A Denoising Method for Ground Penetrating Radar Data Based on Grouped Singular Spectra

Abstract

This invention provides a noise reduction method for ground-penetrating radar (GPR) data based on grouped singular spectra. It employs zero-bias mode GPR and, based on singular spectrum analysis, decomposes the spectral matrix of GPR data into an orthogonal matrix and a singular value matrix. The singular values ​​are grouped using the k-means clustering method, and the singular values ​​of the spectral matrix are reweighted using a grouping weighting function, thereby reducing noise interference in the GPR data.

Description

Technical Field

[0001] This invention belongs to the field of computer digital image processing. The algorithm is based on singular spectrum analysis, singular value grouping and grouping weighting function, which reduces noise interference in ground-penetrating radar data. Background Technology

[0002] Ground-penetrating radar (GPR) transmits high-frequency, broadband electromagnetic waves in pulse form into the ground. A portion of these waves travels directly from the transmitting antenna to the receiving antenna, forming a coupled wave. Another portion, after being transmitted, is reflected back from the air-surface interface without penetrating the ground, forming a direct wave. Coupled and direct waves are often collectively referred to as direct-coupled waves, frequently used to determine the zero-time point as a reference for judging the depth of underground targets. The remaining electromagnetic waves propagate underground. When they encounter underground targets with different electrical properties (such as cavities, water pockets, and loose materials) or interfaces between different media, the electromagnetic waves are reflected back to the surface and received by the receiving antenna. After acquisition, processing, and storage, the received signals become GPR data containing information about the underground medium.

[0003] Ground-penetrating radar (GPR) data, particularly deep signals, is significantly affected by environmental noise, necessitating denoising. This necessitates the research of GPR data denoising methods. To achieve this goal, singular value decomposition (SVD) is employed to decompose the spectral matrix of GPR data into orthogonal matrices and singular value matrices. By using singular value grouping and a grouping weighting function, noise interference in the GPR data is reduced. Singular value decomposition is an important matrix decomposition method in linear algebra, representing a generalization of eigenvalue decomposition to arbitrary matrices. SVD has significant applications in signal processing, statistics, and other fields. Summary of the Invention

[0004] The purpose of this invention is to reduce noise interference in ground-penetrating radar (GPR) data by using singular spectral analysis based on the characteristics of GPR data and by using singular value grouping and grouping weighting functions.

[0005] The specific steps of this method are as follows:

[0006] Step (A1): Perform a one-dimensional Fourier transform on the ground-penetrating radar data D(i,j), where i = 1, 2, ..., n, j = 1, 2, ..., m, to obtain the spectrum matrix D. f (i,j), for this spectrum matrix D f Perform singular value decomposition to obtain D f =USV, where n is the number of rows in the spectrum matrix, m is the number of columns in the spectrum matrix, and n << m, S = [diag(σ1,σ2,...,σ...] n ] is a singular value matrix, where U and V are orthogonal matrices, and σ1,σ2,...,σ nFor the spectrum matrix D f The singular values;

[0007] Step (A2): For the spectrum matrix D f The singular values ​​σ1,σ2,...,σ n The singular values ​​were grouped using the k-means clustering method, resulting in k groups:

[0008]

[0009] Step (A3): Using the grouping weighting function

[0010]

[0011] Each singular value is weighted separately, where S(x) is the grouping weighting function, x is the singular value independent variable, p is the number of elements in each group, k is the number of singular value groups, and a, b, and c are constants.

[0012] Step (A4): The singular value matrix after weighting by the grouping weighting function is Obtain the spectrum matrix D′ f =US′V, for the spectrum matrix D′ f Perform a one-dimensional inverse Fourier transform to obtain the noise-reduced ground-penetrating radar data D′.

[0013] The present invention has the following advantages:

[0014] 1. The singular value grouping proposed in this invention uses the k-means clustering method to automatically complete the grouping process, and the grouping results have high reliability.

[0015] 2. The grouping weighting function proposed in this invention can reweight the singular values ​​of the spectrum matrix, thereby reducing noise interference in ground-penetrating radar data. Attached Figure Description

[0016] Figure 1 Flowchart of the technical method of this invention

[0017] Figure 2 Comparison of ground-penetrating radar data before and after noise reduction in this invention Detailed Implementation

[0018] This invention addresses the issue of significant environmental noise interference in deep signals of ground-penetrating radar (GPR) B-scan data under zero-bias mode. Based on singular spectral analysis, it reduces noise interference in GPR data through singular value grouping and a grouping weighting function. The GPR data enhancement based on singular value scaling involves two processing steps. The first step directly enhances the GPR data, requiring the number of columns to be greater than or equal to the number of rows. The specific steps are as follows:

[0019] (1) Perform a one-dimensional Fourier transform on the ground-penetrating radar data D(i,j), where i=1,2,...,n and j=1,2,...,m, to obtain the spectrum matrix D. f (i,j), for this spectrum matrix D f Perform singular value decomposition to obtain D f =USV, where n is the number of rows in the spectrum matrix, m is the number of columns in the spectrum matrix, and n << m, S = [diag(σ1,σ2,...,σ...] n ] is a singular value matrix, where U and V are orthogonal matrices, and σ1,σ2,...,σ n For the spectrum matrix D f The singular values;

[0020] (2) For the spectrum matrix D f The singular values ​​σ1,σ2,...,σ n The singular values ​​were grouped using the k-means clustering method, resulting in k groups:

[0021]

[0022] (3) Using grouping weighting function

[0023]

[0024] Each singular value is weighted separately, where S(x) is the grouping weighting function, x is the singular value independent variable, p is the number of elements in each group, k is the number of singular value groups, and a, b, and c are constants.

[0025] (4) The singular value matrix after being weighted by the grouping weighting function is: Obtain the spectrum matrix D′ f =US′V, for the spectrum matrix D′ f Perform a one-dimensional inverse Fourier transform to obtain the noise-reduced ground-penetrating radar data D′.

[0026] When the number of columns in the ground-penetrating radar (GPR) data is less than the number of rows, the second process is used to enhance the GPR data. The specific steps are as follows:

[0027] (1) Extend the column of the ground-penetrating radar data D to form a new ground-penetrating radar data T = [DD]. Then determine whether the number of columns of the ground-penetrating radar data is less than the number of rows of the ground-penetrating radar data. If the number of columns of the ground-penetrating radar data is still less than the number of rows of the ground-penetrating radar data, continue to extend the column to obtain a new ground-penetrating radar data T = [DDD]. Continue in this manner until the number of columns of the ground-penetrating radar data is greater than or equal to the number of rows of the ground-penetrating radar data.

[0028] (2) Perform a one-dimensional Fourier transform on the ground-penetrating radar data T(i,j), where i = 1, 2, ..., n and j = 1, 2, ..., m, to obtain the spectrum matrix T. f (i,j), for this spectrum matrix T f Perform singular value decomposition to obtain T f =USV, where n is the number of rows in the spectrum matrix, m is the number of columns in the spectrum matrix, and n << m, S = [diag(σ1,σ2,...,σ...] n ] is a singular value matrix, where U and V are orthogonal matrices, and σ1,σ2,...,σ n For the spectrum matrix T f The singular values;

[0029] (3) For the spectrum matrix T f The singular values ​​σ1,σ2,...,σ n The singular values ​​were grouped using the k-means clustering method, resulting in k groups:

[0030]

[0031] (4) Using grouping weighting function

[0032]

[0033] Each singular value is weighted separately, where S(x) is the grouping weighting function, x is the singular value independent variable, p is the number of elements in each group, k is the number of singular value groups, and a, b, and c are constants.

[0034] (5) The singular value matrix after being weighted by the grouping weighting function is: Obtain the spectrum matrix T′ f =US′V, for the spectrum matrix T′ f Perform a one-dimensional inverse Fourier transform to obtain the noise-reduced ground-penetrating radar data T′.

[0035] (6) Since the number of columns of the ground-penetrating radar data D is m, the first m columns of the ground-penetrating radar data T′ are extracted as the final enhanced ground-penetrating radar data D′.

Claims

1. A noise reduction method for ground-penetrating radar data based on grouped singular spectra. This method is based on singular spectrum analysis and reduces noise interference in ground-penetrating radar data through singular value grouping and grouping weighting functions. The specific steps are as follows: Step (A1): Perform a one-dimensional Fourier transform on the ground-penetrating radar data D(i,j), where i = 1, 2, ..., n, j = 1, 2, ..., m, to obtain the spectrum matrix D. f (i,j), for this spectrum matrix D f Perform singular value decomposition to obtain D f =USV, where, n is the number of rows in the spectrum matrix, m is the number of columns in the spectrum matrix, and n << m, S = [diag(σ1,σ2,...,σ...]]. n ] is a singular value matrix, where U and V are orthogonal matrices, and σ1,σ2,...,σ n For the spectrum matrix D f The singular values; Step (A2): For the spectrum matrix D f The singular values ​​σ1,σ2,...,σ n The singular values ​​were grouped using the k-means clustering method, resulting in k groups: Step (A3): Using the grouping weighting function Each singular value is weighted separately, where S(x) is the grouping weighting function, x is the singular value independent variable, p is the number of elements in each group, k is the number of singular value groups, and a, b, and c are constants. Step (A4): The singular value matrix after weighting by the grouping weighting function is Obtain the spectrum matrix D′ f =US′V, for the spectrum matrix D′ f Perform a one-dimensional inverse Fourier transform to obtain the noise-reduced ground-penetrating radar data D′.

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