A method for suppressing clutter in multi-resolution low-rank sparse decomposition of ground-penetrating radar

Abstract

This invention discloses a multi-resolution low-rank sparse decomposition clutter suppression method for ground-penetrating radar. First, wavelet transform is used to decompose the echo data into multiple scales, obtaining approximate sub-bands, horizontal detail sub-bands, vertical detail sub-bands, and diagonal detail sub-bands at different scales. For the approximate and horizontal detail sub-bands, a robust non-negative matrix factorization algorithm is used to extract the sparse portion of the target, and a regularization parameter is autonomously selected based on the target-clutter peak ratio. For the vertical and diagonal detail sub-bands, wavelet soft thresholding is used for denoising. Finally, inverse wavelet transform is performed on each processed signal component to reconstruct the target signal, achieving clutter suppression. This invention provides high-resolution target signals and achieves a high signal-to-clutter ratio, representing a robust clutter suppression method.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, specifically relating to a method for suppressing clutter in multi-resolution low-rank sparse decomposition of ground penetrating radar. Background Technology

[0002] Ground penetrating radar (GPR) technology is a relatively new geophysical exploration method. This technology utilizes the differences in the dielectric parameters of various underground materials, using broadband electromagnetic waves in pulse form to probe beneath the Earth's surface or determine the internal structure or interior of invisible objects. It has been widely applied both domestically and internationally. Compared to conventional non-destructive testing methods such as resistivity methods and low-frequency electromagnetic induction methods, GPR technology offers advantages such as high detection speed, continuous detection process, high resolution, convenient and flexible operation, and low cost. Furthermore, it possesses strong anti-interference capabilities and strong terrain adaptability. GPR is currently one of the most promising and developing methods for non-destructive detection of underground targets and has always been a hot research topic in international academia. Currently, the application fields of GPR technology have far exceeded the scope of "ground exploration." As an important non-destructive testing method, it plays a vital role in areas such as the detection of hidden hazardous materials, engineering quality inspection, environmental monitoring, geological exploration, and archaeology.

[0003] During detection, the propagation of electromagnetic fields underground is unique, necessitating different approaches than those used by air-to-ground radar to address the challenges encountered by ground-penetrating radar (GPR). Targets detected by GPR often exist in complex environments, and the echo signals contain a significant amount of clutter, such as direct coupling waves from the transmitting and receiving antennas, surface reflections, reflections from non-uniform underground media, and random noise. This greatly impacts target detection and subsequent imaging processing. Therefore, research on clutter suppression algorithms for shallow-surface GPR is of paramount practical importance for improving its detection performance in the face of increasingly complex real-world detection environments.

[0004] Currently, numerous studies have been conducted both domestically and internationally on clutter suppression algorithms for ground-penetrating radar (GPR). Subspace decomposition methods mainly include Principal Component Analysis (PCA), Independent Component Analysis (ICA), and Singular Value Decomposition (SVD). The basic idea is to utilize the different characteristics of clutter and target signals in echo data to decompose it into clutter and target components, and then select the target component to form the target subspace. These algorithms exhibit good adaptability to different environments, but when multiple target signals exist in the echo data or the environmental clutter is complex, clutter cannot be completely removed, and the selection of target components needs further improvement. Methods based on Low-rank and Sparse Matrix Decomposition (LRSD) theory treat echo data as the sum of a low-rank matrix and a sparse matrix. Clutter and target responses are contained in the low-rank and sparse matrices, respectively, and they can be separated by solving the LRSD problem. Representative methods include Robust Principal Component Analysis (RPCA), Robust Nonnegative Matrix Factorization (RNMF), and Robust Autoencoder (RAE), which currently offer the best performance and widest applicability. However, these methods all have certain limitations, such as the significant impact of regularization parameter selection on algorithm performance, the tendency to distort the target signal, and generally limited effectiveness in noise removal. Summary of the Invention

[0005] In view of this, the present invention provides a clutter suppression method for multi-resolution low-rank sparse decomposition of ground penetrating radar, which can overcome the problem that the selection of regularization parameters has a great influence on the effect of the algorithm, easily causes the target signal to be distorted and has a mediocre effect on noise removal.

[0006] The technical solution for implementing the present invention is as follows:

[0007] A multi-resolution low-rank sparse decomposition clutter suppression method for ground-penetrating radar (GPR) first decomposes the echo data into multiple scales using wavelet transform, obtaining approximate sub-bands, horizontal detail sub-bands, vertical detail sub-bands, and diagonal detail sub-bands at different scales. For the approximate and horizontal detail sub-bands, a robust non-negative matrix factorization algorithm is used to extract the sparse portion of the target, and a regularization parameter is autonomously selected based on the target-clutter peak ratio. For the vertical and diagonal detail sub-bands, wavelet soft thresholding is used for denoising. Finally, the target signal is reconstructed by inverse wavelet transform of each processed signal component, thus achieving clutter suppression.

[0008] Furthermore, the method specifically includes the following steps:

[0009] Step 1: Establish a ground-penetrating radar signal receiving model;

[0010] Step 2: Use two-dimensional static wavelet transform to perform multi-scale decomposition on the echo data to obtain approximate subband, horizontal detail subband, vertical detail subband and diagonal detail subband signals at different scales;

[0011] Step 3: Using the principle of low-rank sparse decomposition, an improved robust non-negative matrix decomposition algorithm is applied to the approximate subband and the horizontal detail subband to obtain the target sparse component.

[0012] Step 4: Perform wavelet soft thresholding denoising on the vertical detail subband and the diagonal detail subband to obtain the target high-frequency subband signal;

[0013] Step 5: Perform two-dimensional inverse wavelet transform on each processed sub-band to reconstruct the target signal in order to achieve clutter suppression.

[0014] Furthermore, wavelet decomposition with a decomposition scale of two is adopted.

[0015] Furthermore, in step three, the improved robust nonnegative matrix factorization algorithm specifically refers to the modification of the regularization parameter in the robust nonnegative matrix factorization algorithm. Based on target-clutter peak ratio Make your own choice.

[0016] Furthermore,

[0017]

[0018] in, For the target region peak value, Peak value in the clutter region;

[0019] when hour, .

[0020] Beneficial effects:

[0021] 1. This invention is applied to the field of ground penetrating radar signal processing. Through experiments, it compares various typical algorithms (mean subtraction (MS), singular value decomposition, robust nonnegative matrix decomposition, etc.). When the echo signal contains target signals and multiple clutter signals and random noise exist at the same time, this invention can provide high-definition target signals and obtain a high signal-to-clutter ratio, which is a robust clutter suppression method.

[0022] 2. Because wavelet transform can be used for time-frequency domain processing at different scales, this invention provides a better explanation of the non-stationary performance of ground-penetrating radar echo data and enhances the retention of target signals in the data.

[0023] 3. Based on the principle of low-rank sparsity, this invention employs an improved robust non-negative matrix factorization algorithm for the decomposed approximate subband and horizontal detail subband, thus effectively improving the robustness of the algorithm. At the same time, by performing wavelet soft thresholding denoising on the vertical detail and diagonal detail subbands to filter out random noise, the signal-to-noise ratio is further improved. Attached Figure Description

[0024] Figure 1 This is a flowchart of the signal processing according to an embodiment of the present invention.

[0025] Figure 2 This is a schematic diagram of two-dimensional wavelet transform decomposition in the method of this invention.

[0026] Figure 3 These are the simulation and experimental results used in the experiment of this invention; where (a) is the simulation data and (b) is the experimental data.

[0027] Figure 4 This is a decomposition diagram of the simulation data by wavelet transform in step 2 of the present invention; where (a) is the approximate subband, (b) is the horizontal detail subband, (c) is the vertical detail subband, and (d) is the diagonal detail subband.

[0028] Figure 5 and The fitted curve.

[0029] Figure 6 These are the clutter suppression results of simulation data using different methods of the present invention; where (a) is mean cancellation method, (b) is SVD, (c) is RNMF, and (d) is WT-RNMF.

[0030] Figure 7 These are graphs showing the clutter suppression results of measured data using different methods of the present invention. Among them, (a) is the mean cancellation method, (b) is SVD, (c) is RNMF, and (d) is WT-RNMF. Detailed Implementation

[0031] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0032] This invention provides a method for suppressing clutter in multi-resolution low-rank sparse decomposition ground-penetrating radar. Figure 1 This is a signal processing flowchart of an embodiment of the present invention. Figure 1 As shown, the present invention is achieved through the following steps:

[0033] Step 1: Establish a ground-penetrating radar signal receiving model;

[0034] The received echo signal can be represented as:

[0035]

[0036] Assuming the received signal It is an M×N matrix, where M is the number of sampling points for each detection point, and N is the number of detection points, i.e., the number of acquisition channels. This is the target signal, which is relatively weak. The waveform and magnitude of the signal depend on the size, shape, and material of the target, as well as the environment in which the target is buried. The magnitude of the direct-coupled wave between the transmitting and receiving antennas depends on the antenna design and location. For ground-penetrating radars that commonly use dipole antennas, the antenna mutual-coupled wave can generally be considered a constant value, independent of the measurement location. Ground clutter signals include surface reflections (surface clutter) and reflections from the interface between the background medium and the ground (subsurface clutter). This part of the signal is relatively strong and is the most important to suppress. Ground clutter is usually related to various factors such as antenna height above the ground, soil type and uniformity, and surface roughness. Direct coupling waves between the transmitting and receiving antennas and surface reflections usually account for a large amount of energy in the echo data. This is receiver noise signal, which is also random noise.

[0037] Step 2: Perform multi-scale decomposition of the echo data using two-dimensional static wavelet transform;

[0038] First, a two-dimensional static wavelet transform (SWT) is used to decompose the input image into multiple scales and resolutions, exhibiting translation time invariance. Due to the use of a multi-aperture algorithm, the generated sub-bands have the same size as the input image, making them more suitable for image fusion, segmentation, and denoising applications. This invention employs a two-scale wavelet decomposition, the process of which is as follows: Figure 2 As shown.

[0039] in, , , , , , representing the approximate subband and directional subband (including horizontal detail subband, vertical detail subband and diagonal detail subband) after decomposition, respectively. , where is the number of layers or scale of the decomposition. , These are a one-dimensional low-pass filter and a high-pass filter, respectively. First, one-dimensional filtering is performed on the rows of the input data, and then one-dimensional filtering is performed on the columns to obtain two-dimensional approximate subbands, horizontal detail subbands, vertical detail subbands, and diagonal detail subbands. , It is a wavelet decomposition filter used for scale 2, which is expanded by inserting two zeros between the samples of the first scale filter.

[0040] Using two-dimensional SWT decomposition preserves more detail in the approximate subbands, and because there is no decimation operation, it does not reduce the size of the SWT output. SWT decomposition provides an approximate image and three directional sub-images at each decomposition level, such as... Figure 4 As shown in (a) to (d).

[0041] Step 3: Using the principle of low-rank sparse decomposition, an improved robust non-negative matrix decomposition algorithm is applied to the approximate subband and the horizontal detail subband to obtain the target sparse component;

[0042] In many engineering applications, it's often necessary to impose two constraints on data: nonnegativity and sparsity. A nonnegativity constraint ensures the data is non-negative; in reality, much data is inherently non-negative, forming a non-negative matrix. A sparsity constraint, on the other hand, restricts the data to be sparse rather than dense. This means the data matrix might be corrupted, but the corruption is sparse; that is, most data points are zero, and only a small number are non-zero.

[0043] The following describes the application process of RNMF in GPR images:

[0044] GPR images consist of a rectangular matrix of size M×N. X This means that M represents the number of sampling points per detection point, and N represents the number of detection points, i.e., the number of acquisition channels. X It can be represented as:

[0045]

[0046] Data Matrix Assumed to be the sum of the low-rank and sparse parts, RNMF decomposes the data matrix into a sparse error matrix representing the target components. And a low-rank non-negative matrix representing clutter components, consisting of two non-negative matrices. and The product is represented as:

[0047]

[0048] in , , , , It is the number of low-rank products in nonnegative matrix factorization. For the RNMF problem, its optimization can be solved by the following formula:

[0049]

[0050]

[0051] in, , is the regularization parameter that controls sparsity. To solve the above problem, consider a non-negative quadratic programming problem, and use a multiplication algorithm to complete the following iteration:

[0052]

[0053]

[0054] This completes the solution for the low-rank part. Then, the soft thresholding operator can be used to efficiently solve the problem of updating the sparse matrix. For the convex optimization problem, the soft threshold operator is defined as follows:

[0055]

[0056] in, , ,for To put it another way:

[0057]

[0058] Since the solution to minimizing the objective function is not unique, further requirements are needed to eliminate this degree of freedom. The norm of each column vector in the matrix is ​​1. Then, the norm of the cardinality is compensated to... To keep the value of the objective function unchanged, the two normalization steps are as follows:

[0059]

[0060]

[0061] Thus, the robust nonnegative matrix factorization algorithm yields the processed approximate subband and horizontal detail subband.

[0062] For all methods based on the principle of low-rank sparse decomposition, such as RPCA and RNMF, regularization parameters play a significant role. Currently, some researchers assign fixed values ​​to regularization parameters. In some scenarios, this can achieve good results. However, as the scenarios change, fixed values ​​often cannot adapt to different echo data. As the formula shows, It is directly related to sparsity and also affects the target peak value. Since the target peak value is easier to determine and measure than sparsity, it is chosen as the variable to establish a relationship with sparsity. The connection. The larger the value, the smaller the target area retained, meaning the greater the sparsity and the greater the attenuation of the target peak. Therefore, we can conclude that when the target peak is strong, a larger value can be selected. To reduce the target peak value to a certain extent with minimal impact on detection and recognition, clutter should be removed as much as possible to increase sparsity; when the target peak value is weak, if a larger sparsity is still selected... This will weaken the already low target peak value, which may be detrimental to target detection and recognition. Therefore, a smaller peak value should be selected. This ensures that the target peak is only slightly affected, while also improving sparsity to some extent.

[0063] This invention is based on the target-clutter peak ratio. Provided The autonomous selection method. The target-clutter peak value is defined as follows:

[0064]

[0065] in, For the target region peak value, The peak value represents the clutter region. The RNMF algorithm was applied to four sets of data (two simulations and two field measurements), and the appropriate algorithm was manually selected through adjustments. After achieving good clutter suppression, the target-to-clutter peak ratio was determined. , Four groups were obtained. Using the least squares curve fitting principle, the polynomial formula for s is as follows, and its curve is shown in the figure. Figure 5 As shown.

[0066]

[0067] The research and analysis of this invention show that there is a clear positive correlation between the target-clutter peak ratio and the regularization parameter value. For GPR echo data with unknown input, it is only necessary to calculate its target-clutter peak ratio and substitute it into the above formula to obtain the appropriate regularization parameter, thus completing the process. The right to make one's own choice.

[0068] Step 4: Perform wavelet soft thresholding denoising on the vertical detail subband and the diagonal detail subband to obtain a clearer target high-frequency subband signal;

[0069] After wavelet decomposition of the original data, the vertical and diagonal detail subbands mainly contain high-frequency details of the target signal and low-energy clutter and noise signals. To separate the target signal from the clutter and noise, this invention employs a threshold denoising method. This is a simple and effective wavelet denoising method. The idea behind the threshold denoising method is to process the coefficients with moduli greater than and less than a certain threshold in each layer of the wavelet decomposition, and then perform an inverse transform on the processed wavelet coefficients to reconstruct the denoised signal. The threshold denoising method used in this invention is described below from the aspects of threshold function and threshold estimation.

[0070] Soft threshold function:

[0071]

[0072] in The original wavelet coefficients of the signal are represented. Indicates the selected threshold. This represents the wavelet coefficients after thresholding.

[0073] threshold An adaptive threshold selection method based on Stein unbiased likelihood estimation is adopted, and the specific steps are as follows:

[0074] • Take the absolute value of the wavelet coefficient vector (length is...) Arrange them in ascending order to obtain a new vector to be estimated. ,

[0075] For each element of S, the risk vector is calculated using the following formula: ( For the first (risk vector of elements)

[0076]

[0077] • Find the minimum value in the risk vector as the risk value, and its corresponding index is . Then the threshold is:

[0078]

[0079] Thus, the vertical and diagonal details are obtained after wavelet soft thresholding denoising.

[0080] Step 5: Perform two-dimensional inverse wavelet transform on each processed sub-band to reconstruct the target signal in order to achieve clutter suppression.

[0081] The approximate subband, horizontal detail subband, vertical detail subband, and diagonal detail subband obtained from steps 4 and 5 are subjected to two-dimensional inverse wavelet transform to reconstruct the target signal. Thus, a multi-resolution low-rank sparse decomposition clutter suppression method for ground penetrating radar is completed.

[0082] Example

[0083] To verify the proposed multi-resolution low-rank sparse decomposition clutter suppression method for ground-penetrating radar, experiments were conducted using GPR simulation data and real-world data from actual testing environments to validate the effectiveness of various algorithms, including mean cancellation (MS), singular value decomposition (SVD), robust nonnegative matrix factorization (RNMF), and the proposed wavelet transform-based robust nonnegative matrix factorization algorithm (WT-RNMF). The performance of each algorithm was quantitatively compared and analyzed using performance indicators such as signal-to-clutter ratio. (Echo data were normalized, i.e., the amplitude was converted to the 0-1 range before clutter suppression processing.)

[0084] Since visual inspection is often insufficient to verify algorithm performance, multiple performance metrics are needed to validate the effectiveness of clutter suppression. This invention employs two metrics: signal-to-clutter ratio (SCR) and improvement factor. The SCR is used to determine performance based on the energy ratio of the target signal and pseudo-target signal to the background signal; a higher SCR indicates better performance. The improvement factor compares the SCR of the image after suppression with that of the image before suppression to determine the effectiveness of clutter suppression and the degree of SCR improvement; a higher SCR indicates greater improvement.

[0085] The simulation data was generated using the software gprMax based on the Finite Difference Time Domain (FDTD) method. The target was an irregular loose body in the underground soil environment (loose bodies are often caused by improper backfilling during multiple excavations in the road construction or operation phases, leading to reduced compaction. Based on the degree of impact on urban road safety, they can be classified as severely loose, moderately loose, and slightly loose. Severely loose bodies may develop into cavitary bodies under water and load conditions, and under certain conditions, may eventually form cavities). The obtained GPR images are shown below. Figure 3 As shown in (a), the target echo signal is masked due to the high intensity of the antenna direct-coupled wave and the reflected wave from the ground, coupled with the complex soil environment. Four clutter suppression algorithms were applied, and the results are shown below. Figure 6As shown in (a) to (d), the performance comparison is shown in Table 1. First, the mean cancellation method shows that the hyperbola of the loose target is fully revealed, meaning that the direct antenna wave and the reflected wave from the flat surface can be filtered out. However, a large amount of non-uniform clutter remains on the upper surface, originating from the characteristics of the soil. Furthermore, the "parallel line" at the top of the target caused by the mean operation results in less than ideal clutter suppression. While the singular value decomposition method in subspace decomposition improves the suppression effect compared to the mean cancellation method, a large amount of clutter still exists, and the target echo is not clear enough. The robust non-negative matrix decomposition method based on low-rank sparse decomposition can remove most of the clutter and provide a clear target signal, but overall it is acceptable, although some residual noise and clutter remain. The robust non-negative decomposition method based on wavelet transform proposed in this invention has the best processing effect. While improving target clarity and suppressing most clutter, it basically preserves the target signal, achieving the highest signal-to-clutter ratio.

[0086] Table 1: Comparison of simulation data metrics after processing with different algorithms

[0087]

[0088] The measured data was obtained using the LTD-2600 new intelligent ground-penetrating radar system developed by the China Institute of Radio Waves, which detected the target cavity. The underground medium was white sand, and the obtained GPR images are shown below. Figure 3 As shown in (b), the two approximate horizontal lines represent the upper and lower surfaces of the white sand, respectively, and both contain a significant amount of clutter. Four clutter suppression algorithms were applied, and the results are shown below. Figure 7 As shown in (a) to (d), the performance index comparison is shown in Table 2. Although mean cancellation and singular value decomposition can remove direct-coupled waves and surface reflected waves, there are still many residual reflected waves, and they cannot effectively handle reflected waves from non-uniform underground media. RNMF can remove surface reflected waves to a greater extent and also has a certain suppression effect on reflected waves from non-uniform media, improving the clarity of the target. The robust non-negative matrix decomposition based on wavelet transform proposed in this invention not only further removes surface reflected waves but also suppresses reflected waves from non-uniform media quite ideally, highlighting the target information and having the highest signal-to-noise ratio, thus verifying the effectiveness and robustness of this algorithm.

[0089] Table 2: Comparison of Indicators of Measured Data After Processing with Different Algorithms

[0090]

[0091] The experimental results above demonstrate that the proposed multi-resolution low-rank sparse decomposition clutter suppression method for ground penetrating radar can achieve a high signal-to-clutter ratio while maximizing the preservation of the target signal during the clutter suppression process, thus verifying the effectiveness and robustness of the algorithm. Compared to the classic robust nonnegative matrix factorization (NVB) algorithm, this algorithm uses wavelet transform to decompose the echo data at multiple scales, obtaining approximate subbands, horizontal detail subbands, vertical detail subbands, and diagonal detail subbands at different decomposition levels of the original data. For the approximate and horizontal detail subbands, which exhibit significant low-rank sparsity, robust NNB is used to extract the target sparse portion. For the vertical and diagonal detail subbands, where noise and target components are prominent, wavelet soft thresholding is used for denoising. Finally, inverse wavelet transform is performed on each processed signal component to reconstruct the target signal, achieving in-depth analysis of the echo data. Since wavelet transform can perform time-frequency domain processing at different scales, it provides a good explanation for the non-stationary performance of ground-penetrating radar echo data, enhancing the retention of target signals in the data. Based on the low-rank sparsity principle, robust NNB is applied to the decomposed approximate values ​​and horizontal detail signals, effectively improving the algorithm's robustness. Simultaneously, wavelet soft thresholding denoising of the vertical and diagonal detail signals filters out random noise, further improving the signal-to-noise ratio.

[0092] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for suppressing low-rank sparse decomposition clutter in ground-penetrating radar (GPR), characterized in that, First, the echo data is decomposed into multiple scales using wavelet transform to obtain approximate subbands, horizontal detail subbands, vertical detail subbands, and diagonal detail subbands at different scales. For the approximate subbands and horizontal detail subbands, a robust non-negative matrix factorization algorithm is used to extract the sparse part of the target, and a regularization parameter is selected autonomously based on the target-clutter peak ratio. For the vertical detail and diagonal detail subbands, wavelet soft thresholding is used for noise reduction. Finally, the target signal is reconstructed by inverse wavelet transform of each processed signal component to achieve clutter suppression. The regularization parameter Based on target-clutter peak ratio Make your own choice. ,in, For the target region peak value, Peak value in the clutter region; when hour, ; The threshold selection method in the wavelet soft thresholding denoising adopts an adaptive threshold selection method based on Stein unbiased likelihood estimation. The specific steps are as follows: Take the absolute value of the wavelet coefficient vector and arrange them in ascending order to obtain a new vector to be estimated. , For each element of S, the risk vector is calculated using the following formula: in, For the first A risk vector with n elements, where n is the length of the wavelet coefficient vector; Find the minimum value in the risk vector as the risk value, and its corresponding index is... Then the threshold is: 。 2. The ground-penetrating radar multi-resolution low-rank sparse decomposition clutter suppression method as described in claim 1, characterized in that, The method includes the following steps: Step 1: Establish a ground-penetrating radar signal receiving model; Step 2: Use two-dimensional static wavelet transform to perform multi-scale decomposition on the echo data to obtain approximate subband, horizontal detail subband, vertical detail subband and diagonal detail subband signals at different scales; Step 3: Using the principle of low-rank sparse decomposition, an improved robust non-negative matrix decomposition algorithm is applied to the approximate subband and the horizontal detail subband to obtain the target sparse component. Step 4: Perform wavelet soft thresholding denoising on the vertical detail subband and the diagonal detail subband to obtain the target high-frequency subband signal; Step 5: Perform two-dimensional inverse wavelet transform on each processed sub-band to reconstruct the target signal in order to achieve clutter suppression.

3. A method for suppressing low-rank sparse decomposition clutter in ground-penetrating radar as described in claim 1 or 2, characterized in that, Wavelet decomposition with a decomposition scale of two is adopted.

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