetic data. This deep learning network uses a two-level collaborative approach of "coarse-grained + fine-grained" units to gradually restore the clean signal: the coarse-grained denoising unit mainly focuses on large-scale, obvious noise, initially outlining the signal contour; the fine-grained denoising unit processes the "fine noise" remaining after coarse-grained processing, repairing and optimizing the microscopic features of the signal, and outputting the final denoised geomagnetic signal. This method has high generalization ability for various types of noise (such as unseen sawtooth waves), maintaining a superior denoising effect.

[0041] The technical solution of this invention differs from the traditional method of combining time and frequency domains by designing a dual-frequency fusion module. In particular, this dual-frequency fusion module is based on the U-Net architecture and employs a bidirectional cross-attention module targeting high and low frequency features in the bottleneck layer. This allows the input features to be segmented into low-frequency components (X0) and high-frequency components (X1), which are not processed independently but are guided by cross-information: the low-frequency components provide channel attention to refine the response of high-frequency features, while the high-frequency components provide spatial attention to enhance the details of low-frequency features. This mechanism allows high and low frequency features to be mutually calibrated before fusion, and finally feature fusion is achieved by splicing. This makes fuller use of the advantages of time and frequency domain features and significantly improves the denoising effect. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the time-frequency joint geomagnetic data denoising technology route under multi-scale Mamba provided in Embodiment 1 of the present invention;

[0043] Figure 2 This is a schematic diagram of a time-frequency joint geomagnetic data denoising network under multi-scale Mamba provided in Embodiment 1 of the present invention;

[0044] Figure 3 This is a schematic diagram of the structure of the multi-scale Mamba module provided in Embodiment 1 of the present invention;

[0045] Figure 4 This is a schematic diagram of the dual-frequency fusion module provided in Embodiment 1 of the present invention;

[0046] Figure 5 This is a comparison of the denoising effect of typical noise segments of JGU station data in a certain area during the experimental verification of this invention. The horizontal axis is time (minutes) and the vertical axis is amplitude (nits).

[0047] Figure 6This is the result of a single-layer Haar wavelet decomposition of the measured geomagnetic signal and the TFMSM denoised signal from a JGU station in a certain area during the experimental verification of this invention. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. The technical features involved in the various embodiments of the invention described below can be combined with each other as long as they do not conflict with each other.

[0049] It should be noted that although functional modules are divided in the device schematic diagram and a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than the module division in the device or the order in the flowchart. The terms "first," "second," etc., in the specification, claims, and the aforementioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0050] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0051] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0052] This invention provides a time-frequency joint denoising method for geomagnetic data under multi-scale Mamba, specifically addressing the problem of signal distortion caused by environmental electromagnetic interference in geomagnetic data. This method primarily utilizes wavelet transform and a uniquely designed dual-frequency fusion module to achieve joint time-frequency processing. Simultaneously, it employs a multi-scale Mamba model to perform feature analysis on the geomagnetic data at different scales, thereby achieving high-precision denoising of the geomagnetic data. The following will illustrate this invention with specific examples. Example 1

[0053] This embodiment provides a method for denoising time-frequency joint geomagnetic data under multi-scale Mamba, including the following steps:

[0054] S1: Coarse-grained denoising, inputting the noisy geomagnetic signal into the neural network-based coarse-grained denoising module for initial denoising;

[0055] S2: Fine-grained denoising. This module includes time-domain and frequency-domain branches. The initially denoised signal is split into these branches after channel expansion. Finally, the output features from the time-domain and frequency-domain branches are concatenated and fused, then summed with the residuals of the input noisy geomagnetic signal to obtain the denoised geomagnetic signal. The fused signal is a learned noise signal, i.e., a correction signal, used to correct the original noisy geomagnetic signal.

[0056] like Figure 1 As shown, the frequency domain branch includes a wavelet transform (DWT), a dual-frequency fusion module, a multi-scale Mamba module, and an inverse wavelet transform (IDWT). The DWT transform divides the current signal into high-frequency and low-frequency signals. The high-frequency and low-frequency signals interact through the dual-frequency fusion module. After the interaction, the high-frequency and low-frequency signals are respectively processed by the multi-scale Mamba module for signal feature extraction, and then transformed by IDWT to obtain the output features of the frequency domain branch. The time domain branch includes at least a multi-scale Mamba module. Finally, the two result signals are added together, and then the "fusion module" integrates the time domain and frequency domain feature information and performs residual summation with the input noisy geomagnetic signal to output the denoised geomagnetic signal.

[0057] The process involves constructing a geomagnetic data sample set, training network models for a coarse-grained denoising module and a fine-grained denoising module based on the geomagnetic data sample set, and then inputting the geomagnetic signal to be denoised into the trained coarse-grained denoising module and fine-grained denoising module to obtain the denoised geomagnetic signal.

[0058] In the above network model, one of the core aspects of this invention is the introduction of a multi-scale Mamba module and the clever design of its position in the overall network. The second core aspect is the design and introduction of a dual-frequency fusion module.

[0059] Figure 2 This is a specific implementation structure of the time-frequency joint geomagnetic data denoising model TFMSM in the embodiments of the present invention. The coarse-grained denoising module adopts the DnCNN coarse-grained denoising unit, which is an existing network and therefore will not be described in detail. In the figure, repeating 8 times means repeating the channel dimension of the data 8 times to achieve expansion. In subsequent processes, it is best to preserve the details of the original data, but this is not the core and focus of the present invention, so it is not specifically limited.

[0060] like Figure 2The TFMSM network shown first performs initial noise reduction on the input data (noisy geomagnetic signal) through a coarse-grained denoising unit (DnCNN). Then, a convolutional module expands the feature channels to enrich the feature representation dimensions. The expanded features are then split into two parallel branches for refined processing: one is the time-domain branch, where features are directly input into a multi-scale Mamba module for temporal feature modeling; the other is the frequency-domain branch, where features are first decomposed into high-frequency and low-frequency components via wavelet transform. After cross-frequency feature interaction via a dual-frequency fusion unit (dual-frequency fusion module), these components are fed into the multi-scale Mamba module for frequency-domain feature learning. The processed features are then reconstructed into the IDWT using inverse wavelet transform as the frequency-domain branch output. Finally, the outputs of the time-domain and frequency-domain branches are concatenated and integrated, and then summed with the residuals of the input noisy geomagnetic signal to obtain the final denoised geomagnetic data.

[0061] The calculation process of the TFMSM network is as follows:

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] In the formula, It is the input noisy geomagnetic signal. It is a signal that has undergone primary denoising using the DnCNN network. For the set of real numbers, and These are the denoised signals from the time domain and frequency domain branches, respectively. This is the final denoised signal. These represent the results of high-frequency and low-frequency signals in the frequency domain branch after passing through a multi-scale Mamba module, respectively. DnCNN represents the DnCNN network, Mconv represents the processing after two convolutional modules, and DWT and iDWT represent the discrete wavelet transform and inverse wavelet transform operations, respectively. BiFMU represents the multi-scale Mamba module, BiFMU represents the dual-frequency fusion module, and Fuse represents the fusion module. Represents the time-domain denoised signal and frequency domain denoised signal The splicing is performed in the channel dimension. Represents the signal after time-frequency fusion. This indicates the signal processed by the convolution module.

[0070] like Figure 3 As shown in the figure, the preferred embodiment of the present invention uses the multi-scale Mamba module shown in the figure. The specific data processing procedure is as follows:

[0071] First, the input data of the multi-scale Mamba module is fed into the first residual module, which uses residual connections to enhance feature representation and maintain gradient propagation during model training.

[0072] Subsequently, the output data of the first residual module is fed into the Mamba operation to achieve long sequence feature modeling.

[0073] Next, the data passes through a second residual module to maintain gradient flow.

[0074] Then, the output features of the second residual module are input into three branches: one branch is left unprocessed as the residual branch, which helps to better preserve gradients during model training; in this embodiment, the other two branches are downsampled using convolutions with strides of 2 and 4, respectively, to perform multi-scale feature analysis. For each of these two downsampling branches, after the downsampling operation, regularization is performed using a dropout layer, followed by further feature mining using the Mamba module. Then, upsampling is performed using a transposed convolution to restore the features to their original scale. Subsequently, the features are concatenated and fused with those from the residual branch. Finally, the concatenated features are processed sequentially by the third residual module and the Mamba module to complete the feature output of this module. The calculation process of the multi-scale Mamba module in this embodiment is as follows:

[0075]

[0076]

[0077]

[0078]

[0079]

[0080] In the formula, Conv represents a convolutional layer, IN represents an instance normalization layer, PReLU represents a nonlinear activation function layer, Res represents the output of the residual module, and formula (6) corresponds to the processing of the first residual block; Mamba represents Mamba network operation. and These represent using downsampling units with strides of 2 and 4, respectively. "Drop" indicates discarding layers to prevent overfitting. This indicates that upsampling is achieved through data rearrangement. This represents the input to the multi-scale Mamba module. , , These represent data signal features at the original scale, half scale, and quarter scale, respectively. This represents the output of the multi-scale Mamba module.

[0081] It should be noted that the multi-scale Mamba module in this embodiment uses convolutional downsampling. In other feasible embodiments, max pooling downsampling or methods that perform interval sampling of the data and then stack the channels are also acceptable in principle. However, convolutional downsampling is more effective in this field, while the latter two methods leave more residual noise glitches. The selection principle for the downsampling module in the technical solution of this invention is that it should be insensitive to noise while retaining more data details.

[0082] like Figure 4 As shown, the dual-frequency fusion module in this embodiment can simultaneously enhance both the low-frequency approximation component and the high-frequency detail component of the signal. This embodiment adopts a U-Net architecture of encoder-bottleneck layer-decoder and introduces grouped convolution and attention mechanisms to effectively extract multi-scale features while maintaining the independence between different channels and enhancing the expressive power of key features.

[0083] The network forward propagation process is as follows:

[0084] Encoder: First, it converts the low-frequency component F of the input... L With high frequency component F H The sequence is concatenated along the channel dimension and shallow feature extraction is performed through an initial fusion module consisting of grouped convolutions and PReLU activation functions. Subsequently, the feature maps are passed sequentially through two downsampling encoder modules, gradually compressing the sequence length to 1 / 4 of the original length while increasing the channel dimension to expand the feature space.

[0085] Bottleneck layer: Employs a bidirectional cross-attention module targeting high and low frequency features.

[0086] First, the feature map is equally divided along the channel dimension to obtain the corresponding low-frequency feature X0 and high-frequency feature X1;

[0087] Then, channel attention features are extracted from low-frequency feature X0, and high-frequency feature X1 is modulated to obtain fused high-frequency features; spatial attention features are extracted from high-frequency feature X1, and low-frequency feature X0 is modulated to obtain fused low-frequency features.

[0088] Finally, the processed results are reassembled to adaptively fuse and calibrate the high and low frequency characteristic responses.

[0089] The decoder performs upsampling through transposed convolutions to restore spatial resolution and fuses feature maps of the same scale from the encoder path via skip connections to supplement details that may have been lost during downsampling. Finally, the output module converts the decoded feature maps into a format similar to the input F. L F H The residual maps, matched with the number of component channels, are interleaved and stitched together with the original input to obtain the enhanced low-frequency output F. OUTL With high frequency output F OUTH .

[0090] In this bottleneck layer, the input features are segmented into low-frequency (X0) and high-frequency (X1) components. These components are not processed independently, but rather guided by cross-information: the low-frequency components provide channel attention to refine the responses of the high-frequency features, while the high-frequency components provide spatial attention to enhance the details of the low-frequency features. This mechanism allows the high- and low-frequency features to be mutually calibrated before fusion, ultimately achieving feature fusion through concatenation.

[0091] The specific processing procedure of the bidirectional cross-attention module is as follows:

[0092] For feature data input to the bottleneck layer ,Will Segmented into low-frequency features along the channel dimension and high frequency characteristics , , These represent the number of channels and the data length, respectively.

[0093] Low frequency characteristics After global average pooling Obtain global feature information, that is, generate statistical feature sequences at the channel level. Then based on statistical characteristic sequences High-frequency features are modulated through linear transformation and a gating mechanism with a sigmoid activation function. Obtain the calibrated high-frequency components ;

[0094] ;

[0095] ;

[0096] In the formula, To enhance the representation of statistical information features, a linear transformation function is used, where w is the data length. Low frequency characteristics Eigenvalues i , Yes Parameters for scaling and offsetting. It is the sigmoid activation function. This refers to the calibrated high-frequency components.

[0097] High frequency components After group normalization Obtaining spatial-level statistical information Then based on statistical information Low-frequency components are modulated through linear transformation and a gating mechanism with a sigmoid activation function. Obtain the calibrated low-frequency component ;

[0098] ;

[0099] In the formula, Yes Parameters for scaling and offsetting. This refers to the calibrated low-frequency components.

[0100] Finally, for and By concatenating the data to make the number of output and input channels equal, the calibrated feature data is obtained. This serves as the output of the bottleneck layer.

[0101] In summary, by cross-modulating high and low frequency feature information, high and low frequency component data with richer details can be generated, effectively improving the denoising effect of the model.

[0102] It should also be noted that the bottleneck layer of this invention uses a cross-attention mechanism instead of convolution for processing, and when the architecture decodes to the original length L, it does not concatenate with the input again (i.e., the same length of data before the first downsampling and after the last deconvolution (upsampling) is not concatenated). In other words, compared with the original architecture, there is one less concatenation of the original length of data. This design allows the high and low frequencies to modulate each other to the best effect. If there is an extra layer of connection, additional noise will be mixed into the interaction information, reducing the denoising effect.

[0103] Furthermore, by using grouped convolutions in the encoder and decoder, it can be ensured that high- and low-frequency information will only enrich their respective feature information in the encoding and decoding links without interactive pollution, thus improving the effect of cross-attention at the bottleneck layer.

[0104] Regarding the construction of geomagnetic data sample sets, there are already many feasible techniques in this field, and this invention does not impose specific limitations on them. In this embodiment, the preferred noisy geomagnetic signal samples are obtained by adding several square waves, pulses, Gaussian white noise, triangular wave noise, and mixed noise of different amplitudes to high-quality samples, and all samples have undergone minimum value removal processing to enhance the differences between samples.

[0105] For example, high-quality data was selected from publicly available geomagnetic data from geomagnetic observatories in different regions of the world. The geomagnetic data used was minute-by-minute, with 1440 sampling points as the sample length (corresponding to a 24-hour day), which conforms to the diurnal periodic variation of geomagnetic signals. 2480 high-quality samples were carefully selected, and 10 different amplitudes of square wave, pulse, Gaussian white noise, triangular wave noise, and mixed noise were added, ultimately resulting in 124,000 samples, including 99,200 training samples (80%) and 24,800 validation samples (20%).

[0106] Regarding model training, this embodiment selects the Adam optimizer with a learning rate of 0.001%, a loss function of mean squared error (MSE), and an epoch of 100. The training process is based on existing technology and therefore will not be described in detail.

[0107] Experimental verification

[0108] To comprehensively evaluate the performance of this network model, samples were input into the improved U-Net network and the DRS network, respectively. ] The TFMSM network model (in this invention) was trained, and the training results are shown in Table 1. It can be seen that the TFMSM network proposed in this paper has the best performance, with a training set loss of 0.0000027532 and a validation set loss of 0.0000145065. The model achieves good denoising effect, improving the average signal-to-noise ratio of the sample library from 17.76 to 42.76, which is better than the results of the improved Unet and DRS networks.

[0109] Table 1 Training results of improved U-Net, DRS, and TFMSM networks

[0110]

[0111] Data containing significant noise was selected to test the effectiveness of the method proposed in this invention, while high-quality data collected from the same station was used to verify the reliability of the method. Figure 5 and Figure 6 The time-domain and frequency-domain processing results of a JGU station located in a certain region are shown. Figure 5The denoising effect is shown in the figure for a typical noise segment, where all three components of the data are subject to strong pulse interference. Blue represents the measured noisy geomagnetic signal with significant strong pulse interference, while red represents the denoised signal processed by the TFMSM network. The denoising effect closely matches the overall trend of the measured signal, effectively suppressing strong pulse interference, and the temporal domain denoising effect is clearly visible. Figure 6 The results of single-level Haar wavelet decomposition of the measured geomagnetic signal from the JGU station and the TFMSM-denoised signal are presented, i.e., the frequency domain processing results. It can be seen that the denoised signal continues its excellent performance in the time domain, and the noise suppression effect is equally outstanding: its high-frequency detail components are cleaner, the sharp noise present in the original measured signal has been basically eliminated, and the spectral characteristics are more regularized. (See Figure 5 for details.) Figure 6 The analysis results show that the TFMSM network can effectively suppress most of the noise in geomagnetic data in both the time and frequency domains. It not only ensures the consistency between the denoised signal and the original valid information, but also achieves accurate filtering of interference noise, fully verifying its good effect in processing geomagnetic station measured data.

[0112] In summary, the technical solution of this invention achieves precise suppression of geomagnetic noise of different scales and types through the collaboration of two-level denoising: "coarse-grained" and "fine-grained". This effectively improves the signal-to-noise ratio of geomagnetic data and preserves signal fluctuation information to the maximum extent. It provides an efficient and reliable solution for noise processing of geomagnetic data and is expected to provide high-quality data support for basic research and applications in fields such as Earth's internal structure analysis and space environment monitoring.

[0113] In some embodiments, the present invention provides a system based on the above-described denoising method, including a coarse-grained denoising module, a fine-grained denoising module, a sample set construction module, and a training module that are connected in sequence or to each other.

[0114] The coarse-grained denoising module is used to input noisy geomagnetic signals into the neural network-based coarse-grained denoising module for initial denoising.

[0115] The fine-grained denoising module is used to split the signal after preliminary denoising into time domain branch and frequency domain branch after channel expansion. Finally, the output features of the time domain branch and frequency domain branch are spliced ​​and fused together, and the residual is summed with the input noisy geomagnetic signal to obtain the denoised geomagnetic signal.

[0116] The sample set construction module is used to construct geomagnetic data sample sets.

[0117] The training module is used to train the network models of the coarse-grained denoising module and the fine-grained denoising module using a geomagnetic data sample set.

[0118] The frequency domain branch includes a DWT transform, a dual-frequency fusion module, a multi-scale Mamba module, and an IDWT transform. The DWT transform splits the current signal into high-frequency and low-frequency signals. The high-frequency and low-frequency signals exchange information through the dual-frequency fusion module. After information exchange, the high-frequency and low-frequency signals undergo feature extraction by the multi-scale Mamba module, and then are transformed by IDWT to obtain the output features of the frequency domain branch. The time domain branch includes at least a multi-scale Mamba module. The specific implementation process is described in the aforementioned method embodiment.

[0119] It should also be understood that the specific implementation process of each module is described in the above method. This invention will not repeat it here. The above division of functional modules is only for illustrative purposes. In some embodiments, some functional modules can be combined and some functional modules can be separated. Each functional module can be implemented in software, hardware, or a combination of software and hardware. The software and hardware devices include, but are not limited to, general-purpose computer equipment, programmable gate arrays, digital signal processors, microprocessors and their corresponding programming or burning software.

[0120] For example, in some implementations, the coarse-grained denoising module and the fine-grained denoising module can be integrated as a model building and training module, used to build a time-frequency joint geomagnetic data denoising model and train the model based on the geomagnetic data sample set; the constructed time-frequency joint geomagnetic data denoising model includes at least a coarse-grained denoising module and a fine-grained denoising module.

[0121] In some embodiments, the present invention also provides a computer device, including: one or more processors and a memory storing one or more computer programs; wherein the processor invokes the computer programs to implement:

[0122] The steps of a multi-scale Mamba-based time-frequency joint geomagnetic data denoising method. For example, the specific execution is as follows:

[0123] A geomagnetic data sample set is constructed, and network models for coarse-grained denoising and fine-grained denoising modules are trained based on the geomagnetic data sample set. Then, the geomagnetic signal to be denoised is input into the trained coarse-grained denoising and fine-grained denoising modules to obtain the denoised geomagnetic signal.

[0124] For example, in specific implementation:

[0125] First, pre-trained coarse-grained denoising and fine-grained denoising modules are loaded. Then, coarse-grained denoising is performed by inputting the noisy geomagnetic signal into the neural network-based coarse-grained denoising module for initial denoising. Finally, fine-grained denoising is performed. The fine-grained denoising module has time-domain and frequency-domain branches, which are used to split the initially denoised signal into the time-domain and frequency-domain branches after channel expansion. Finally, the output features of the time-domain and frequency-domain branches are spliced ​​and fused, and the residuals are summed with the input noisy geomagnetic signal to obtain the denoised geomagnetic signal.

[0126] For details on the implementation of each step, please refer to the description of the aforementioned denoising method.

[0127] It should be understood that, in the embodiments of the present invention, the processor may be a Central Processing Unit (CPU), or it may be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor. The memory may include read-only memory and random access memory, and provides instructions and data to the processor. A portion of the memory may also include non-volatile random access memory. For example, the memory may also store device type information.

[0128] In some embodiments, the present invention also provides a computer-readable storage medium storing a computer program, which is invoked by a processor to implement the following:

[0129] The steps of a time-frequency joint geomagnetic data denoising method under multi-scale Mamba.

[0130] For example, in specific implementation:

[0131] A geomagnetic data sample set is constructed, and network models for coarse-grained denoising and fine-grained denoising modules are trained based on the geomagnetic data sample set. Then, the geomagnetic signal to be denoised is input into the trained coarse-grained denoising and fine-grained denoising modules to obtain the denoised geomagnetic signal.

[0132] For example, in specific implementation:

[0133] First, pre-trained coarse-grained denoising and fine-grained denoising modules are loaded. Then, coarse-grained denoising is performed by inputting the noisy geomagnetic signal into the neural network-based coarse-grained denoising module for initial denoising. Finally, fine-grained denoising is performed. The fine-grained denoising module has time-domain and frequency-domain branches, which are used to split the initially denoised signal into the time-domain and frequency-domain branches after channel expansion. Finally, the output features of the time-domain and frequency-domain branches are spliced ​​and fused, and the residuals are summed with the input noisy geomagnetic signal to obtain the denoised geomagnetic signal.

[0134] For details on the implementation of each step, please refer to the description of the aforementioned denoising method embodiment.

[0135] The readable storage medium is a computer-readable storage medium, which can be an internal storage unit of the hardware and software device described in any of the foregoing embodiments, such as the hard drive or memory of the controller. The readable storage medium can also be an external storage device of the controller, such as a plug-in hard drive, Smart MediaCard (SMC), Secure Digital (SD) card, or Flash Card equipped on the controller. Further, the readable storage medium can include both internal storage units and external storage devices of the controller. The readable storage medium is used to store the computer program and other programs and data required by the controller. The readable storage medium can also be used to temporarily store data that has been output or will be output.

[0136] Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned readable storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0137] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-readable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. This application refers to flowchart illustrations and / or instructions executed by a processor of a method, apparatus (system), and computer program product according to embodiments of this application to create means for implementing the functions specified in one or more flowchart illustrations and / or one or more block diagrams. These computer program instructions may also be stored in a computer-readable storage medium capable of directing a computer or other programmable data processing apparatus to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means that implement the functions specified in one or more flowchart illustrations and / or one or more block diagrams. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, such that the instructions, which execute on the computer or other programmable apparatus, provide steps for implementing the functions specified in one or more flowcharts and / or one or more blocks of a block diagram.

[0138] It should be emphasized that the examples described in this invention are illustrative rather than limiting. Therefore, this invention is not limited to the examples described in the specific embodiments. Any other embodiments derived by those skilled in the art based on the technical solutions of this invention, without departing from the spirit and scope of this invention, whether modifications or substitutions, are also within the protection scope of this invention.

Claims

1. A method for denoising time-frequency joint geomagnetic data under multi-scale Mamba, characterized in that: Includes the following steps: S1: Coarse-grained denoising, inputting the noisy geomagnetic signal into the neural network-based coarse-grained denoising module for initial denoising; S2: Fine-grained denoising, wherein the fine-grained denoising module is provided with a time-domain branch and a frequency-domain branch, which are used to split the signal after preliminary denoising through channel expansion to the time-domain branch and the frequency-domain branch. Finally, the output features of the time-domain branch and the frequency-domain branch are spliced ​​and fused together and then the residuals are summed with the input noisy geomagnetic signal to obtain the denoised geomagnetic signal. The frequency domain branch is equipped with a wavelet transform (DWT), a dual-frequency fusion module, a multi-scale Mamba module, and an inverse wavelet transform (IDWT). The wavelet transform (DWT) divides the current signal into high-frequency and low-frequency signals. The high-frequency and low-frequency signals interact through the dual-frequency fusion module. After the interaction, the high-frequency and low-frequency signals are respectively processed by the multi-scale Mamba module for signal feature extraction, and then processed by the inverse wavelet transform (IDWT) to obtain the output features of the frequency domain branch. The time domain branch is equipped with a multi-scale Mamba module. The dual-frequency fusion module adopts a U-Net architecture of encoder-bottleneck layer-decoder. Specifically, in the bottleneck layer, a bidirectional cross-attention mechanism targeting high and low frequency features is used to replace convolutional operations. For feature data input to the bottleneck layer ,Will Segmented into low-frequency features along the channel dimension and high frequency characteristics , , These represent the number of channels and the data length, respectively; low-frequency characteristics. After global average pooling Obtain global feature information, that is, generate statistical feature sequences at the channel level. Then based on statistical characteristic sequences High-frequency features are modulated through linear transformation and a gating mechanism with a sigmoid activation function. Obtain the calibrated high-frequency components High-frequency components After group normalization Obtaining spatial-level statistical information Then based on statistical information Low-frequency components are modulated through linear transformation and a gating mechanism with a sigmoid activation function. Obtain the calibrated low-frequency component Finally, regarding and By concatenating the data to make the number of output and input channels equal, the calibrated feature data is obtained. Feature data As the output of the bottleneck layer Represent real numbers; The processing procedure of the multi-scale Mamba module is as follows: First, the input data of the multi-scale Mamba module is fed into the first residual module, where residual connections are used to enhance feature representation and maintain gradient propagation during model training. Then, the output of the first residual module is fed into a Mamba operation to model long-sequence features, and then into the second residual module. Next, the output of the second residual module is divided into three branches: one branch is left unprocessed, while the other two branches undergo downsampling operations at different scales, followed by a dropout layer, Mamba operation, and upsampling to restore the features to their original scale. Then, the output features from the three branches are concatenated and fused. Finally, the fused features are sequentially processed through the third residual module and Mamba operation to obtain the output features of the multi-scale Mamba module. Specifically, a geomagnetic data sample set is constructed, and the network models of the coarse-grained denoising module and the fine-grained denoising module are trained based on the geomagnetic data sample set. Then, the geomagnetic signal to be denoised is input into the trained coarse-grained denoising module and the fine-grained denoising module to obtain the denoised geomagnetic signal.

2. The method according to claim 1, characterized in that: In the dual-frequency fusion module, the high-frequency signal and the low-frequency signal are spliced ​​along the channel dimension and then input into the encoder; the output feature map of the decoder is a feature sequence that matches the number of channels of the high-frequency signal and the low-frequency signal, and is spliced ​​with the low-frequency signal and the high-frequency signal respectively to obtain the high-frequency signal and the low-frequency signal after information interaction.

3. The method according to claim 1, characterized in that: The process involves two branches performing downsampling operations at different scales. One branch performs downsampling through a convolution with a stride of 2, while the other branch performs downsampling through a convolution with a stride of 4.

4. The method according to claim 1, characterized in that: The noisy geomagnetic signal samples in the geomagnetic data sample set were obtained by adding square waves, pulses, Gaussian white noise, triangular wave noise and mixed noise of different amplitudes to high-quality samples, and all samples were normalized to remove minimum values.

5. A system based on the method of any one of claims 1-4, characterized in that: include: The coarse-grained denoising module is used to input noisy geomagnetic signals into the neural network-based coarse-grained denoising module for initial denoising. The fine-grained denoising module is used to split the signal after preliminary denoising through channel expansion to the time domain branch and the frequency domain branch. Finally, the output features of the time domain branch and the frequency domain branch are spliced ​​and fused together and then summed with the residual of the input noisy geomagnetic signal to obtain the denoised geomagnetic signal. The frequency domain branch includes a wavelet transform (DWT), a dual-frequency fusion module, a multi-scale Mamba module, and an inverse wavelet transform (IDWT). The wavelet transform (DWT) divides the current signal into high-frequency and low-frequency signals. The high-frequency and low-frequency signals interact through the dual-frequency fusion module. After interaction, the high-frequency and low-frequency signals undergo feature extraction by the multi-scale Mamba module, and then the output features of the frequency domain branch are obtained by the inverse wavelet transform (IDWT). The time domain branch includes a multi-scale Mamba module. The sample set construction module is used to construct geomagnetic data sample sets; The training module is used to train the network models of the coarse-grained denoising module and the fine-grained denoising module based on the geomagnetic data sample set.

6. A computer device, characterized in that: include: One or more processors; A memory that stores one or more computer programs; The processor invokes a computer program to achieve the following: The steps of the method according to any one of claims 1-4.

7. A computer-readable storage medium, characterized in that: The computer program is stored and is invoked by the processor to implement: The steps of the method according to any one of claims 1-4.

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