Distributed optical fiber sound wave sensing signal denoising and encryption integrated method and system based on compressed sensing theory

Abstract

The invention belongs to the field of signal processing and geophysical exploration, and discloses a distributed optical fiber sound wave sensing signal denoising and encryption integrated method and system based on a compressed sensing theory, and the method comprises the steps: measuring the phase change of a DAS system based on an optical fiber Rayleigh scattering signal, arranging the phase change into time-gather domain waveform data, and carrying out the time-gather domain waveform data; performing non-uniform sampling according to the sparse characteristic of an effective frequency band signal in the time-gather domain waveform data to obtain under-sampling data; transform domain sparsity analysis in compressed sensing is carried out on the undersampled data, and optimal transformation is selected; carrying out compressed sensing FISTA algorithm iterative convergence on the optimal transformation, then carrying out wavelet thresholding denoising coefficient comparison, and carrying out data channel encryption on the basis of data intrinsic sparsity characteristics by applying compressed sensing and applying a CS-POCS algorithm; and carrying out compressed sensing reconstruction after coefficient screening on the processed sparse representation, and finally obtaining a de-noised and encrypted DAS waveform-gather data set.

Description

Technical Field

[0001] This invention belongs to the field of signal processing and geophysical exploration, specifically relating to an integrated method and system for denoising and encrypting distributed fiber optic acoustic wave sensing signals based on compressed sensing theory. Background Technology

[0002] In the fields of signal processing and geophysical exploration, especially in shallow exploration, distributed optical fiber acoustic sensing (DAS) systems are increasingly becoming the mainstream method for shallow surface exploration. DAS systems achieve real-time sensing of subtle strain disturbances over a large spatial scale by continuously sampling along the fiber optic axis, thereby obtaining multidimensional time-series data with high spatial resolution and high temporal sampling rate. It has increasingly wide applications in full waveform inversion and background noise inversion. However, since DAS systems are essentially based on the phase change of the Rayleigh scattering signal in the optical fiber, the observation results are easily affected by various factors such as optical coherence, fiber coupling state, environmental disturbances, and system electronic noise, resulting in the acquired raw data exhibiting significant non-stationarity and strong noise characteristics. Due to limitations in system bandwidth, sampling rate, and storage resources, the DAS data acquired in some application scenarios may also suffer from incomplete sampling, missing data, or limited spatial resolution, thus preventing the observation data from directly and accurately reflecting the continuous changing characteristics of the measured physical field. Currently, there are very few methods for systematically purifying, denoising, and reliably encrypting DAS signals. Therefore, how to effectively reconstruct and suppress noise from raw DAS data under the aforementioned complex data conditions has become a key technical problem restricting its further application in engineering monitoring and signal analysis. Summary of the Invention

[0003] To address the problems existing in the prior art, this invention provides an integrated method and system for denoising and encrypting distributed optical fiber acoustic wave sensor signals based on compressed sensing theory. This method is effective in purifying and reconstructing shallow seismic DAS data signals and can significantly aid in shallow exploration inversion.

[0004] To achieve the above objectives, the present invention provides the following solution: A method for integrated denoising and encryption of distributed fiber optic acoustic wave sensing signals based on compressed sensing theory, the method comprising: The phase change of the fiber Rayleigh scattering signal of the DAS system is measured and processed into time-gathered domain waveform data. Based on the sparsity characteristics of the effective frequency band signal in the time-gathered domain waveform data, non-uniform sampling is performed to obtain undersampled data. Perform sparsity analysis of the transform domain in compressed sensing on undersampled data and select the optimal transform; After the optimal transform is iteratively converged by the compressed sensing FISTA algorithm, the wavelet thresholding denoising coefficients are compared, and the data channels are encrypted by applying the CS-POCS algorithm based on the intrinsic sparsity characteristics of the data using compressed sensing. Compressed sensing reconstruction is performed on the processed sparse representation after filtering coefficients to finally obtain a denoised and encrypted DAS waveform-gather dataset.

[0005] Preferably, the method for obtaining undersampled data by performing non-uniform sampling based on the sparsity characteristics of the effective frequency band signal in the time-gather domain waveform data includes: Based on the sparse distribution characteristics of the effective frequency band signals of DAS time-gather domain waveform data in the wavelet domain, an observation matrix is ​​constructed and a sparse basis is selected. The observation matrix is ​​a two-dimensional numerical matrix of DAS time-gather domain waveform data; the sparse basis is a wavelet transform basis, a discrete cosine transform basis, and a frequency-wavenumber transform basis. Undersampled data is obtained by non-uniform downsampling of the two-dimensional numerical matrix of DAS time-gather domain waveform data containing effective signals using the observation matrix and sparse basis.

[0006] Preferably, the sparsity analysis of the transform domain in compressed sensing for undersampled data includes comparing the sparsity performance of wavelet transform, discrete cosine transform (DCT), and frequency-wavenumber transform (FK).

[0007] Preferably, the iterative convergence of the compressed sensing FISTA algorithm for the optimal transform includes: The threshold calculation formula is as follows , The standard deviation of noise. Given the signal length, a threshold scaling factor of 2.0, and the actual threshold... ; The formula for calculating residuals is: , For observation signals containing noise, It is a linear transformation matrix. For the first The signal estimate of the next iteration; The formula for calculating relative energy is: , This is the initial signal.

[0008] Preferably, the method for comparing wavelet thresholding denoising coefficients includes: For signals Perform wavelet transform to obtain coefficients denoised coefficients for: ; In the formula, The threshold value is used.

[0009] Preferably, methods for encrypting data channels using the CS-POCS algorithm based on the intrinsic sparsity characteristics of data through compressed sensing include: Based on Compressed Sensing-Alternating Direction Multiplier Method (CS-POCS), assuming the DAS data is a two-dimensional signal. ,in The number of time sampling points, For the number of channels, the interpolation objective is to extract from the sparse channel set. Restoration of the dense Dao collection ; Based on compressed sensing CS theory, DAS data exhibits sparsity in the transform domain, namely: ; In the formula, It is a sparse transformation matrix. The original signal is a sparse coefficient vector. It is sparse in the transform domain, and the sampling satisfies the finite isometry property; The POCS algorithm is used to solve the inverse problem by alternately projecting the original signal onto multiple convex sets.

[0010] Preferably, the method of solving the inverse problem by alternately projecting the original signal onto multiple convex sets using the POCS algorithm includes: Sparse constraint set: , To achieve sparsity, a threshold operation is used: ; In the formula, For the first The sparse representation after the next iteration. For the first The signal estimate of the next iteration Transformation of the basis matrix transpose For soft thresholding function: , For input values, For threshold parameters; Data consistency constraint set: ,in For the sampling matrix, the projection operation is as follows: ; Iteration formula: ; Iterate until the residual ,in, This is the threshold for the residual to terminate the iteration.

[0011] The present invention also provides an integrated system for denoising and encryption of distributed optical fiber acoustic wave sensing signals based on compressed sensing theory. The system is used to implement the aforementioned method and includes: a signal acquisition and sparse sampling module, a sparse basis selection module, a sparse optimization and channel encryption module, and a sparse reconstruction and data recovery module. The signal acquisition and sparse sampling module is used to measure the phase change of the fiber Rayleigh scattering signal of the DAS system, organize it into time-gather domain waveform data, and perform non-uniform sampling based on the sparsity characteristics of the effective frequency band signal in the time-gather domain waveform data to obtain undersampled data. The sparse basis selection module is used to perform sparsity analysis of the transform domain in compressed sensing on undersampled data and select the optimal transform. The sparse optimization and channel encryption module is used to compare wavelet thresholding denoising coefficients after the optimal transform is iteratively converged by the compressed sensing FISTA algorithm, and to apply the CS-POCS algorithm to encrypt the data channels based on the intrinsic sparsity characteristics of the data using compressed sensing. The sparse reconstruction and data recovery module is used to perform compressed sensing reconstruction on the processed sparse representation after filtering coefficients, and finally obtain a denoised and encrypted DAS waveform-gather dataset.

[0012] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention discloses an integrated method for denoising and encryption of Distributed Acoustic Sensing (DAS) signals based on compressed sensing theory. This method is specifically designed for the purification and reconstruction of shallow seismic DAS data signals, providing significant assistance for shallow exploration inversion. First, strain rate waveform data output from the DAS system is acquired and subjected to non-uniform undersampling to achieve data compression. Then, a joint sparse representation model is constructed by combining multi-scale hybrid sparse basis functions (Discrete Cosine Transform (DCT), wavelet basis, and FK domain basis functions). A Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) is used to reconstruct the undersampled signal with high precision, effectively recovering the effective signal components in key frequency bands of DAS impact events. Based on the reconstruction, an incompressible random noise modeling mechanism is further introduced to adaptively threshold and protect significant coefficients in the sparse domain, suppressing non-essential noise interference. For the retained core sparse coefficients, interpolation enhancement and encryption mapping operations are implemented, ensuring signal structural integrity while achieving information-level security masking. Finally, the processed sparse representation is restored to the time domain through inverse transform, obtaining a DAS signal with high signal-to-noise ratio (SNR), high resolution, and robust noise resistance. This invention is aimed at the purification and reconstruction of shallow seismic DAS data signals, and it greatly assists in shallow inversion. It not only achieves effective noise suppression and accurate reconstruction of signal details at the physical level, outperforming traditional dimensionality-increasing denoising techniques, but also applies the CS-POCS algorithm for data channel encryption based on the intrinsic sparsity characteristics of the data. This invention significantly improves the spatial resolution and signal integrity of DAS data, while reducing sensitivity to external environmental noise, possessing value for high-fidelity information reconstruction and promising applications in shallow surface seismic exploration engineering. Attached Figure Description

[0013] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0014] Figure 1 This is a schematic diagram of the strain rate processing waveform data output by the DAS system in an embodiment of the present invention, wherein (a) is a schematic diagram of the total data window containing the effective signal; (b)-(c) are schematic diagrams of the hammer impact signal detail window; Figure 2This is a step diagram of sparse domain analysis using DB4 wavelet in an embodiment of the present invention, wherein (a) is a two-dimensional visualization of the original DAS waveform data; (b) is a schematic diagram of the approximation coefficients of the fourth level of wavelet decomposition; (c) is a histogram of all wavelet coefficients; (d)-(g) are schematic diagrams of the horizontal, vertical, and diagonal detail coefficients of each level; and (h) is a schematic diagram of the logarithmic magnitude curve of the wavelet coefficients of this level arranged in descending order of magnitude. Figure 3 The following are comparison diagrams of sparsity in the transform domain during compressed sensing according to embodiments of the present invention: (a) is a schematic diagram of the original DAS signal; (b) is a heatmap of the low-frequency approximate components after wavelet transform (db4 wavelet basis); (c) is a heatmap of coefficients after DCT transform; (d) is a heatmap of coefficients after FK transform; (e) is a schematic diagram of the amplitude attenuation curve of wavelet coefficients; (f) is a schematic diagram of the amplitude attenuation of DCT coefficients; (g) is a schematic diagram of the amplitude attenuation of FK coefficients; (h) is a sparsity comparison histogram; (i) is a line graph showing the relationship between reconstruction error and threshold; and (j) is a schematic diagram of calculation parameters. Figure 4 This is a schematic diagram of compressed sensing noise analysis according to an embodiment of the present invention, wherein (a) is a schematic diagram of the distribution of the original DAS waveform data under different times and channels; (b) is a schematic diagram of the amplitude distribution of the signal window data; (c) is a schematic diagram of the amplitude distribution of the noise window data; (d) is a high-frequency wavelet coefficient distribution diagram; (e) is a comparison diagram of the power spectrum of noise and signal; and (f) is a schematic diagram of the noise analysis results. Figure 5 This is a schematic diagram of the compressed sensing iterative convergence process in an embodiment of the present invention, wherein (a) is a schematic diagram of the convergence curve of the compressed sensing FISTA algorithm; (b) is a schematic diagram of the threshold decay curve; (c) is a schematic diagram of the energy preservation curve; and (d) is a schematic diagram of the parameters for sparse representation using db4 wavelet transform. Figure 6 The above is a comparison diagram of the compressed sensing wavelet denoising coefficients in an embodiment of the present invention. (a) is a schematic diagram of the low-frequency layer dimension of the wavelet transform of the signal in the "approximate domain"; (b) is a schematic diagram of the numerical distribution of all coefficients in the original and denoised versions; (c)-(f) are schematic diagrams of a scale layer corresponding to the wavelet transform. Figure 7 This is a schematic diagram comparing the denoising results of an embodiment of the present invention, wherein (a) is a schematic diagram of the original data; (b) is a schematic diagram of the data after denoising; (c) is a schematic diagram of the removed noise; (d)-(f) are magnified display diagrams of specific channel ranges in the data; (g) is a schematic diagram of the amplitude change of the original single channel 275 over time; (h) is a schematic diagram of the frequency distribution of the amplitude value; and (i) are the statistical indicators and parameters of denoising. Figure 8The following diagram illustrates the application of compressed sensing in this invention to embed an encryption mechanism based on the intrinsic sparsity characteristics of data. (a) shows the time-track amplitude diagram of the original 600 DAS data channels; (b) shows a schematic diagram of the 900 seismic data channels after compressed sensing interpolation; (d) is a magnified view of the original signal; (e) is a magnified view of the local window after interpolation; and (f) is a schematic diagram comparing the correlation between adjacent trajectories before and after interpolation. Figure 9 This is a schematic diagram of SNR analysis during compressed sensing in an embodiment of the present invention, wherein (a) shows the SNR and SNR gain of the original signal and the processed signal; (b) shows the power of the original signal and the processed signal; (c) shows the noise power of the original signal and the processed signal; (d) shows the spatiotemporal waveform of the original signal; and (e) shows the waveform of the signal after compressed sensing processing. Figure 10 This is a schematic diagram of compressed sensing frequency analysis according to an embodiment of the present invention, wherein (a) shows the single-channel spectrum diagram of the "original" and "processed" signal of channel 275; (b) shows the average spectrum diagram of all signal channels; (c) shows the quantization of the gain / attenuation of each frequency component by the "processing"; (d) shows the energy distribution diagram of the original signal in the FK domain; (e) shows the FK spectrum diagram of the processed signal; and (f) shows the quantization of the effect of the "processing" on the energy of different frequency bands. Figure 11 The following are detailed comparison diagrams of compressed sensing in embodiments of the present invention: (a) shows a schematic diagram of the time-channel amplitude distribution in region W1 of the original data; (b) shows a schematic diagram of the time-channel amplitude distribution in region W1 after compressed sensing processing; (c) shows a schematic diagram comparing the amplitude-time curves of a selected channel (or average channel) in region W1 with the original and processed data; (d) shows a histogram of the amplitude distribution in region W1 with the original and processed data; (e)-(j) show schematic diagrams of region W2. Figure 12 This is a schematic diagram of the final cross-section of the encrypted gather in an embodiment of the present invention, wherein (a) is a schematic diagram of the original DAS hammer signal; (b) is a schematic diagram of the encrypted hammer signal (900 channels) after compressed sensing denoising; (c) is a parameter representation diagram; (d) is a schematic diagram of the signal-to-noise ratio of the original and reconstructed data; (e) is a schematic diagram showing the details of a local area of ​​the original data; and (f) is a schematic diagram showing the details of a local area after processing. Detailed Implementation

[0015] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0016] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0017] Example 1 This invention provides an integrated method for denoising and encryption of distributed fiber optic acoustic wave sensing signals based on compressed sensing theory, the method comprising: The phase change of the DAS based on the fiber Rayleigh scattering signal implemented in this example is measured and processed into time-gather domain waveform data. Based on the sparsity characteristics of the effective frequency band signal in the DAS waveform data, non-uniform sampling is performed to obtain undersampled data. We conducted a sparsity analysis of the transform domain in compressed sensing. By comparing the sparsity performance of wavelet transform, discrete cosine transform (DCT), and frequency-wavenumber transform (FK), we selected the optimal transform for subsequent compressed sensing processing. After the FISTA algorithm of compressed sensing converges iteratively, the wavelet thresholding denoising coefficients are compared, and the CS-POCS algorithm is applied to encrypt the data channels based on the intrinsic sparsity characteristics of the data using compressed sensing. After filtering coefficients, compressed sensing reconstruction finally yields a DAS waveform-gather dataset that features overall noise suppression, improved continuity of the effective signal phase axis, preservation of effective information energy, reduced noise amplitude ratio, more concentrated effective signal amplitude, enhanced sparsity, and increased encryption.

[0018] In this embodiment, the time-gather domain waveform data processed by DAS includes: The DAS (Digital Optical Array) was deployed in an underground cavern, with a total length of 6.0 km. During data acquisition, a sampling rate of 1000 Hz was set in time, and a channel spacing of 2.0 m was set in space. The first channel acquired was the 100th channel, and a total of 2254 channels were collected. The entire acquisition process lasted 2 hours. During this time, a hammer was used to tap the ground along the optical fiber every 8 m to provide active seismic source data for the DAS. Other operations were conducted within the cavern during the acquisition process, increasing environmental noise interference in the data.

[0019] Figure 1 This is the strain rate waveform data output by the DAS system in this embodiment of the invention. Figure 1(a) is the total data window containing valid signals. The green window represents valid hammer signals, and the red window represents noise strip signals. Figure 1 (b) Figure 1 (c) is the detail window for the hammer strike signal.

[0020] In this embodiment, the strain rate-velocity conversion relationship in the time-gather domain waveform data includes: The average strain rate response of a DAS can be replaced by the velocity difference between the two ends of the gauge length. First, determine the position of each receiving point of the DAS, then determine the position of the two ends of the gauge length of each receiving point, and then calculate the velocity at the two ends (any forward modeling method can calculate the velocity response). Then, subtract the velocities at the two ends and divide by the gauge length to obtain the DAS response at that point.

[0021] In this embodiment, the process of obtaining undersampled data includes: Based on the sparse distribution characteristics of the effective frequency band signal of DAS time-gather domain waveform data in the wavelet domain, an observation matrix is ​​constructed and a sparse basis is selected: The observation matrix is ​​a two-dimensional numerical matrix of waveform data in the DAS time-gather domain; The sparse basis is wavelet transform basis, discrete cosine transform basis, and frequency-wavenumber transform basis.

[0022] Undersampled data is obtained by non-uniform downsampling of the two-dimensional numerical matrix of DAS time-gather domain waveform data containing effective signals using the observation matrix and sparse basis: Calculate the undersampled data: in, This indicates undersampled data. x This represents a two-dimensional numerical matrix of DAS time-gather domain waveform data containing valid signals. Represents the sparse basis observation matrix. n Indicates noise.

[0023] In this embodiment, the wavelet transform basis, discrete cosine transform basis, and frequency-wavenumber transform basis for performing transform domain sparsity analysis in compressed sensing include: The wavelet transform basis (dB4, Daubechies 4th order wavelet) is a compactly supported orthogonal wavelet. The scaling function (φ) and wavelet function (ψ) of dB4 are determined by a recursive relation. The coefficients in the scaling function (low-pass filter) are: The scaling function satisfies: In the formula, The scaling function for the Daubechies 4th order wavelet (dB4) is a compactly supported orthogonal function used for low-frequency partial decomposition and reconstruction in multiresolution analysis. The coefficients of the low-pass filter corresponding to the scaling function are weight parameters in the recursive relation. This represents the translation and scaling forms of the scaling function. "2t" represents the scaling of the variable t (scale 2). -1 The expression "-k" represents an integer translation of the scaled function (the translation amount is k), where k = 0, 1, 2, 3 corresponds to four different translation positions for the scaling function. (Summation symbol) This represents the summation of four terms from k to 3, meaning the recursive relation is a linear combination of four weighted scaling and translation functions. The wavelet function (high-pass filter) coefficients are: (Mirror image and alternate signs), that is: . The wavelet function (high-pass filter) of the th A number of coefficients are used to extract the high-frequency components of the signal. The corresponding low-pass filter coefficients are obtained by mirroring (index 3-k) and alternating signs ( )generate . This is an integer index; the range of values ​​here is... The wavelet function satisfies: . The mother wavelet function is determined by the scaling function. and high-pass coefficient Generates through linear combination. The scaling function (related to low-pass filtering) is shifted. and stretch The form after that. These are still high-pass filter coefficients. The Discrete Wavelet Transform (DWT) basis functions are defined as follows: for a discrete signal, the wavelet basis is generated through integer shift and binary scaling. In the formula, This represents the discrete wavelet basis function, used for multi-resolution analysis of signals. The scaling parameter (binary scaling factor) controls the width of the wavelet. 1x scaling The larger the value, the wider the wavelet (low-frequency analysis); The smaller the wavelet, the narrower it is (high-frequency analysis). The normalization factor ensures that the wavelet energy remains constant. ). The translation parameter determines the wavelet's position on the time axis; Definition of Discrete Cosine Transform (DCT) basis: The basis functions of an N-point DCT (DCT-II is the most commonly used example) are: The normalization coefficients are used to ensure the orthogonality of the basis functions and to ensure the energy conservation of the DCT transform, and take the form: . The corresponding DC component (mean) has a relatively small coefficient. The time coefficient is scaled uniformly. Number of signal points: The dimension of the DCT transform, i.e., the number of sampling points of the input signal or the length of the discrete sequence. This is a time / space index, representing the discrete-time position of the input signal or sequence, corresponding to the sampling point number of the original signal. This is the frequency index, representing the number of the transformed frequency component. The larger the value, the higher the frequency of the component. For symmetry design, ensure even-symmetric boundary conditions for DCT-II (signal spreads evenly at the boundary). For the frequency interval, control the frequency distribution of the basis functions so that The frequency increases linearly with each increase. It is a length of A discrete sequence, representing a cosine wave of a specific frequency. The time is a constant sequence (DC component); This is the highest frequency oscillation. Different. The corresponding basis functions satisfy orthogonality: Normalization coefficient make sure .Signal The DCT-II transformation result is as follows: The inverse transform reconstructs the signal using the same basis functions.

[0024] Frequency-wavenumber transform basis (FK transform) definition: For two-dimensional signals (time ,space The FK transform basis is a complex exponential function, which satisfies orthogonality in both the continuous and discrete domains, ensuring the transform is invertible while capturing time and space frequency characteristics. In the formula, For time frequency, The wave number represents the spatial frequency; the transformed frequency domain signal is obtained through a two-dimensional Fourier transform: Implementation. Discrete form for size For discrete signals, the basis functions are: In the formula, For time-discrete indexes (dimensionless); Spatial discrete index (dimensionless); This is a time-frequency index (dimensionless), corresponding to the discrete-time frequency components (step size). ); Wavenumber index (dimensionless), corresponding to the component number (step size) of discrete spatial frequency. ); Discrete signal size (dimensionless) represents the number of sampling points in both time and spatial dimensions. It is the imaginary unit.

[0025] dB4 wavelet basis: ψ is recursively defined by h0~hs.

[0026] DCT base: , This is the normalization coefficient.

[0027] FK base: (continuous); (Discrete).

[0028] In this embodiment, the transform domain sparsity analysis includes: The three transformations described above were performed on the original DAS data respectively. Wavelet transform (db4) generated wavelet coefficients, exhibiting multi-scale characteristics and a concentration of non-zero coefficients. DCT transform generated DCT coefficients, smoothing the signal energy and concentrating it in the low frequency range. FK transform generated FK coefficients, concentrating the linear in-phase axis energy in a specific wavenumber-frequency region. Sparsity quantization included coefficient amplitude sorting (arranging the transform coefficients in descending order of amplitude) and sparsity calculation (statistically calculating the percentage of non-zero coefficients at a certain threshold (e.g., 95th quantile), showing that the sparsity of wavelet and FK transforms was 95.0%, while DCT was 35.0%). Sparsity verification threshold reconstruction error (inverse transforms were performed on coefficients at different thresholds (50%-100th quantiles), and the reconstruction error was calculated; wavelet transform showed the smallest error at low thresholds, verifying its advantage in sparse representation). Wavelet transform has better sparsity due to its multi-scale localization capability (good localization in the time and frequency domain), DCT is suitable for smooth signals, and FK is suitable for linear events. Considering both sparsity and reconstruction error, wavelet transform and FK transform have better sparsity. Through the above steps, wavelet transform and FK transform exhibit a sparsity of 95.0% on this data, which is significantly better than DCT's 35.0%. Moreover, wavelet transform has the lowest reconstruction error, making it the optimal sparse transform basis.

[0029] Figure 2 This is a step diagram of sparse domain analysis using DB4 wavelet according to an embodiment of the present invention. Figure 2 (a) is a two-dimensional visualization of the original DAS waveform data (two-dimensional expansion of gathers and time series), with color depth indicating numerical magnitude. Figure 2 (b) shows the approximation coefficients for the fourth level of wavelet decomposition. In wavelet decomposition, the approximation coefficients are the result of low-pass filtering, representing the low-frequency components of the signal. Level 4 is the fourth level of decomposition, with a smaller dimension than the original data because it is downsampled after decomposition. The approximation part of the fourth level is shown here. Figure 2 (c) is a histogram of all wavelet coefficients, showing the distribution of coefficient values. Most coefficients have very small absolute values, with only a few being very large, reflecting the statistical characteristics of sparsity: most coefficients are close to zero, while a few are significantly non-zero. Figure 2 (d)-(g) represent the horizontal, vertical, and diagonal detail coefficients for each Level (Level x: Horizontal / Vertical / Diagonal): these are the high-frequency details of each decomposition level, corresponding to edges / changes in the horizontal, vertical, and diagonal directions, respectively, showcasing detail information at different scales. Color indicates the magnitude of the coefficients, and non-zero concentrated areas correspond to local changes in the original data. Level 4 (cV) is the vertical detail coefficient, and Level 4 (cD) is the diagonal detail coefficient. Then, Level 3, Level 2, and Level 1's cH, cV, and cD are the detail coefficients for lower levels (more refined scales), with Level 1 being the lowest level decomposition, where the detail coefficient dimension is closer to the original data (because there are fewer decomposition levels and fewer downsampling times). Figure 2 The final curves (d)-(g) represent the logarithmic magnitude curves of the wavelet coefficients at each level after sorting by magnitude. It can be seen that the coefficient magnitudes decrease rapidly as the index increases (i.e., after sorting by magnitude from largest to smallest). Most coefficients have very small magnitudes (close to the bottom on the logarithmic scale), with only the top few coefficients having large magnitudes. This reflects the sparsity of the wavelet domain: a few large coefficients and most small coefficients (which can be considered zero), with a sparsity of 90%. Figure 2 (h) shows the logarithmic magnitude curves of the wavelet coefficients in this layer, arranged in descending order of magnitude. A few coefficients have extremely large magnitudes, while the magnitudes of subsequent coefficients rapidly decay to near zero—a direct manifestation of "sparseness." Most coefficients have magnitudes below the 90% threshold (below the red dashed line), with only about 123,182 coefficients (approximately 10% of the total) exceeding the threshold, corresponding to a sparsity of around 90%. This verifies that the signal in the DB4 wavelet domain exhibits high sparsity, making it suitable for compressed sensing (because compressed sensing utilizes the sparsity of the signal in a certain transform domain to reconstruct it with a small number of measurements).

[0030] Figure 3 This is a comparison diagram of the sparsity of the transform domain in compressed sensing according to an embodiment of the present invention. By comparing the sparsity performance of wavelet transform, discrete cosine transform (DCT), and frequency-wavenumber transform (FK), the optimal transform is selected for subsequent compressed sensing processing. Figure 3(a) shows the original DAS signal (the purple area represents the signal energy, and a clear vertical strip structure is visible, corresponding to the hammering event). Figure 3 (b) is a heatmap of the low-frequency approximate components after wavelet transform (db4 wavelet basis). The red area shows that the energy is concentrated in a few low-frequency levels (vertical bright line), which reflects the wavelet's ability to focus on local time-frequency features. Figure 3 (c) is the coefficient heatmap after DCT transformation (logarithmic scale enhances weak signals). The overall color is yellow (the energy distribution is relatively uniform), indicating that DCT has a certain sparsity for smooth signals (such as continuous stripes in the original data), but the energy dispersion is wider than that of the wavelet. Figure 3 (d) is a heatmap of coefficients after FK transformation (logarithmic scale). The yellow area covers most of the area, and the energy distribution is the most dispersed, indicating that the sparsity of FK transformation on this data is relatively weak (possibly due to the high proportion of nonlinear events in the original data). Figure 3 (e) shows the amplitude decay curve of the wavelet coefficients, which shows a rapid decay (steep decrease), indicating that a few large coefficients concentrate most of the energy, which is in line with the definition of sparsity (most coefficients are close to zero). Figure 3 (f) indicates that the amplitude decay of the DCT coefficients is relatively gentle and the decay rate is slower than that of wavelets, which means that the energy is more dispersed and the sparsity is weaker than that of wavelets. Figure 3 (g) represents the FK coefficient with the most gradual amplitude decay, the most severe energy dispersion, and the worst sparsity. Figure 3 (h) is a histogram comparing sparsity: Wavelet: 95.5% (95.5% of the coefficient amplitudes are below the threshold, i.e., close to zero). DCT: 35.0% (only 35% of the coefficients can be considered zero, indicating poor sparsity). FK: 95.0% (close to wavelet, but considering the coefficient decay curve, the actual effective sparsity may be even lower). Wavelet transform has the best sparsity, while DCT has the worst. Figure 3 (i) is a line graph showing the relationship between reconstruction error and threshold. The horizontal axis represents the percentage of threshold values ​​retained, with the top x% of coefficients having the largest amplitudes, and the rest set to zero. This is used to simulate the "undersampling" reconstruction process in compressed sensing. Wavelet (blue) has the lowest RMSE (root mean square error, which measures the accuracy of the reconstructed original signal from the transform domain coefficients; the lower the error, the more effective the sparse representation). It also has the slowest growth, indicating that retaining a small number of coefficients (such as when the threshold is 90%) is sufficient for high-precision reconstruction. DCT (orange) has the highest RMSE, and its error increases rapidly as the threshold decreases (retaining fewer coefficients), indicating poor sparsity and weak reconstruction performance. FK (green) has an RMSE between wavelet and DCT, but is generally higher than wavelet, indicating that although its sparsity is close to that of wavelet, its dispersed energy distribution leads to low reconstruction efficiency. Figure 3 (j) represents the computational parameters. In this computational example, the wavelet transform (db4) exhibits the highest sparsity (95.5%) and the lowest reconstruction error, making it the optimal transform choice for compressed sensing. The DCT exhibits the worst sparsity, while the FK transform, although approaching the sparsity of the wavelet, suffers from low reconstruction efficiency.

[0031] Figure 4 This is a compressed sensing noise analysis according to an embodiment of the present invention. Figure 4 (a) Distribution of raw DAS waveform data at different times and channels. The signal windows, containing valid signals (e.g., dark clumps around times 0.3–0.8 seconds and channels 300–400), are marked with solid green boxes. The noise windows, containing no valid signals (e.g., uniformly light-colored areas around times 0–0.2 seconds and 1.8–2.0 seconds), are marked with dashed red boxes. This windowing separates the signal-dominant and noise-dominant regions, providing data for subsequent noise analysis. Figure 4 (b) shows the amplitude distribution of the signal window data, with the vertical axis representing the frequency density of the amplitude value. The central peak is close to 0 (but the overall range is wide), and the standard deviation (std) is 1137.75. The distribution exhibits a certain degree of asymmetry, indicating that the signal contains large-amplitude fluctuations, which is consistent with the characteristics of an effective signal. Figure 4 (c) shows the amplitude distribution of the noise window data, which is approximately Gaussian (with a central peak at 0 and symmetrical attenuation on both sides), with a standard deviation (std) of 387.27. The amplitude range is significantly smaller than that of the signal distribution. Figure 4 (d) shows the distribution of high-frequency wavelet coefficients. The horizontal axis represents the wavelet coefficient values, indicating the coefficients of the high-frequency components of the signal after wavelet transform (-20000~30000). In the figure, the blue curve represents the amplitude distribution of the high-frequency wavelet coefficients, the red dashed line marks the absolute median deviation (MAD=84.00), and the green dashed line corresponds to the estimated noise standard deviation (σ =124.5367, usually calculated from MAD×1.4826). The high-frequency wavelet coefficients are mainly concentrated near 0, which is consistent with the characteristic that noise dominates in high-frequency components (wavelet transform is often used in compressed sensing to separate sparse components of the signal from noise). Figure 4 (e) is a comparison of the power spectra of noise and signal. The vertical axis represents the logarithmic scale of amplitude, used to compress the dynamic range and highlight the power differences at different frequencies. The blue curve represents the power spectrum of the signal window data (the distribution of signal power with frequency), with obvious peaks in the low-frequency range (e.g., 0~50Hz), indicating that the signal energy is concentrated at low frequencies. The red curve represents the power spectrum of the noise window data (the distribution of noise power with frequency), which is generally flat and has a low amplitude, consistent with the power spectrum characteristics of white noise, with approximately equal power at each frequency. Figure 4(f) shows the noise analysis results, providing key parameters (such as noise level σ and SNR) for the compressed sensing reconstruction algorithm, guiding the threshold selection during the reconstruction process. This figure systematically quantifies the characteristics of signal and noise through methods such as window partitioning, statistical distribution analysis, wavelet transform, and power spectrum comparison. The core objective is to accurately estimate the noise level (such as standard deviation σ) and SNR, providing necessary prior information for subsequent signal reconstruction in compressed sensing, such as sparse recovery based on the L1 norm, ensuring the robustness and accuracy of the reconstruction algorithm.

[0032] In this embodiment, the iterative convergence of the compressed sensing FISTA algorithm includes: The threshold calculation formula is as follows , This is the noise standard deviation (which needs to be estimated using the signal). This represents the signal length (number of data points). The threshold scaling factor is 2.0, therefore the actual threshold... ; The formula for calculating residuals is: , The observation signal contains noise. It is a linear transformation matrix (db4 wavelet transform, Level=4). For the first The signal estimate of the next iteration; The formula for calculating relative energy is: . For the first The signal estimate for the next iteration. The initial signal (such as the original noisy signal); FISTA algorithm iterative convergence steps: 1. Gradient descent: ,in Let be the Lipschitz constant, representing the gradient of the objective function. The upper limit of smoothness satisfies , These are discrete values. For the first The intermediate variables of the next iteration are used for subsequent threshold updates. For the first The estimated value of the next iteration. For the objective function exist gradient at, It is a linear transformation matrix (such as an observation matrix). For observation data (or measurement vectors); 2. Threshold update: ,in, For the first The updated solution (sparse or structured solution) for the next iteration. This is a soft threshold function. For the first The threshold parameter of each iteration controls the intensity of sparsification (usually decreasing with each iteration). These are intermediate variables derived from the gradient descent step; 3. Momentum acceleration: , ,in, This is a momentum acceleration parameter used to adjust the weights of historical solutions and improve the convergence speed. As a new intermediate quantity, combined with an understanding of the current situation and historical interpretation Information. , This represents the solution of the current iteration and the solution of the previous iteration.

[0033] By dynamically adjusting the threshold (threshold + linear decay) and accelerating iteration with FISTA, rapid residual convergence and effective preservation of signal energy were achieved.

[0034] Figure 5 Analysis of the compressed sensing iterative convergence process in an embodiment of the present invention. Figure 5 (a) shows the convergence curve of the compressed sensing FISTA algorithm. The vertical axis represents the logarithmic form of the residual. The residual is defined as the error between the original signal and the signal reconstructed in the current iteration, and is an L2 norm, i.e. ,in It is an observation signal. It is a perception matrix. This is the reconstructed signal. The logarithm is used here to more clearly illustrate the rapid decreasing trend of the residuals with iteration. The blue curve shows that the logarithm of the residuals decreases monotonically with the number of iterations, and the rate of decrease gradually slows down, eventually stabilizing at 50 iterations. This indicates that the algorithm continuously optimizes the reconstructed signal through iteration, gradually reducing the reconstruction error and converging to a smaller value, verifying the convergence of the algorithm. Figure 5 (b) shows the threshold decay curve. The vertical axis represents the relative size of the threshold used in sparse reconstruction in compressed sensing, with an initial value of 2.0, eventually decaying to 1.0. The red curve shows that the threshold decays linearly with the number of iterations. In the iterative algorithm of compressed sensing, a dynamic threshold strategy is adopted: a larger threshold is used in the initial iteration to quickly remove noise and minor components; as iterations proceed, the threshold gradually decreases to retain more details, eventually stabilizing at a smaller threshold (1.0 in this case). This "threshold decay" strategy helps to balance denoising effect and signal detail preservation, improving reconstruction accuracy. Figure 5(c) Energy retention curve. The vertical axis represents the ratio of the energy of the reconstructed signal to the energy of the original signal (ranging from 0 to 1.1), measuring the degree to which signal energy is retained during the iteration process. The green curve shows that the relative energy decreases rapidly with the number of iterations, and then gradually stabilizes (finally to approximately 0.73). The initial energy decrease is because the algorithm removes noise and non-sparse components (low-energy redundant information) through a threshold; the later energy stabilization indicates that the main signal components have been retained, and further iterations will not significantly lose effective energy. This verifies that the algorithm can effectively retain the key information of the original signal while removing noise. Figure 5 (d) describes the parameters for sparse representation using the db4 wavelet transform (wavelets are commonly used as a sparse basis in compressed sensing). The thresholding method is a general threshold, and the formula is... , denoted as the noise standard deviation, and n as the signal length. The scaling factor is 2.0 (the amplification factor of the initial threshold). The signal protection factor is 0.5 (controlling the degree to which the threshold protects the signal components). The original signal mixing ratio is 0.35 (used for fusion with the original signal during iteration, enhancing stability). This uses ISTA (Iterative Shrinking Thresholding Algorithm) accelerated by FISTA (Fast Iterative Thresholding Algorithm), which improves convergence speed through Nesterov acceleration technology.

[0035] In this embodiment, the comparison of wavelet thresholding denoising coefficients includes: Compare wavelet thresholding denoising coefficients to evaluate the signal. Perform wavelet transform to obtain coefficients denoised coefficients for: In the formula, The threshold is set using the Universal Threshold method. ( The standard deviation of noise. The signal length is represented by a scaling factor of 2.0. ).

[0036] Figure 6 This is a comparison chart of compressed sensing wavelet denoising coefficients in an embodiment of the present invention. Figure 6 (a) represents the low-frequency layer dimension of the wavelet transform of the signal in the "approximation domain". The right figure shows the coefficient distribution of the approximation part of the signal after denoising. By comparing with the left figure, we can observe the change in the low-frequency coefficients after noise removal, and the "noise" caused by noise is reduced. Figure 6(b) shows the numerical distribution of all coefficients in the original (blue) and denoised (red) versions. After denoising, the "extreme values" caused by noise, such as large positive / negative values, are reduced, and the distribution is more concentrated in the range of coefficients of the effective signal. Figures (c)-(f) correspond to one scale layer of wavelet transform (L4 is the highest frequency layer, L1 is the lowest frequency layer), with the structure as follows: original detail coefficients → denoised detail coefficients → removed coefficients → coefficient decay curve. The horizontal axis of the coefficient decay curve is the index of the coefficients after sorting them by absolute value from largest to smallest, with 0 being the largest coefficient and 500 being the smallest coefficient. The vertical axis is the absolute value of the coefficients, using a logarithmic scale, showing the trend of "large coefficients decaying rapidly and small coefficients decaying slowly". After sorting all coefficients in this scale layer by absolute value, after denoising, a large number of "noise-dominated small coefficients" are removed, so the curve will be lower in the small coefficient region (right side of the horizontal axis), reflecting the suppression effect of denoising on small coefficients (noise). The multi-scale wavelet transform (L4 to L1) corresponds to the high-frequency to low-frequency decomposition of the signal. L4 (the highest layer) represents the finest-grained high-frequency details (such as sharp noise and rapidly changing edges). L3 / L2 represent medium-scale details (such as texture and medium-frequency components). L1 (the lowest layer) represents the coarsest-grained low-frequency details (such as the slow variation trend of the signal). Therefore, the detail coefficients of different layers reflect the "variation information" of the signal at different frequency scales. The denoising process needs to selectively retain effective signal coefficients and remove noise coefficients at each layer. This figure visually demonstrates how denoising algorithms retain effective signal coefficients and suppress noise coefficients in the sparse domain of compressed sensing by comparing multiple scales (L4→L1) and multiple dimensions (approximate / detail coefficients, distribution, attenuation, removal terms).

[0037] In this embodiment, applying compressed sensing to encrypt data channels using the CS-POCS algorithm based on the intrinsic sparsity characteristics of the data includes: Based on compressed sensing-alternating direction multiplier method, CS-POCS, assuming DAS data is a two-dimensional signal ,in The number of time sampling points, For the number of channels (enter the number of channels) Output channel number The interpolation objective is to obtain data from sparse pass sets. Restoration of the dense Dao collection ; The theoretical basis of compressed sensing (CS) is that DAS data exhibits sparsity in the transform domain (such as the Fourier domain and curvelet domain), that is: In the formula, It is a sparse transformation matrix. It is a sparse coefficient vector (most elements are 0).

[0038] Key assumption: original signal In the transform domain The sampling (channel selection) is sparse and satisfies the finite isometric property (RIP). The POCS (Projection Onto Convex Sets) algorithm solves the inverse problem by alternately projecting onto multiple convex sets. The core steps are as follows: 1. Sparse constraint set: ( (sparseness) The signal or data vector to be solved (usually coefficients in a sparse representation domain, such as wavelet or Fourier coefficients). For a sparse representation of the signal, i.e. ,in The transformation basis matrix; for Norm, representing a vector The most in A non-zero element. This is achieved through a threshold operation: In the formula, For the first Sparse representation after the next iteration; For the first The signal estimate of the next iteration; The transpose of the transform basis matrix (such as the inverse wavelet transform) is used to transform the signal... Project onto the sparse region; For soft thresholding, which is continuously differentiable and suitable for gradient optimization; hard thresholding (direct truncation) may introduce oscillations. Parameters Controlling threshold strength: , For input values ​​(usually (a certain component). This is a threshold parameter that determines the magnitude of contraction. If... Larger values ​​result in greater sparsity, but may lead to loss of signal details; if Smaller size retains more information but reduces sparsity. For symbolic functions, retain The positive and negative aspects. Will Absolute value contraction If the result is less than 0, set it to 0.

[0039] 2. Data consistency constraint set: ,in, This is the complete data vector to be recovered. This is the sampling matrix (retaining the original channels and setting the interpolated channels to 0). This is for incomplete observation data. The projection formula is: In the formula, For the first Data after the next iteration. For the first Data after the next iteration. It is the identity matrix (a diagonal matrix with the same dimension as P). Transformation matrix. This represents a sparse representation in the transform domain. Iterative formula: In the formula, Transformation matrix The transpose (inverse transformation) of the derivative. Iterate until the residual is found. , Iteration termination residual threshold, Figure 8 The final residual in (c) is . for Norm.

[0040] Interpolation implementation details: Input / Output: 600 inputs, 900 outputs, interpolation factor ( Sparse Transform: Curvelet Transform is commonly used due to its strong ability to represent the directional sparseness of seismic phase axes. Convergence Criterion: Iteration stops when the residuals meet the requirements after 48 iterations. Correlation verification, the correlation between adjacent channels is defined as: This formula is the discrete form of the Pearson correlation coefficient, used to quantify the linear correlation between two datasets. This formula represents the... The road and its neighbors The correlation coefficient of the Tao. In the formula, This is the seismic trace sequence number. This represents the sampling point number in the time domain. For the first The Way in the The amplitude value at any given time. These represent the total number of sampling points in the time domain. For the first The time-domain mean of the Dao. Figure 8 The data in f shows that the average correlation after interpolation is 0.708 (close to the original 0.732), which verifies the rationality of the interpolation.

[0041] Sparse Transformation and Thresholding: Data consistency projection: Iteration stopping condition: ( ) Through the steps described above, the CS-POCS method utilizes sparsity constraints and data consistency to obtain 900 seismic data from 600 interpolated channels.

[0042] In this embodiment, sparsity constraints and data consistency are utilized in the CS-POCS method to obtain 900 seismic data from 600 reconstructed interpolations. The final result is a DAS waveform-trace dataset with overall noise suppression, improved continuity of effective signal phase axes, preservation of effective information energy, reduced noise amplitude ratio, more concentrated effective signal amplitude, enhanced sparsity, and increased density.

[0043] Figure 7 This is a comparison of the denoising results of embodiments of the present invention. Figure 7 (a), (b), and (c) represent the original data, the data after denoising, and the removed noise, respectively. The horizontal axis of these three graphs represents the channel of the acquired signal, and the vertical axis represents time, in seconds, ranging from approximately 0 to 2 seconds. These three graphs are visualizations of the time-channel domain. Compared to the original data, the background noise (the darker, random parts) in the denoised data has been significantly removed, while effective signal areas, such as strong signals at specific times and channels, are preserved, resulting in a "cleaner" overall image. The distribution of the removed noise in the time-channel domain shows the time-domain and channel-domain characteristics of the noise. Figure 7 (d), (e), and (f) represent the gather on the x-axis and time on the y-axis. These three graphs are magnified displays of specific ranges within the data, showing the local effects. After window denoising, local noise is reduced, and the effective signal is clearer. Figure 7 (g) shows the change in amplitude of the original single-channel 275 over time, while the red line represents the amplitude of the single-channel 275 after denoising. This demonstrates a comparison of the time-domain waveforms of a specific channel before and after denoising. The signal is smoother after noise removal, and the effective components are also preserved. Figure 7 (h) The horizontal axis represents the amplitude value, and the vertical axis represents the probability density, i.e., the frequency distribution of the amplitude values. Blue represents the amplitude distribution of the original data, and red represents the amplitude distribution of the data after denoising. After denoising, the small amplitudes or randomly distributed amplitudes corresponding to noise are reduced, and the amplitude distribution of the effective signal is more concentrated or regular. Figure 7 (i) Statistical indicators and parameters for denoising. These include the standard deviation of noise in the original and denoised states, the energy in the original and denoised states, the percentage of energy retained, the threshold scale, the signal protection level, and the blurring factor. These values ​​quantify the denoising effect. For example, an original standard deviation of 471.04 and a denoised standard deviation of 374.20 indicate a reduction in noise, and an energy retention of 91.9% indicates that a large amount of effective signal is retained.

[0044] Figure 8 This invention provides a diagram illustrating the application of compressed sensing to embed encryption mechanisms based on the intrinsic sparsity characteristics of data. Figure 8 (a) Displays the time-track amplitude plot of the original 600 DAS data. Darker colors indicate stronger amplitudes, and lighter colors indicate weaker amplitudes. The plot shows a clear in-phase axis (hammer signal wave), but the track spacing is large, and some areas exhibit discontinuities due to data sparsity. Figure 8 (b) Displays 900 seismic data channels after compressed sensing interpolation. (Comparison) Figure 8 (a) The track density increased significantly (from 600 to 900), the continuity of the in-phase axis was better, and the signal details were richer. The color distribution remained consistent with the original data, indicating that the interpolation did not introduce significant noise. Figure 8 (d) is a magnified view of the original signal, focusing on 50 channels of data from channels 250 to 300. It can be seen that the in-phase axis is discontinuous in a "step-like" manner due to the large channel spacing, and some details are blurred (such as the waveforms at 0.3 seconds, 0.6 seconds, and 0.9 seconds). Figure 8 (e) is a magnified view of the local window after interpolation (corresponding to the original 250~300 channels, expanded to 75 channels after interpolation). The continuity of the in-phase axis is significantly improved, the originally discontinuous waveform (such as at 0.3 seconds) becomes smooth, and the signal details are clearer, verifying the optimization effect of CS interpolation on local data. Figure 8 (f) Comparison of the correlation between adjacent trajectories before (blue) and after (red) interpolation. The average correlation coefficient of adjacent trajectories in the original data is 0.732, with fluctuations (dropping to 0.2 at index 30). The average correlation coefficient after interpolation decreases slightly (0.708), but the overall fluctuation is smaller, indicating that while maintaining the correlation, the interpolated data reduces local noise or discontinuities in the original data, thus improving overall consistency.

[0045] Figure 9 This is an example of SNR analysis during compressed sensing in an embodiment of the present invention. Figure 9 (a) shows that the original signal's SNR was 9.36 dB, and the processed signal's SNR increased to 13.66 dB, with an SNR gain of 4.30 dB (13.66 - 9.36). Compressed sensing effectively suppresses noise through sparse reconstruction, significantly improving signal quality. Figure 9 (b) shows that the original signal power was approximately 1.29 × 10^6 (green bar), and the processed signal power was approximately 9.62 × 10^5 (dark green bar). The signal power retention rate was 74.3% (9.62 × 10^5 / 1.29 × 10^6 ≈ 0.743), indicating that compressed sensing effectively preserved useful signal energy while denoising. Figure 9(c) shows that the original signal noise power was approximately 1.50 × 10^5 (red bar), and the noise power was reduced to 4.14 × 10^4 (dark red bar) after processing. The noise power reduction rate was 72.4% (1 - 4.14 × 10^4 / 1.50 × 10^5 ≈ 0.724), which verifies the strong noise suppression capability of compressed sensing. Figure 9 (d) shows the spatiotemporal waveform of the original signal, with color intensity indicating signal amplitude. Obvious noise interference (background "spiking") is visible in the figure, and the effective signal is masked by the noise. Figure 9 (e) shows the signal waveform after compressed sensing processing. Background noise is significantly reduced ("spurs" are reduced), and the outline of the useful signal is clearer, intuitively demonstrating the effect of compressed sensing in removing noise and restoring signal details through sparse reconstruction. This figure demonstrates the advantages of compressed sensing in low signal-to-noise ratio scenarios through multi-dimensional comparison of SNR, power, and waveform: while retaining 74.3% of the useful signal power, it suppresses 72.4% of the noise power, ultimately achieving an SNR gain of 4.30 dB, significantly improving signal quality.

[0046] Figure 10 This is a compressed sensing frequency analysis according to an embodiment of the present invention. Figure 10 (a) Shows the single-channel spectra of the 275th channel signal: "Original" (blue line) and "Processed" (red line). The spectrum reflects the correspondence between "frequency → amplitude," and the logarithmic vertical axis facilitates observation of the detailed differences between low-amplitude and high-amplitude components. By comparing the two curves, the modification of the amplitude of each frequency component of the single-channel signal by "processing" can be seen intuitively. Figure 10 (b) Display the average spectrum of all signal channels (original blue line, processed red line). Unlike the "single-channel spectrum", this is a statistical average of multiple channels, reflecting the changes in the "overall frequency domain characteristics" of the signal. Figure 10 (c) To quantify the gain / attenuation of each frequency component by the "processing". If the ratio is >1 (green line above the Unity line), it means that the amplitude of the frequency component is enhanced after processing; if the ratio is <1 (green line below the Unity line), it means that the amplitude is suppressed. Peaks or valleys represent that the processing effect is severe at that frequency, and the noise band is significantly suppressed. Figure 10 (d) Shows the energy distribution of the original signal in the FK domain. Different frequency-wavenumber combinations correspond to different propagation characteristics. The distribution areas of noise / effective signal can be identified through the FK spectrum. Figure 10 (e) The FK spectrum of the processed signal is shown. Compared with the original FK spectrum, it can be observed that the color in the FK domain region is darker, indicating that the noise frequency-wavenumber component is suppressed. Figure 10(f) To quantify the effect of “processing” on energy in different frequency bands. In the five intervals of 0-20Hz, 20-50Hz, 50-100Hz, 100-150Hz, and 150-200Hz, the total energy (energy is proportional to the square of the amplitude) in each frequency band decreased, indicating that the processing suppressed noise in each frequency band.

[0047] Figure 11 This is a comparison diagram of compressed sensing details in an embodiment of the present invention. Figure 11 (a) Shows the time-channel amplitude distribution of region W1 in the original data, reflecting the spatiotemporal characteristics of the original signal in this region. Figure 11 (b) Displaying the time-channel amplitude distribution of region W1 after compressed sensing processing. Figure 11 (c) To select a channel (or average channel) in the W1 region, compare the original (blue) and processed (red) amplitude-time curves to focus on the detailed changes in the signal in the time domain. Figure 11 (d) is a histogram of the amplitude distribution in the W1 region, showing the changes in amplitude statistics caused by the processing. The noise amplitude distribution is narrowed and the effective signal amplitude is more concentrated, indicating that the noise is suppressed. Figure 11 (e)-(j) represent the situation in region W2. Compared to the original full profile, the processed complete time-trace seismic profile shows overall noise suppression, improved continuity of phase axes, disappearance of noise spikes, preservation of effective waveforms, reduced proportion of noise amplitude, more concentrated effective signal amplitude, and enhanced sparsity.

[0048] Figure 12 This is the final profile of the encrypted gather in this embodiment of the invention. The number of channels in the processed data increases from 600 to 900, demonstrating the effect of compressed sensing's "undersampling reconstruction + interpolation." The increase in the number of channels represents an improvement in spatial resolution. In the compressed sensing processed data, the green box corresponds to the signal region of the original image. It can be seen that the noise is significantly reduced, the signal is clearer, and the background is cleaner, indicating that the processing effectively removes noise and reconstructs the signal. Figure 12 (d) indicates that the higher the SNR, the higher the signal "purity" (logarithmic ratio of signal power to noise power). Signal quality before and after quantization. Original SNR = 9.4 dB, processed SNR = 13.7 dB, an increase of 4.3 dB, proving that noise was significantly suppressed and the signal strength was improved after processing. Figure 12 (e) Shows details of a local area of ​​the original data, where noise and signal are mixed (lots of noise and blurred signal edges). Figure 12(f) Showing the details of the processed local area, compared with the original image, the noise is significantly reduced and the signal structure is clearer (sharp edges, less noise), indicating that compressed sensing can effectively enhance the signal and suppress noise at the local scale. This set of images verifies the effectiveness of compressed sensing processing from four dimensions: global data distribution, local details, quantization index (SNR), and algorithm parameters. Global noise is reduced, and the signal is more prominent; Locally: details are clearer, and noise is suppressed; Quantization: SNR is improved by 4.3dB, and signal quality is significantly improved; Technology: "High-quality signal recovery under undersampling" is achieved through wavelet denoising, reconstruction, and interpolation techniques.

[0049] Example 2 The present invention also provides an integrated system for denoising and encryption of distributed optical fiber acoustic wave sensing signals based on compressed sensing theory. The system is used to implement the method described in Embodiment 1. The system includes: a signal acquisition and sparse sampling module, a sparse basis selection module, a sparse optimization and channel encryption module, and a sparse reconstruction and data recovery module. The signal acquisition and sparse sampling module is used to measure the phase change of the fiber Rayleigh scattering signal of the DAS system, organize it into time-gather domain waveform data, and perform non-uniform sampling based on the sparsity characteristics of the effective frequency band signal in the time-gather domain waveform data to obtain undersampled data. The sparse basis selection module is used to perform sparsity analysis of the transform domain in compressed sensing on undersampled data and select the optimal transform. The sparse optimization and channel encryption module is used to analyze the iterative convergence process of the compressed sensing FISTA algorithm for the optimal transform, compare the wavelet thresholding denoising coefficients, and apply the CS-POCS algorithm to encrypt the data channels based on the intrinsic sparsity characteristics of the data using compressed sensing. The sparse reconstruction and data recovery module is used to perform compressed sensing reconstruction on the processed sparse representation after filtering coefficients, and finally obtain a denoised and encrypted DAS waveform-gather dataset.

[0050] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for integrated denoising and encryption of distributed fiber optic acoustic wave sensing signals based on compressed sensing theory, characterized in that, The method includes: The phase change of the fiber Rayleigh scattering signal of the DAS system is measured and processed into time-gathered domain waveform data. Based on the sparsity characteristics of the effective frequency band signal in the time-gathered domain waveform data, non-uniform sampling is performed to obtain undersampled data. Perform sparsity analysis of the transform domain in compressed sensing on undersampled data and select the optimal transform; After the optimal transform is iteratively converged by the compressed sensing FISTA algorithm, the wavelet thresholding denoising coefficients are compared, and the data channels are encrypted by applying the CS-POCS algorithm based on the intrinsic sparsity characteristics of the data using compressed sensing. Compressed sensing reconstruction is performed on the processed sparse representation after filtering coefficients to finally obtain a denoised and encrypted DAS waveform-gather dataset.

2. The method according to claim 1, characterized in that, Based on the sparsity characteristics of the effective frequency band signal in the time-gather domain waveform data, methods for obtaining undersampled data through non-uniform sampling include: Based on the sparse distribution characteristics of the effective frequency band signals of DAS time-gather domain waveform data in the wavelet domain, an observation matrix is ​​constructed and a sparse basis is selected. The observation matrix is ​​a two-dimensional numerical matrix of DAS time-gather domain waveform data; the sparse basis is a wavelet transform basis, a discrete cosine transform basis, and a frequency-wavenumber transform basis. Undersampled data is obtained by non-uniform downsampling of the two-dimensional numerical matrix of DAS time-gather domain waveform data containing effective signals using the observation matrix and sparse basis.

3. The method according to claim 1, characterized in that, Sparsity analysis of the transform domain in compressed sensing for undersampled data includes comparing the sparsity performance of wavelet transform, discrete cosine transform (DCT), and frequency-wavenumber transform (FK).

4. The method according to claim 1, characterized in that, The iterative convergence of the compressed sensing FISTA algorithm for the optimal transform includes: The threshold calculation formula is as follows , The standard deviation of noise. Given the signal length, a threshold scaling factor of 2.0, and the actual threshold... ; The formula for calculating residuals is: , The observation signal contains noise. It is a linear transformation matrix. For the first The signal estimate of the next iteration; The formula for calculating relative energy is: , This is the initial signal.

5. The method according to claim 1, characterized in that, Methods for comparing wavelet thresholding denoising coefficients include: For signal Perform wavelet transform to obtain coefficients denoised coefficients for: ； In the formula, The threshold value is used.

6. The method according to claim 1, characterized in that, Methods for data channel encryption using compressed sensing and the CS-POCS algorithm based on the intrinsic sparsity characteristics of data include: Based on Compressed Sensing-Alternating Direction Multiplier Method (CS-POCS), assuming the DAS data is a two-dimensional signal. ,in The number of time sampling points, For the number of channels, the interpolation objective is to extract from the sparse channel set. Restoration of the dense Dao collection ; Based on compressed sensing CS theory, DAS data exhibits sparsity in the transform domain, namely: ； In the formula, It is a sparse transformation matrix. The original signal is a sparse coefficient vector. It is sparse in the transform domain, and the sampling satisfies the finite isometry property; The POCS algorithm is used to solve the inverse problem by alternately projecting the original signal onto multiple convex sets.

7. The method according to claim 6, characterized in that, The method of solving the inverse problem by using the POCS algorithm to alternately project the original signal onto multiple convex sets includes: Sparse constraint set: , To achieve sparsity, a threshold operation is used: ； In the formula, For the first The sparse representation after the next iteration. For the first The signal estimate of the next iteration Transpose of the basis matrix. For soft thresholding function: , For input values, For threshold parameters; Data consistency constraint set: ,in For the sampling matrix, projection operation: ； Iteration formula: ； Iterate until the residual ,in, This is the threshold for the residual to terminate the iteration.

8. A distributed fiber optic acoustic wave sensing signal denoising and encryption integrated system based on compressed sensing theory, the system being used to implement the method described in any one of claims 1-7, characterized in that, The system includes: a signal acquisition and sparse sampling module, a sparse basis selection module, a sparse optimization and channel encryption module, and a sparse reconstruction and data recovery module; The signal acquisition and sparse sampling module is used to measure the phase change of the fiber Rayleigh scattering signal of the DAS system, organize it into time-gather domain waveform data, and perform non-uniform sampling based on the sparsity characteristics of the effective frequency band signal in the time-gather domain waveform data to obtain undersampled data. The sparse basis selection module is used to perform sparsity analysis of the transform domain in compressed sensing on undersampled data and select the optimal transform. The sparse optimization and channel encryption module is used to compare wavelet thresholding denoising coefficients after the optimal transform is iteratively converged by the compressed sensing FISTA algorithm, and to apply the CS-POCS algorithm to encrypt the data channels based on the intrinsic sparsity characteristics of the data using compressed sensing. The sparse reconstruction and data recovery module is used to perform compressed sensing reconstruction on the processed sparse representation after filtering coefficients, and finally obtain a denoised and encrypted DAS waveform-gather dataset.

Images