CN111667435A

CN111667435A - GPR noise suppression method and system based on Bayes nonnegative matrix factorization

Info

Publication number: CN111667435A
Application number: CN202010565943.4A
Authority: CN
Inventors: 原达; 苗翠
Original assignee: Shandong Technology and Business University
Current assignee: Shandong Technology and Business University
Priority date: 2020-06-19
Filing date: 2020-06-19
Publication date: 2020-09-15

Abstract

The invention provides a GPR noise suppression method and a GPR noise suppression system based on Bayesian nonnegative matrix factorization, which belongs to the technical field of data image processing and has the specific scheme that: preprocessing the acquired GPR image to obtain the horizontal gradient of the GPR image; carrying out nonnegative matrix decomposition on the horizontal gradient of the obtained GPR image by adopting a Bayesian probability method, and selecting a first principal component subjected to nonnegative matrix decomposition as noise for removal; the noise suppression method is high in noise suppression stability, achieves better robustness while pursuing speed, extracts the horizontal gradient of the ground penetrating radar as input instead of pixel intensity, and obtains a more effective clutter suppression effect.

Description

GPR noise suppression method and system based on Bayes nonnegative matrix factorization

Technical Field

The disclosure relates to the technical field of image processing, in particular to a GPR noise suppression method and a GPR noise suppression system based on Bayesian nonnegative matrix factorization.

Background

The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.

Ground Penetrating Radar (GPR) is a common Ground Penetrating nondestructive detection technology, and has wide application in the exploration of underground buried objects and underground structures. However, in the actual detection process, due to the complexity of the underground medium and the influence of the detection environment, a certain error is often caused to the measurement result, so that a very high false alarm rate occurs, and a challenge is brought to effective and accurate target detection. In the acquired ground penetrating radar signals, clutter may be defined as those signals that are not related to the scattering characteristics of the target but occur in the same sampling time window and have spectral characteristics similar to the target wavelength. Most high frequency clutter reflects high intensity energy and masks the signals of other more important reflected waves. The source of this may be due to penetration between the transmitting and receiving antennas and multiple reflections between the antennas and the ground, local changes in ground characteristic impedance and a small set of reflection sources contained in the material also causing clutter. How to remove the high-frequency clutter signal from the complex GPR reflected wave to retain the target signal is an important issue that needs to be studied.

The present inventors have found that, for the problem of clutter processing of a ground penetrating radar signal, subspace techniques based on Principal Component Analysis (PCA) and Robust Principal Component Analysis (RPCA), Singular Value Decomposition (SVD), Independent Component Analysis (ICA) and the like tend to exhibit better performance, and this method decomposes a GPR image into components corresponding to clutter and a target, treats the Principal Component as clutter and the remaining components as target signals, but this method cannot completely remove the clutter if the GPR image contains multiple clutter or multiple target signals.

In a Morphological Method (MCA) proposed in last two years, clutter and a target Component of a GPR image are sparsely represented by a curvelet and a non-sampled discrete wavelet Transform (UDWT) dictionary respectively to suppress the clutter, although a visual effect is good in representation, the algorithm complexity is high, and the processing speed is not fast enough; the method based on multi-resolution also obtains a better effect in the processing of GPR clutter removal, such as multi-scale Bilateral filtering (MDBF), multi-direction multi-scale Decomposition is carried out by means of geometric difference presented by clutter and targets in reflected waveforms, an Empirical Mode Decomposition (EEMD) is integrated to decompose a ground penetrating radar signal into a series of Mode Functions (IMFs) and calculate the displacement Entropy (PE) of the IMFs, and the discrimination of noise and the targets is carried out by setting a relevant threshold, so that the resolution of the targets can be effectively improved, but the image quality is difficult to guarantee; the method based on the Radial Basis Function (RBF) neural network is also used for filtering clutter of the GPR image, and the zero offset Green Function is used as expected output of training data, so that the vertical resolution of the ground penetrating radar can be improved, but the retention of target components is not clear.

Disclosure of Invention

In order to solve the defects of the prior art, the GPR noise suppression method and the GPR noise suppression system based on Bayesian non-negative matrix decomposition are provided, the noise suppression stability is high, better robustness is obtained while speed is pursued, the horizontal gradient of the ground penetrating radar is extracted as input instead of pixel intensity, and a more effective clutter suppression effect is obtained.

In order to achieve the purpose, the following technical scheme is adopted in the disclosure:

the first aspect of the disclosure provides a GPR noise suppression method based on Bayesian non-negative matrix factorization.

A GPR noise suppression method based on Bayes nonnegative matrix factorization comprises the following steps:

preprocessing the acquired GPR image to obtain the horizontal gradient of the GPR image;

and performing nonnegative matrix decomposition on the horizontal gradient of the obtained GPR image by adopting a Bayesian probability method, and selecting the first principal component subjected to nonnegative matrix decomposition as noise for removal.

A second aspect of the disclosure provides a GPR noise suppression system based on bayesian nonnegative matrix factorization.

A GPR noise suppression system based on Bayesian non-negative matrix factorization comprises:

a pre-processing module configured to: preprocessing the acquired GPR image to obtain the horizontal gradient of the GPR image;

a noise removal module configured to: and performing nonnegative matrix decomposition on the horizontal gradient of the obtained GPR image by adopting a Bayesian probability method, and selecting the first principal component subjected to nonnegative matrix decomposition as noise for removal.

A third aspect of the present disclosure provides a medium having a program stored thereon, wherein the program, when executed by a processor, implements the steps in the GPR noise suppression method based on bayesian nonnegative matrix factorization according to the first aspect of the present disclosure.

A fourth aspect of the present disclosure provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor, where the processor executes the program to implement the steps in the GPR noise suppression method based on bayesian nonnegative matrix factorization according to the first aspect of the present disclosure.

Compared with the prior art, the beneficial effect of this disclosure is:

1. according to the method, the system, the medium and the electronic equipment, the probability method is adopted to carry out non-negative matrix decomposition, posterior distribution of matrix parameters after decomposition is obtained, then the first principal component after matrix decomposition is selected as a clutter to be removed, and for a real complex environment, the probability model is often higher in stability than the non-probability method.

2. According to the method, the system, the medium and the electronic equipment, variational Bayes is used as an approximate reasoning method of non-negative matrix decomposition, speed is pursued, and meanwhile, good robustness is obtained.

3. According to the method, the system, the medium and the electronic equipment, in the using process, the horizontal gradient of the ground penetrating radar is extracted as an input instead of the pixel intensity, and compared with the prior art, a more effective clutter suppression effect is obtained.

Drawings

The accompanying drawings, which are included to provide a further understanding of the disclosure, illustrate embodiments of the disclosure and together with the description serve to explain the disclosure and are not to limit the disclosure.

Fig. 1 is a schematic flowchart of a GPR noise suppression method based on bayesian nonnegative matrix factorization provided in embodiment 1 of the present disclosure.

Fig. 2 is a schematic diagram illustrating comparison of noise suppression effects of two PNMF on three analog GPR images according to embodiment 1 of the present disclosure.

Fig. 3 is a schematic diagram illustrating a PSNR comparison between a pixel PNMF and a gradient PNMF provided in embodiment 1 of the present disclosure.

Fig. 4 is a schematic diagram of SNR values processed by NMF, RNMF, and PNMF algorithms provided in embodiment 1 of the present disclosure.

Fig. 5 is a schematic diagram illustrating comparison of clutter suppression effects of three algorithms on three real GPR images according to embodiment 1 of the present disclosure.

Detailed Description

The present disclosure is further described with reference to the following drawings and examples.

It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs.

It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present disclosure. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.

The embodiments and features of the embodiments in the present disclosure may be combined with each other without conflict.

As described in the background art, the existing GPR noise suppression method has poor stability, and neither the signal-to-noise ratio nor the robustness can meet the requirement of higher accuracy, and therefore, the present disclosure provides a GPR noise suppression method, system, medium, and electronic device based on bayesian nonnegative matrix factorization, as follows.

Example 1:

as shown in fig. 1, embodiment 1 of the present disclosure provides a GPR noise suppression method based on bayesian nonnegative matrix factorization, including the following steps:

The method specifically comprises the following steps:

(1) construction of probabilistic NMF model

When the GPR image is processed by NMF, the pixel intensity matrix F is considered as a composite structure of target components and clutter components:

F＝F_target+F_clutter(1)

and carrying out non-negative matrix decomposition on the matrix F to obtain:

F≈WH s.t.W,H≥0 (2)

wherein F ∈ R^M×N，W∈R^M×KAs a basis matrix, H ∈ R^K×NIs a matrix of coefficients. Equation (2) can be further translated into optimization of the following problem:

where D (-) represents the distance metric function, and since it is known that using KL divergence as the metric has the best effect, the update rule of parameters W, H at this time is as follows:

when the non-negative matrix solution is carried out by using the Lagrange multiplier method, the non-negative matrix solution is usually characterized by simplicity and rapidness, but the NMF under the non-probability model has instability while pursuing speed. In NMF under probabilistic model, the potential basis matrix W and coefficient matrix H to be decomposed are considered as two random variables, the values in the data F come from the product of W and H, and some gaussian noise E, as the following expression:

F＝WH+E s.t.W,H≥0 (5)

wherein W ∈ R^M×KAs a basis matrix, H ∈ R^K×NAs a matrix of coefficients, E ∈ R^M×NIs Gaussian white noise in the GPR image, E-N (0, sigma)²)。

Let the likelihood function of F follow a gaussian distribution:

F～N(F|WH,σ²)

N(x；μ,σ²)＝(2πσ²)^-1/2exp(-(x-μ)²/(2σ²)) (6)

the posterior distribution of the relevant parameters theta can be deduced through observation data F by using Bayesian theorem:

P(θ|F)∝P(F|θ)P(θ) (7)

wherein, the parameter theta to be solved is { W, H, sigma²P (F | θ) is the conditional probability of the data F under the parameter θ, obeying a gaussian distribution of equation (6), P (θ) is the prior distribution of the parameter.

(2) Non-negative matrix based on variational Bayesian decomposition

Prior to variational bayesian inference, the prior distribution P (θ) of the variables is assumed, given the non-negativity constraint of PNMF, the prior obeys exponential distribution of W and H:

where, (x, λ) ═ λ exp (- λ x) u (x), and u (x) is a unit step function.

The prior of the noise variance is set as the inverse gamma distribution:

in PNMF, the posterior distribution of parameters is inferred by using Variational Bayes (VB), the true probability distribution is approximated by solving an approximate posterior distribution, and the Variational Bayes has the characteristics of high speed and good stability for the parameter solution in the probability model. In the case of a complex multivariate parameter θ, VB decomposes it into a set of mutually independent variables θ_iExpressed as follows:

wherein q (θ) corresponds to the distribution of the parameter θ, resulting in a posterior distribution:

in formula (11), G (. cndot.) is a gamma distribution, and TN (. cndot.) is a truncated Gaussian distribution:

where φ (-) is a cumulative distribution function obeying the N (0,1) distribution, and after obtaining the posterior distribution of W and H and related parameters, a component representation of clutter can be obtained:

F_clutter＝W^M×KH^K×N(13)

and K represents the rank of the matrix, and a low-rank matrix corresponding to the clutter can be obtained through the value. For high-frequency clutter, the contribution of the front K component components to the clutter is maximum; w is the base matrix, H is the coefficient matrix, and M and N are the number of rows and columns, respectively, of the GPR image.

(3) Example analysis

(3-1) background of Experimental data

The experiment adopts GPR simulation data and real data acquired by an application environment to carry out method verification analysis, and verifies the effectiveness and robustness of the algorithm of the text through the signal-to-noise ratios and the visual effects of different algorithms.

(3-2) simulation of GPR data

The simulation data was obtained by simulation using Finite Difference Time Domain (FDTD) of the gprMax software. In the simulation, the aluminum disks were used as burial and then placed in soil environments with three different characteristics (dry soil dry _ sand, moist soil damp _ sand, moist soil wet _ sand), respectively, and the dielectric constant and conductivity of the burial and the three soils were derived from the following table 1.

Table 1: electromagnetic properties of materials

The obtained GPR image is shown as a (1) -a (3) in fig. 1, and corresponds to the reflection results of the aluminum disk buried in the dry soil dry _ sand, the wet soil damp _ sand and the wet soil wet _ sand environments, respectively, and it is clear from the figure that their target reflection waveforms vary in position height and downward opening size with the change of the environments, but all possess horizontal noise waves with the same characteristics. In the case of performing an experiment using the PNMF algorithm, the processing results of b (1) -b (3) in fig. 1 are obtained by substituting the pixel intensities of the image itself, and it is seen that the horizontal clutter is not completely removed, and the hyperbolic target vertex portions in b (1) and b (2) are also weakened. When PNMF processing is performed using image-level gradients, the results correspond to c (1) -c (3) in fig. 1. It can be seen that the processing result not only can well retain the hyperbolic wave signal, but also can obviously inhibit the clutter.

Peak signal-to-noise ratio (PSNR) is the most common objective evaluation index in image processing and is based on a pure reference image I and a processed image

And judging the quality of image processing according to the error of the corresponding pixel point.

Is typically defined by Mean Square Error (MSE):

in the analog GPR data, a clutter-free reference image I is obtained by subtracting a clutter-containing target reflection image and a clutter-containing image. In non-negative matrix factorization using a probabilistic model, a set of comparison histograms are obtained by calculation of PSNR values using image pixel intensities and horizontal gradients as inputs, respectively, as shown in fig. 2. The PSNR value obtained when the PNMF ground penetrating radar image clutter processing is carried out by using the gradient can be intuitively obtained.

The visual quality and the PSNR are compared, and the processing effect is better when the horizontal gradient of the GPR image is selected as an input matrix in the de-aliasing process of the PNMF algorithm.

In the GPR image clutter processing, clutter components are generally present in the first few principal components after matrix decomposition, and K is selected to be 1, 2, 3, 4, and 5, respectively, and the post-processing PSNR values are compared, and the results are shown in table 2. The data results show that the GPR image reflected by the aluminum disk in dry soil has a high PSNR value after subtraction when K is taken as 2, while the peak signal-to-noise ratio of PNMF is high when K is taken as 1 under reflection in moist and humid soil environments. And combining the experience of GPR image clutter removal in the subspace technology, and selecting a first principal component as a clutter component, namely K is 1.

Table 2: PSNR for PNMF algorithms at different values of K.

	K＝1	K＝2	K＝3	K＝4	K＝5
						dry_sand	10.2312	10.3478	10.2308	10.2308	10.1063
damp_sand	13.0970	12.9541	12.9541	12.9540	12.9539
						wet_sand	20.0962	19.8986	19.8986	19.8986	19.8985

(3-2) true GPR data

The experimental data are real GPR data measured in a real environment, as shown by a (1) -a (3) in fig. 4. The clutter is generally horizontal, and has the characteristics of large quantity and partial overlapping with the target components. During experiments, a traditional non-Negative Matrix Factorization (NMF) method and a robust non-negative matrix factorization (RNMF) method are selected as comparison, and the effectiveness and robustness of the PNMF algorithm are verified by using two evaluation indexes, namely a signal-to-noise ratio and visual quality.

The signal-to-noise ratio of an image is a parameter for comparing the quality of the processed image with the quality of an original image, and the quality of the image is better when the value of the signal-to-noise ratio is larger. The calculation of the signal-to-noise ratio often requires the use of an original clean reference image, but since the actual measured GPR image lacks a reference image, the experiment uses the ratio of the mean to the variance of the image to calculate the signal-to-noise ratio for the metric. The actual GPR data are shown in fig. 4 as a (1) -a (3), and the SNR results are shown in the form of a line graph in fig. 3 by processing NMF, RNMF and PNMF of this embodiment, respectively, and it can be seen that in the clutter processing of GPR images, the signal-to-noise ratio of RNMF algorithm is higher than that of NMF, and the signal-to-noise ratio of PNMF algorithm is higher than that of RNMF and NMF algorithms.

In the field of image processing, the visual quality is the most intuitive and important evaluation index, and the NMF, the RNMF and the PNMF in the text are respectively used for removing clutter aiming at the GPR image in three different measurement environments. The effect diagram is shown in fig. 4. Wherein a (1) -a (3) are real GPR data, b (1) -b (3) are results corresponding to traditional non-Negative Matrix Factorization (NMF) processing, c (1) -c (3) are effects of a robust non-negative matrix factorization (RNMF) algorithm, and d (1) -d (3) are results of clutter suppression of the PNMF algorithm.

It can be seen from the original drawing that the clutter of the three ground penetrating radar images is different, a (1) in fig. 4 has a high-frequency horizontal clutter (frame line 1) and a cluttered background clutter (frame line 2), the horizontal clutter is weakened to a certain extent after the processing by the NMF and RNMF algorithms, but the background clutter of the frame line 2 is still unchanged, see b (1) and c (1) in fig. 4. But after the PNMF algorithm processing (d (1) in fig. 4), the clutter in both areas is well suppressed, a purer background is obtained, and the target signal is well preserved.

Fig. 4 a (2) contains a plurality of thin high-frequency horizontal clutter (frame lines), which are closely spaced and cover part of information of the top of the hyperbolic wave. In the NMF algorithm, the first stronger clutter is attenuated, see b (2) in fig. 4. The RNMF (see c (2) in fig. 4) algorithm in this image performs the worst, and does not have the effect of clutter suppression. The PNMF does not suppress completely for several clutter in the figure, but the background under contrast is purer and the edge details of the target remain good, see d (2) in fig. 4.

In fig. 4, c (1) includes three thick high-frequency horizontal clutter (frame lines), which are far apart from each other and overlap with the hyperbolic wave portion in a large amount. The NMF and RNMF suppress clutter better in this figure (b (3) and c (3) in fig. 4), but the interference situation of clutter inside the hyperbolic wave is not improved. The PNMF can accurately and efficiently extract the target information (d (3) in fig. 4) of the image, and the processing result is clear and natural.

The above experimental results show that in the process of high-frequency clutter suppression of a GPR image, a higher signal-to-noise ratio can be obtained by using the PNMF algorithm, so that the background of the GPR image is clear, and target information is highlighted. Thereby verifying the effectiveness and robustness of the algorithm.

Different from the conventional NMF, in the embodiment, a probability method is adopted to perform non-negative matrix decomposition to obtain posterior distribution of matrix parameters after decomposition, and then the first principal component after matrix decomposition is selected as a clutter to be removed. For real complex environments, probabilistic models tend to have greater stability than non-probabilistic methods. The PNMF uses variational Bayes as an approximate inference method of nonnegative matrix decomposition, obtains better robustness while pursuing speed, extracts the horizontal gradient of the ground penetrating radar as input instead of pixel intensity in the using process, and obtains more effective clutter suppression effect. Finally, the NMF algorithm and the RNMF algorithm are respectively compared through experiments, and the fact that the algorithm can effectively keep the target inhibition clutter in the aspect of vision and can obtain a higher signal-to-noise ratio is found. Therefore, the algorithm has good effectiveness and robustness in the problem of clutter suppression of a GPR image.

Example 2:

the embodiment 2 of the present disclosure provides a GPR noise suppression system based on bayesian nonnegative matrix factorization, including:

The working method of the system is the same as the GPR noise suppression method based on the bayesian nonnegative matrix factorization described in embodiment 1, and is not described herein again.

Example 3:

the embodiment 3 of the present disclosure provides a medium, on which a program is stored, and when the program is executed by a processor, the program implements the steps in the GPR noise suppression method based on the bayesian nonnegative matrix factorization according to the embodiment 1 of the present disclosure, where the steps are:

The detailed steps are the same as those of the GPR noise suppression method based on the bayesian nonnegative matrix factorization described in embodiment 1, and are not described herein again.

Example 4:

the embodiment 4 of the present disclosure provides an electronic device, which includes a memory, a processor, and a program stored in the memory and executable on the processor, where the processor implements the steps in the GPR noise suppression method based on the bayesian nonnegative matrix factorization according to the embodiment 1 of the present disclosure when executing the program, and the steps are:

As will be appreciated by one skilled in the art, embodiments of the present disclosure may be provided as a method, system, or computer program product. Accordingly, the present disclosure may take the form of a hardware embodiment, a software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present disclosure may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, and the like) having computer-usable program code embodied therein.

The present disclosure is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the disclosure. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by a computer program, which can be stored in a computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), or the like.

The above description is only a preferred embodiment of the present disclosure and is not intended to limit the present disclosure, and various modifications and changes may be made to the present disclosure by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present disclosure should be included in the protection scope of the present disclosure.

Claims

1. A GPR noise suppression method based on Bayes nonnegative matrix factorization is characterized by comprising the following steps:

2. The method according to claim 1, wherein the horizontal gradient matrix of the GPR image is a combination of the target component and the clutter component, specifically a sum of a product of a basis matrix and a coefficient matrix and gaussian noise.

3. The method of claim 2, wherein a likelihood function of a pixel intensity matrix of a GPR image obeys a gaussian distribution.

4. The method of claim 3, wherein the posterior distribution of the parameters of the likelihood function is inferred using variational Bayes.

5. The bayesian nonnegative matrix factorization based GPR noise suppression method of claim 3 wherein prior to performing variational bayesian inference, a prior distribution of parameters of the likelihood functions is assumed, the prior of the basis matrix and coefficient matrix obeying an exponential distribution, and the prior of the noise variance obeying an inverse gamma distribution.

6. The method of claim 2, wherein the clutter component is derived based on a posterior distribution of parameters that yields a basis matrix and a coefficient matrix and a likelihood function.

7. The method according to claim 5, wherein the clutter components are products of a basis matrix and a coefficient matrix, and wherein the rows of the basis matrix and the columns of the coefficient matrix are the rows and the columns of the GPR image, respectively.

8. A GPR noise suppression system based on Bayesian non-negative matrix factorization, comprising:

9. A medium having a program stored thereon, wherein the program, when executed by a processor, implements the steps in the method for GPR noise suppression based on bayesian nonnegative matrix factorization of any of claims 1-7.

10. An electronic device comprising a memory, a processor, and a program stored on the memory and executable on the processor, wherein the processor implements the steps in the method for GPR noise suppression based on bayesian nonnegative matrix factorization of any of claims 1-7 when executing the program.