Ground penetrating radar clutter suppression method based on noise reduction source separation and wavelet transform

Abstract

The invention discloses a ground penetrating radar clutter suppression method based on noise reduction source separation and wavelet transformation, and the method comprises the steps: collecting the echo signal amplitude and echo signal phase of each frequency point of a stepping frequency continuous wave ground penetrating radar, and further obtaining an observation matrix; denoising the echo signal amplitude of each frequency point and the echo signal phase of each frequency point based on a wavelet threshold denoising method and the observation matrix to obtain the echo signal amplitude and the echo signal phase; and performing nonlinear distortion compensation on the phase of the echo signal to obtain the phase after nonlinear distortion compensation, and further calculating the echo signal based on the phase. Compensation of phase waveform nonlinear distortion is introduced, interference of phase noise on a measurement result is avoided, and the precision of underground target midpoint measurement is improved.

Description

Technical Field

[0001] The present invention relates to the field of remote sensing, and specifically relates to a ground penetrating radar clutter suppression method based on noise reduction source separation and wavelet transform, which is applicable to the detection of the position of underground targets. Background Art

[0002] Ground Penetrating Radar (GPR) is an important and rapidly developing geophysical method. As an effective tool for realizing the identification and positioning of underground targets by using the reflection and scattering phenomena of electromagnetic waves at medium discontinuities, it is widely used in fields such as the detection of hidden road diseases, the health monitoring of hydraulic tunnels, the detection of underground transmission lines, and the detection of glacier thickness due to advantages such as fast speed, continuous process, high imaging clarity, and non-destructive detection.

[0003] The methods for suppressing underground clutter in ground penetrating radar mainly include two aspects. One is to add a spatial isolation structure in the antenna system to reduce the ability of the ground penetrating radar system to receive clutter. In 2012, Yingbo Hua et al. used time-domain beamforming technology to obtain deep nulls at specified positions to achieve coupling suppression between the transmitting and receiving antennas within a 30 MHz bandwidth. In addition, in 2019, Gu Xiaoxuan et al. proposed an F-shaped hybrid isolator to achieve coupling suppression between the transmitting antenna and the receiving antenna within a bandwidth not exceeding 500 MHz. However, for most spatial isolation structures, their fractional bandwidth is less than 25%, which does not meet the definition of ultra-wideband. Considering the ultra-wideband characteristics of SFCW, it is difficult to introduce a spatial isolation structure into SFCW-GPR. Another method is to establish a signal subspace in the time domain or train a specific clutter suppression neural network to identify and eliminate the clutter interference terms hidden in the signal. First, in order to effectively suppress the clutter interference caused by air-to-ground direct coupling and surface reflection, a mean filtering method was proposed. To quickly extract the characteristics of weak underground echoes, they used the average value of the echo characteristics in the target-free area to filter out background clutter. But they are only applicable to stationary random clutter. For non-stationary random clutter, such as the clutter caused by uneven moisture distribution in the soil, some clutter suppression methods based on signal subspace were proposed, including singular value decomposition (SVD), principal component analysis (PCA), independent component analysis (ICA), etc. Once the clutter intensity is similar to the target echo, it is difficult for the above methods to correctly extract the echo. Therefore, deep learning was introduced to solve the above problems. In 2022, Zhi-Kang Ni et al. proposed a non-linear underground clutter suppression method based on a robust autoencoder (RAE), and Eyup-Temlioglu et al. proposed a network model based on a convolutional autoencoder (CAE) to remove clutter in 2D B-scans using a synthetic dataset. In summary, compared with the subspace-based clutter suppression methods, the deep learning-based methods have better clutter suppression effects. However, the implementation of the above methods is carried out from signal interference. For SFCW-GPR, in addition to clutter interference, there are also measurement errors caused by medium dispersion. Soil is a typical dispersive medium. In soil, electromagnetic waves of different frequencies propagate at different speeds. For the electromagnetic waves reflected from underground targets, different frequency components have different refractive indices and delays, which may lead to measurement errors in the measurement results. Although the above methods suppress clutter, they cannot eliminate the measurement errors caused by soil scattering. Summary of the Invention

[0004] The object of the present invention is to propose a ground penetrating radar clutter suppression method based on denoising source separation (DSS) and wavelet transform for the problem of measurement errors caused by soil medium dispersion in the prior art. This method can effectively reduce the measurement errors of the ground penetrating radar for the positions of underground targets.

[0005] The above object of the present invention is achieved by the following technical means:

[0006] A ground penetrating radar clutter suppression method based on noise source separation and wavelet transform, comprising the following steps:

[0007] Step 1: Collect the echo signal amplitude and echo signal phase of each frequency point of a stepped-frequency continuous wave ground penetrating radar, and further obtain an observation matrix;

[0008] Step 2: Based on the wavelet threshold denoising method and the observation matrix, denoise the echo signal amplitude and echo signal phase of each frequency point to obtain the echo signal amplitude and the echo signal phase

[0009] Step 3: Perform nonlinear distortion compensation on the echo signal phase to obtain the phase after nonlinear distortion compensation Based on and further calculate the echo signal s r .

[0010] The observation matrix in Step 1 above is obtained based on the following steps:

[0011] Remove the DC components in the echo signal amplitude and echo signal phase of each frequency point by means of centering processing,

[0012] Randomly sample the echo signal amplitude and echo signal phase at each frequency point, construct an echo signal amplitude input signal matrix and an echo signal phase input signal matrix based on the echo signal amplitude and echo signal phase of each frequency point, and perform dimensionality reduction processing on the echo signal amplitude input signal matrix and the echo signal phase input signal matrix by means of principal component analysis to obtain the echo signal amplitude input signal matrix and the echo signal phase input signal matrix after dimensionality reduction,

[0013] Construct a whitening matrix based on the echo signal amplitude input signal matrix and the echo signal phase input signal matrix after dimensionality reduction, and obtain the observation matrix for noise source separation through the whitening matrix.

[0014] The denoising of the echo signal amplitude and echo signal phase of each frequency point as described above includes the following steps:

[0015] Use the observation matrix to iteratively separate the Gaussian noise in the echo signal amplitude and echo signal phase of each frequency point to obtain the amplitude independent components corresponding to the echo signal amplitude of each frequency point and the phase independent components of the echo signal phase of each frequency point,

[0016] Calculate the negentropy of the amplitude independent component and the phase independent component after iterative separation of the amplitude and phase of the echo signal.

[0017] Delete the amplitude independent components smaller than the amplitude independent component threshold, and reconstruct and restore the amplitude independent components after deleting those smaller than the amplitude independent component threshold to the amplitude of the echo signal. Delete the phase independent components smaller than the phase independent component threshold, and reconstruct and restore the phase independent components after deleting those smaller than the phase independent component threshold to the phase of the echo signal.

[0018] The phase after non - linear distortion compensation as described above is obtained based on the following steps:

[0019] Step 3.1: Fit and calculate the solution X according to the following formula

[0020] Φ = AX

[0021] X = [aτ r T

[0022] where is the matrix of the ideal value of the rate of change of the phase of the distortion - free echo signal in the frequency domain, is the element corresponding to each frequency point of the matrix Φ,

[0023] parameter matrix

[0024] a is the undetermined coefficient used to assist in the solution,

[0025] τ r is the phase delay of the electromagnetic wave propagation distance,

[0026] p is the undetermined coefficient used to assist in the solution,

[0027] f d is the frequency step of the stepped - frequency signal,

[0028] X is the solution,

[0029] K is the total number of frequency point labels,

[0030] Step 3.2: Calculate the phase after non - linear distortion compensation

[0031] Step 3.3: Differentiate the phase after non - linear distortion compensation with respect to k to obtain the rate of change of the compensated echo signal phase in the frequency domain Assign to the elements corresponding to each frequency point of the matrix respectively Obtain the satisfaction of The phase after corresponding non - linear distortion compensation

[0032] The echo signal s as described above r is obtained based on the following formula:

[0033]

[0034] where: n is the unit time of signal sampling, and k is the frequency point label.

[0035] A ground - penetrating radar clutter suppression method based on noise - source separation and wavelet transform further includes the calculation step of the Cramer - Rao lower bound:

[0036] Satisfying The minimum and satisfying The minimum are used as the Cramer - Rao lower bound,

[0037] where The ideal value (V) of the amplitude of the echo signal after suppressing Gaussian noise;

[0038] The ideal value (reg) of the phase of the echo signal after non - linear distortion compensation;

[0039] σ 2 : The variance of the noise signal in the echo signal (V 2 );

[0040] N f : The discrete time maintained at each frequency point;

[0041] SNR M,k : The signal - to - noise ratio of the echo signal at frequency point k.

[0042] E[]: Mathematical expectation operation.

[0043] A computer device includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, the steps of the above - mentioned suppression method are implemented.

[0044] A computer - readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the above - mentioned suppression method are implemented.

[0045] A computer program product includes a computer program, and when the computer program is executed by a processor, the steps of the above - mentioned suppression method are implemented.

[0046] The present invention has the following beneficial effects compared with the prior art:

[0047] (1) Through the present invention, for the first time, the theoretical upper limit of the measurement accuracy of the system at the target position is obtained through the Cramér-Rao lower bound, making up for the deficiency in the quantitative analysis of the measurement results of traditional underground target positions.

[0048] (2) Compared with other clutter suppression methods, the improved method of the present invention introduces the compensation for the non-linear distortion of the phase waveform, avoids the interference of phase noise on the measurement results, and improves the accuracy of the midpoint measurement of underground targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a flow chart of the present invention.

[0050] Figure 2 It is a comparison diagram of the processing effects of one-dimensional echo signals between the present invention and traditional methods. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0051] In order to facilitate the understanding and implementation of the present invention by those of ordinary skill in the art, the present invention will be further described in detail below in conjunction with embodiments. The embodiments described herein are only used to illustrate and explain the present invention and are not intended to limit the present invention.

[0052] Embodiment 1:

[0053] A ground penetrating radar clutter suppression method based on noise source separation and wavelet transform, comprising the following steps:

[0054] Step 1: Preprocessing of the echo profile.

[0055] Step 1.1: Collect the echo signal amplitude and echo signal phase of each frequency point of the stepped-frequency continuous wave ground penetrating radar, and remove the DC components in the echo signal amplitude and echo signal phase of each frequency point through the means of centering processing;

[0056] Step 1.2: Randomly sample the echo signal amplitude and echo signal phase at each frequency point. One frequency point corresponds to one echo signal amplitude and one echo signal phase. Based on the echo signal amplitude and echo signal phase of each frequency point, construct an echo signal amplitude input signal matrix and an echo signal phase input signal matrix, and perform dimensionality reduction processing on the echo signal amplitude input signal matrix and the echo signal phase input signal matrix through the principal component analysis method to obtain the dimensionality-reduced echo signal amplitude input signal matrix and echo signal phase input signal matrix;

[0057] Step 1.3: Based on the dimensionality-reduced echo signal amplitude input signal matrix and echo signal phase input signal matrix, construct a whitening matrix through the decorrelation method, and obtain an observation matrix for noise source separation through the whitening matrix.

[0058] Step 2: Gaussian noise separation.

[0059] Step 2.1: Based on the wavelet threshold denoising method, use the observation matrix to iteratively separate the Gaussian noise in the echo signal amplitude of each frequency point and the echo signal phase of each frequency point, and obtain the amplitude independent component corresponding to the echo signal amplitude of each frequency point and the phase independent component of the echo signal phase of each frequency point;

[0060] Step 2.2: Calculate the negentropy of the amplitude independent component and the phase independent component after iterative separation of the echo signal amplitude and the echo signal phase, and evaluate the non-Gaussianity of each independent component after iterative separation of the echo signal amplitude and the echo signal phase through the value of the negentropy. The lower the negentropy of the independent component, the higher the Gaussianity of the independent component, and the greater the possibility that the independent component is used as a clutter signal. The purpose of suppressing Gaussian noise can be achieved by removing the independent components with low negentropy less than the negentropy threshold. Delete the amplitude independent components less than the amplitude independent component threshold, and reconstruct and restore the amplitude independent components with the amplitude independent components less than the amplitude independent component threshold deleted to the echo signal amplitude Delete the phase independent components less than the phase independent component threshold, and reconstruct and restore the phase independent components with the phase independent components less than the phase independent component threshold deleted to the echo signal phase After suppressing Gaussian noise, the nonlinear distortion in the echo signal phase will be compensated in Step 3.

[0061] Step 3: Nonlinear distortion compensation.

[0062] For the echo signal phase extracted in Step 2.2 Establish a nonlinear distortion model as shown in Equation (1):

[0063]

[0064] In the formula: f d : Frequency step of the stepped-frequency signal, MHz.

[0065] k: Frequency point label (k ∈ [1, 100]), k ∈ [1, K], and the total number of frequency point labels K = 100 in this embodiment.

[0066] N k : Nonlinear distortion term of the change rate of the echo signal phase in the frequency domain at the kth frequency point.

[0067] a: Undetermined coefficient for auxiliary solution.

[0068] Observed value of the change rate of the echo signal phase in the frequency domain.

[0069] τ r : Phase delay of the electromagnetic wave propagation distance.

[0070] p: The undetermined coefficient used for auxiliary solution.

[0071] k p is the p-th power of k.

[0072] Define the ideal value of the change rate of the phase of the distortionless echo signal in the frequency domain as Establish a linear solution model based on the least squares method of formula (2) for solving the phase delay τ of the electromagnetic wave propagation distance r :

[0073]

[0074] In the formula:

[0075] is the matrix constructed by the observed values of the change rate of the phase of the echo signal in the frequency domain;

[0076] is the matrix constructed by the ideal values of the change rate of the phase of the distortionless echo signal in the frequency domain.

[0077] The relationship between and Φ is as follows:

[0078] Phase observation matrix: Among them, the definitions of each parameter are as follows:

[0079] Parameter matrix A:

[0080] The solution of the model represented by formula (3): X = [a τ r T (5)

[0081] Residual Gaussian noise change rate matrix: N = [N 1 N 2 ...N K T (6)

[0082] At this time, the solution of the above problem can be expressed as:

[0083]

[0084] Step 3.1: Fit and calculate the solution X according to the following formula,

[0085] Φ = AX

[0086] X = [a τ r T

[0087] Among them, is the ideal value of the change rate of the phase of the distortionless echo signal in the frequency domain, ​​​is the element corresponding to each frequency point of the matrix Φ,

[0088] Parameter matrix

[0089] a is the undetermined coefficient used to assist in the solution,

[0090] τ r is the phase delay of the electromagnetic wave propagation distance,

[0091] Step 3.2: Calculate the phase after nonlinear distortion compensation

[0092] Step 3.3: Differentiate the phase after nonlinear distortion compensation with respect to k, to obtain the change rate of the phase of the compensated echo signal in the frequency domain Assign to the elements corresponding to each frequency point of the matrix respectively Obtain the phase after nonlinear distortion compensation that satisfies corresponding

[0093] Step 3.4: Based on the phase after nonlinear distortion compensation that satisfies corresponding

[0094] and the amplitude of the echo signal reconstruct the echo signal s described in Equation (8) r , and obtain the high-precision ground penetrating radar A-Scan signal s through matched filtering r .

[0095]

[0096] In the formula: n: the unit time of signal sampling.

[0097] Compared with the traditional method, the method shown in the present invention avoids the interference of phase noise on the measurement result and improves the accuracy of the midpoint measurement of underground targets.

[0098] Step 4: Calculate the theoretical limit of the underground target position measurement accuracy. For the amplitude of the echo signal after suppressing Gaussian noise obtained in Step 2 and the phase of the echo signal after nonlinear distortion compensation obtained in Step 3 that satisfies corresponding their theoretical minimum value of the root mean square error will be calculated by the following method, that is, their Cramer-Rao lower bound:

[0099]

[0100] In the formula The ideal value (V) of the amplitude of the echo signal after suppressing Gaussian noise;

[0101] The ideal value (reg) of the phase of the echo signal after non-linear distortion compensation;

[0102] σ 2 : The variance of the noise signal in the echo signal (V 2 );

[0103] N f : The discrete time maintained at each frequency point;

[0104] SNR M,k : The signal-to-noise ratio of the echo signal at frequency point k.

[0105] E[]: Mathematical expectation operation.

[0106] The smallest and the smallest satisfying Formula 8 are used as the Cramer-Rao lower bound.

[0107] Figure 2 is the specific implementation effect of the method described in this paper. In an actual scenario, the peak of the stepped-frequency radar A-Scan signal should point to the position of 10 ns. However, affected by the environment and internal system interference, the peak of the A-Scan signal processed by the traditional method (before clutter suppression) in Figure 1 points to 15.69 ns. After being processed by the method described in this paper (after clutter suppression), the peak of the obtained A-Scan signal points to 11.21 ns, and the pulse width is significantly narrowed. In summary, the results show that the method proposed in this paper can significantly reduce the measurement error of phase delay.

[0108] Those of ordinary skill in the art can understand that all or part of the processes in implementing the methods in the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the above method embodiments.

[0109] Embodiment 2:

[0110] In this embodiment, a computer device is further provided, including a memory and a processor. A computer program is stored in the memory, and when the processor executes the computer program, the steps in the above method embodiments are implemented.

[0111] Embodiment 3:

[0112] In this embodiment, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0113] Embodiment 4:

[0114] In this embodiment, a computer program product is provided, including a computer program. When the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0115] The specific embodiments described herein are merely illustrative of the spirit of the present invention. Those skilled in the art to which the present invention pertains can make various modifications or supplements to the described specific embodiments or use similar methods for substitution, but will not deviate from the spirit of the present invention or exceed the scope defined by the appended claims.

Claims

1. A method for suppressing clutter in ground penetrating radar based on noise source separation and wavelet transform, comprising the following steps: Step 1: Collect the echo signal amplitude and echo signal phase of each frequency point of the stepped frequency continuous wave ground penetrating radar, and further obtain the observation matrix; Step 2: Based on the wavelet threshold denoising method and the observation matrix, the echo signal amplitude and the echo signal phase of each frequency point are denoised to obtain the echo signal amplitude. and echo signal phase Step 3: Phase the echo signal Perform nonlinear distortion compensation to obtain the phase after nonlinear distortion compensation Based on and further calculating the echo signal s r .

2. The method for suppressing clutter of ground penetrating radar based on noise source separation and wavelet transform according to claim 1, characterized in that: The observation matrix in step 1 is obtained based on the following steps: The DC component in the echo signal amplitude and phase of each frequency point is removed by means of central processing. The echo signal amplitude and echo signal phase at each frequency point are randomly sampled, and the echo signal amplitude input signal matrix and the echo signal phase input signal matrix are constructed based on the echo signal amplitude and the echo signal phase at each frequency point. The echo signal amplitude input signal matrix and the echo signal phase input signal matrix are reduced in dimension by the principal component analysis method to obtain the echo signal amplitude input signal matrix and the echo signal phase input signal matrix after dimension reduction. A whitening matrix is ​​constructed based on the echo signal amplitude input signal matrix and the echo signal phase input signal matrix after dimensionality reduction, and an observation matrix for noise reduction source separation is obtained through the whitening matrix.

3. The method for suppressing clutter of ground penetrating radar based on noise source separation and wavelet transform according to claim 1, characterized in that: The denoising of the echo signal amplitude at each frequency point and the echo signal phase at each frequency point comprises the following steps: The measurement matrix is ​​used to iteratively separate the Gaussian noise in the echo signal amplitude and the echo signal phase of each frequency point, and the amplitude independent component corresponding to the echo signal amplitude of each frequency point and the phase independent component of the echo signal phase of each frequency point are obtained. Calculate the negative entropy of the amplitude independent component and phase independent component after iterative separation of the echo signal amplitude and the echo signal phase, Delete the amplitude independent components that are smaller than the amplitude independent component threshold, and reconstruct the deleted amplitude independent components that are smaller than the amplitude independent component threshold to restore them to the echo signal amplitude. Delete the phase independent components smaller than the phase independent component threshold, and reconstruct the phase independent components smaller than the phase independent component threshold to restore the echo signal phase.

4. The method for suppressing clutter of ground penetrating radar based on noise source separation and wavelet transform according to claim 1, characterized in that: The phase after nonlinear distortion compensation Based on the following steps: Step 3.1: Calculate the solution X according to the following formula: Φ=AX X=[aτ r ] T in, is the matrix of the ideal value of the change rate of the phase of the distortion-free echo signal in the frequency domain, is the element corresponding to each frequency point of the matrix Φ, Parameter Matrix a is the unknown coefficient used to assist in solving the problem. τ r is the phase delay of electromagnetic wave propagation distance, p is the unknown coefficient used to assist in solving the problem. f d is the frequency step of the step frequency signal, X is the solution, K is the total number of frequency point numbers. Step 3.2: Calculate the phase after nonlinear distortion compensation Step 3.3: Phase after nonlinear distortion compensation Relative to k differential, the rate of change of the compensated echo signal phase in the frequency domain is obtained Will Assign values ​​to the matrix The elements corresponding to each frequency point Get satisfaction The corresponding phase after nonlinear distortion compensation 5. The method for suppressing clutter of ground penetrating radar based on noise source separation and wavelet transform according to claim 4, characterized in that: The echo signal s r Based on the following formula: Where: n is the unit time of signal sampling, k is the frequency point number.

6. The method for suppressing clutter of ground penetrating radar based on noise source separation and wavelet transform according to claim 1, characterized in that: It also includes the steps for calculating the Cramer-Rao lower bound: satisfy the smallest and satisfy the smallest As a Cramer-Rao lower bound, in The ideal value of the echo signal amplitude after suppressing Gaussian noise (V); The ideal value of the echo signal phase after nonlinear distortion compensation (reg); σ 2 : Variance of the noise signal in the echo signal (V 2 ); N f : The discrete time each frequency point is maintained; SNR M,k : The signal-to-noise ratio of the echo signal at frequency k. E[]: Mathematical expectation operation.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, the steps of the suppression method according to any one of claims 1 to 6 are implemented.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the suppression method according to any one of claims 1 to 6 are implemented.

9. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the suppression method according to any one of claims 1 to 6 are implemented.

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