CN108961181B - Shearlet transform-based ground penetrating radar image denoising method - Google Patents
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Abstract
The invention discloses a ground penetrating radar image denoising method based on shearlet transformation, which comprises the steps of firstly carrying out frequency domain Fourier transformation on collected ground penetrating radar data, then carrying out frequency domain windowing, carrying out non-downsampling shearlet transformation on the ground penetrating radar data subjected to windowing, then carrying out threshold shrinking treatment on shearlet coefficients in different directions of different scales by using a bivariate model based on maximum posterior probability estimation, updating coefficients, and carrying out inverse shearlet transformation on new shearlet coefficients to obtain a denoised ground penetrating radar frequency domain image. The algorithm is simple to implement, good in denoising effect and good in engineering practical value.
Description
Technical Field
The invention belongs to the technical field of ground penetrating radar image denoising, and particularly relates to a ground penetrating radar image denoising method based on shearlet transformation.
Background
In geological exploration, the application of the ground penetrating radar is more and more extensive, because the underground has target bodies with different physical properties, the discontinuity becomes the basis that the radar technology can effectively detect the underground target bodies, compared with other geological exploration, the ground penetrating radar technology has great advantages in the exploration of the underground shallow target bodies, not only has very high resolution ratio, but also can not cause destructiveness to the exploration field, the exploration efficiency is high, the exploration speed is high, and the advantages enable the ground penetrating radar technology to play an important role in the exploration of the shallow underground target bodies. The application field relates to the fields of underground pollution detection in environmental engineering, environmental evaluation of building foundations and road surfaces, archaeological investigation and the like. Due to the advantages of the ground penetrating radar technology, the ground penetrating radar is more and more widely applied to geological exploration in China and plays a greater and greater role. Meanwhile, researchers at home and abroad increase the research on radar technology and produce a series of radar instruments applied to geological exploration.
Although the ground penetrating radar instrument is developed rapidly and has high resolution at present, the research and development speed of the ground penetrating radar signal processing software is far from the research and development speed of the ground penetrating radar instrument. The geological conditions of the subsurface being detected are intricate and complex, plus noise present in the instrument itself or the system. Interference of various human factors such as reflected waves of communication cables, pipelines and the like on the earth surface and in the air. Irregular operation of an operator, reflected waves from a local inhomogeneity in the subsurface that is not the target of exploration. These uncertain factors all affect our ability to obtain true geology of the subsurface. If the data measured by the ground penetrating radar instrument cannot truly reflect the underground geological condition, the judgment of researchers is greatly influenced. And thus no correct conclusion can be drawn. The existence of these factors makes it necessary to eliminate them as much as possible when using ground penetrating radar for exploration studies.
Currently, the research results on ground penetrating radar signal processing mainly focus on noise suppression of signals (mainly expressed as one-dimensional signals), performing corresponding clutter interference elimination, deconvolution processing applied to aspects of channel balance and the like, time-varying gain, filtering processing by converting signals from a time domain to a frequency domain, and the like. The development of signal processing is not independent of the development of mathematics, and the mathematical theory provides a solid theoretical basis for the development of signal processing. In the process of researching radar signal processing, the mathematical tool of Fourier transform plays an important role. The signals obtained generally exist in the form of time domain spectra, i.e., the abscissa is time and the ordinate is amplitude. When extracting the signal, the noise is doped inevitably, so that the signal is distorted. But it is difficult to remove noise in the time domain analysis. The general signal can be obtained by the weighted summation of a plurality of simple sine and cosine quantities with single frequency. In order to solve the noise problem, a time domain spectrum is converted into a frequency domain spectrum (namely, the abscissa is frequency, and the ordinate is amplitude), the energy of a signal is mainly concentrated in a certain frequency interval, and noise is concentrated in another frequency interval. The noise signal can be removed from the original signal, so as to achieve the effect of signal processing.
Fourier transforms also have their own limitations. It can reflect only the global characteristics of the signal, but in practical studies the local range characteristics of the signal are of interest. And the method is only suitable for analyzing steady signals, and the main harmonic components of the signals are characterized by a frequency spectrum function so as to show the relation between a time domain function and a frequency domain function.
Wavelet analysis is a breakthrough development following fourier analysis. The wavelet function shows good capability of characterizing signal characteristics, because wavelets have good local characteristics in both time domain and frequency domain, and the wavelet transform has a capability of gathering signal energy, i.e. wavelet transform is performed on a noisy image, in the obtained wavelet coefficients, low-frequency coefficients and some large high-frequency coefficients represent main energy of the image, and noise energy is uniformly distributed on the low-frequency coefficients and each high-frequency coefficient. Thus, in the wavelet transform domain, the signal and noise exhibit different characteristics, and thus, the signal coefficient and the noise coefficient can be well distinguished. Based on this idea, in 1992, Mallat utilizes wavelet transform to perform image denoising, and then Donoho proposes an image denoising algorithm with hard threshold and soft threshold in the wavelet domain, wherein the wavelet-based soft threshold algorithm is widely applied. However, both the wavelet hard threshold and the wavelet soft threshold are global thresholds, and do not reflect local statistical characteristics of the image, so the denoising effect is not ideal.
By utilizing the statistical information of the wavelet coefficients in the image, the denoising effect is greatly improved, and the algorithm also gradually becomes a research hotspot and a mainstream in the field of image noise suppression. However, wavelet analysis itself is also limiting. Wavelets are the optimal basis for objective functions with punctiform singularities, and wavelet coefficients are sparse when analyzing such objects, but the excellent characteristics of wavelet analysis when processing one-dimensional signals cannot be easily generalized to two-dimensional or higher. This is because the two-dimensional separable wavelet formed by one-dimensional wavelets has only three limited directions of horizontal, vertical and diagonal, and in the case of high dimension, it cannot fully utilize the specific geometrical characteristics of the data itself, and it cannot optimally represent the high-dimensional function including line or plane singularities. In fact, the direction information of the two-dimensional image is often represented by singularity of a straight line or a curve, but not just point singularity, and when the signals are analyzed, the wavelet cannot well mine the direction information in the signals.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a ground penetrating radar image denoising method based on shearlet transformation aiming at the defects in the prior art, the method is simple to realize, has excellent effect, can well remove noise interference around a target, clearly presents the target, and has good practical engineering application value.
The invention adopts the following technical scheme:
a ground penetrating radar image denoising method based on shearlet transformation comprises the steps of firstly carrying out frequency domain Fourier transformation on collected ground penetrating radar data, then carrying out frequency domain windowing, carrying out non-downsampling shearlet transformation on the ground penetrating radar data after windowing, then carrying out threshold shrinking processing on shearlet coefficients in different directions of different scales by using a bivariate model based on maximum posterior probability estimation, updating coefficients, and carrying out inverse shearlet transformation on new shearlet coefficients to obtain denoised ground penetrating radar frequency domain images.
Specifically, the method comprises the following steps:
s1, carrying out azimuth Fourier transform on the collected ground penetrating radar data, windowing, and dividing the windowed frequency domain image into image blocks;
s2, performing nonsubsampled shearlet transformation on the image blocks obtained in the first step one by one to obtain transformed sub-band images;
s3, denoising the transformed sub-band image based on a neighborhood bivariate model threshold;
and S4, carrying out inverse shearlet transformation on the dried sub-band images to obtain de-noised image blocks, sequentially and correspondingly combining the de-noised image blocks according to the positions before transformation, removing the filled positions, and obtaining the final de-noised ground penetrating radar frequency domain image.
Further, in step S1, the obtained frequency domain data is block-filled, fourier transform is performed only on the azimuth direction of the echo data, and a one-dimensional fourier transform is performed, and a rectangular window is added in the slow time-frequency domain to remove a direct-current component, high-frequency interference, and a target vibration higher harmonic component due to stationary background noise.
Further, the windowed frequency domain image is divided into image blocks with a size of 256 × 256.
Further, in step S2, the image block is input, the shearlet transform wavelet basis is selected, the number of decomposition scale layers is determined, the shearlet basis is constructed, and the noise image is decomposed on the shearlet basis.
Further, threshold denoising based on a neighborhood bivariate model comprises the following steps:
s301, determining noise variance for sub-band images with different scales and different directions
And the mean square value of the estimated observed value
Obtaining a mean square estimate of the shearlet coefficient
S302, the different treatment is carried out according to the different direction numbers, the direction numbers are the same, the direction numbers are in one-to-one correspondence, when the direction numbers are different, the direction numbers of the sub-bands are more than the direction numbers of the father sub-bands and are generally in integral multiple relation, the division result of the sub-band numbers and the multiple is adopted to correspond, and the father coefficient of each coefficient is determined;
s303, determining a contraction value corresponding to each coefficient according to the bivariate model;
s304, taking a window for the coefficient by taking the coefficient to be processed as the center, calculating the contraction value of the contraction value corresponding to each position in the window to the center coefficient, then obtaining the updated value of the coefficient after final processing by using the contraction value in the Gaussian window weighting window, and obtaining the denoising result of the frequency domain block image by adopting inverse shearlet transformation.
Further, in step S301, the mean square value of the shearlet coefficient is estimated
The calculation is as follows:
wherein the content of the first and second substances,
to estimate the variance of the noise in this scale direction,
the estimated observation mean square value is obtained.
Further, in step S303, the shrinkage value corresponding to each coefficient is calculated as follows:
wherein, y1、y2Coefficients after shearlet transform for noisy images, and y2Is y1Is the parent coefficient, s1Is y1The coefficient of contraction of (a).
Further, in step S304, the gaussian matrix is as follows:
further, in step S4, the denoised block frequency domain images are re-integrated according to the original corresponding positions, and then the filled zeros are removed to obtain the frequency domain denoised image with the same size as the original image.
Compared with the prior art, the invention has at least the following beneficial effects:
the invention relates to a ground penetrating radar image denoising method based on shearlet transformation, which comprises the steps of firstly carrying out frequency domain Fourier transformation on collected ground penetrating radar data, then carrying out frequency domain windowing, carrying out non-downsampling shearlet transformation on the ground penetrating radar data subjected to windowing, then carrying out threshold shrinking treatment on shearlet coefficients in different directions of different scales by using a bivariate model based on maximum posterior probability estimation, updating coefficients, and carrying out inverse shearlet transformation on new shearlet coefficients to obtain denoised ground penetrating radar frequency domain images. The method can well remove noise signals around the target, clearly present the target, provide a better method for de-noising the actual ground penetrating radar image, is convenient and simple, and provides technical support for image preprocessing in practical application.
Furthermore, the ground penetrating radar data is subjected to Fourier transform in the azimuth direction, then frequency domain windowing is performed, static clutter and some high-frequency interference are filtered, and then blocking processing is performed, so that the speed is increased, and the hardware load is reduced.
Furthermore, as the ground penetrating radar image is large, time is consumed in subsequent decomposition and transformation, and therefore the image is partitioned into image blocks with the size of 256 × 256, and zero padding is performed due to insufficient data.
Furthermore, non-downsampling shearlet transformation is adopted for the frequency domain block images, optimal sparse approximation is carried out on the images, meanwhile, spectrum aliasing is avoided, and direction selectivity and translation invariance of the frequency domain block images are enhanced.
Furthermore, bivariate threshold denoising is carried out on the transformed sub-band coefficients, the correlation between parent-child coefficients is fully considered, the correlation between neighborhoods is also considered, Gaussian window weighting processing is adopted according to the difference of the correlation between adjacent coefficients at different distances, and the inter-scale correlation and the intra-direction correlation of the coefficients are fully excavated, so that a good denoising effect is achieved.
Furthermore, the method has a good denoising effect on the ground penetrating radar image, can well remove noise around the image target, and clearly presents the target.
In conclusion, the algorithm is simple to implement, good in denoising effect and good in engineering practical value.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a general flow chart of the present invention;
FIG. 2 is a diagram of the denoising effect of several different algorithms on an actually measured ground penetrating radar image, wherein (a) is an original echo image, (b) is an image after wavelet denoising, (c) is an image after non-local mean denoising, and (d) is an image after the algorithm denoising.
Detailed Description
The invention provides a method for denoising a ground penetrating radar image based on shearlet transformation, which only needs actually acquired ground penetrating radar data, does not need to pay attention to whether additive noise or multiplicative noise is mixed in the radar data, and does not need to know the variance of the noise in advance; decomposing the ground penetrating radar image by adopting the sparse representation characteristic of high-dimensional geometric structure of shearlet transformation; performing threshold shrinkage by adopting a neighborhood bivariate model; and carrying out Gaussian weighted average processing on a plurality of estimated values of the same coefficient; the denoising effect of the scheme on the ground penetrating radar image is superior to that of the existing algorithm, noise interference around the target can be well removed, the target is clearly presented, and the method has good engineering practical application value.
Referring to fig. 1, according to the ground penetrating radar image denoising method based on shearlet transform, firstly, frequency domain fourier transform is performed on collected ground penetrating radar data, then frequency domain windowing processing is performed, nonsubsampled shearlet transform is performed on the ground penetrating radar data after windowing processing, then threshold shrinkage processing is performed on shearlet coefficients in different directions of different scales by using a bivariate model based on maximum posterior probability estimation, the coefficients are updated, and inverse shearlet transform is performed on new shearlet coefficients to obtain a denoised ground penetrating radar frequency domain image. The method comprises the following specific steps:
s1, carrying out azimuth Fourier transform on the collected ground penetrating radar data, windowing, and dividing the windowed frequency domain image into image blocks with the size of 256 × 256;
filling the obtained frequency domain data in blocks, performing Fourier transform only on the azimuth direction of echo data, wherein the Fourier transform is one-dimensional Fourier transform, and removing direct-current components, high-frequency interference and target vibration higher harmonic components caused by static background clutter by adding a rectangular window in a slow time-frequency domain; for the block filling of the frequency domain data, the time is consumed in the subsequent decomposition and transformation because the ground penetrating radar image is large, so that the image is divided into image blocks with the size of 256 × 256, and zero filling is performed when the data is insufficient.
S2, performing nonsubsampled shearlet transformation on the image blocks obtained in the first step one by one to obtain transformed sub-band images;
the method comprises the following steps: inputting an image block, selecting a shearlet transform wavelet base, determining the number of decomposition scale layers to construct a shearlet base, and decomposing a noise image on the shearlet base.
S3, denoising based on a threshold value of a neighborhood bivariate model, which is specifically as follows:
s301, determining noise variance for sub-band images with different scales and different directions according to the formula (1) and the formula (3)
And the mean square value of the estimated observed value
Wherein, yiThe coefficient after shearlet decomposition in the direction under the scale is taken as mean (),
is the estimated noise variance in the dimension direction;
wherein, yiIs the shearlet decomposed coefficient of the direction at the scale,w(k) for estimating the window, M is the window size,
to estimated viewMeasuring the mean square value;
equation (1) and equation (2) are combined to obtain a mean square estimate of the shearlet coefficient
Comprises the following steps:
(g)+the definition is as follows:
s302, determining a parent coefficient of each coefficient: when finding out the corresponding father coefficient, the father coefficient is treated differently according to the difference of the direction number, when the direction number is the same, the father coefficient corresponds to the direction number one by one, when the direction number is different, the direction number of the sub-band is generally the relation of the direction number of the father sub-band and the integer multiple, so the division result of the sub-band number and the multiple is adopted to correspond;
s303, determining a contraction value corresponding to each coefficient according to the bivariate model, wherein the contraction value is shown as a formula (5):
wherein, y1、y2Coefficients after shearlet transform for noisy images, and y2Is y1Is the parent coefficient, s1Is y1The coefficient of contraction of;
s304, taking a window for the coefficient by taking the coefficient to be processed as the center, calculating the contraction value of the contraction value corresponding to each position in the window to the center coefficient, then obtaining the updated value of the coefficient after final processing by using the contraction value in the Gaussian window weighting window, and obtaining the denoising result of the frequency domain block image by adopting inverse shearlet transformation.
The gaussian matrix used is as follows:
and S4, performing inverse shearlet transformation on the processed sub-bands to obtain image blocks after denoising, sequentially and correspondingly combining the image blocks according to the positions before transformation, and removing the filled positions to obtain a final denoised ground penetrating radar frequency domain image.
And (4) re-integrating the denoised block frequency domain images according to the original corresponding positions, and then removing the filled zeros to obtain the frequency domain denoised image with the same size as the original one.
Based on the parent-child relationship between adjacent scale shearlet coefficients and the similarity between adjacent pixels, the threshold shrinkage coefficient is determined by using the strong correlation between the parent-child coefficients on the basis of the Bayes posterior probability, and then the processed coefficients are obtained by weighting through a Gaussian window according to the influence between adjacent pixels, so that the noise-removed image is reconstructed.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A. The experimental scheme is as follows:
the invention compares the denoising effect of the ground penetrating radar image based on Shearlet transform with the denoising effect of the ground penetrating radar image based on a wavelet method and a non-local mean denoising method (NL-means).
B. The experimental conditions are as follows:
the ground penetrating radar measured data with data size 4096 x 3051 is used as test data. In the experimental process, the frequency domain window range is 5-103, and the size of the coefficient estimation window is 3 multiplied by 3. The gaussian weighting window size is 3 × 3.
The denoising effect diagrams of the ground penetrating radar image denoising algorithm and the comparison algorithm based on the shearlet transformation provided by the invention are given below, and as shown in fig. 2, the denoising effect diagrams are respectively an original echo frequency domain image, a wavelet denoised image, a non-local mean denoising image and an algorithm denoising image of the invention.
By analyzing and comparing the white frames, the denoising effect of the ground penetrating radar image compared with wavelet denoising and non-local mean denoising can be seen.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.
Claims (6)
1. A ground penetrating radar image denoising method based on shearlet transformation is characterized in that firstly, frequency domain Fourier transformation is carried out on collected ground penetrating radar data, then frequency domain windowing processing is carried out, nonsubsampled shearlet transformation is carried out on the ground penetrating radar data after the windowing processing, then threshold shrinking processing is carried out on shearlet coefficients in different directions of different scales by utilizing a bivariate model based on maximum posterior probability estimation, the coefficients are updated, and inverse shearlet transformation is carried out on new shearlet coefficients to obtain denoised ground penetrating radar frequency domain images, and the method comprises the following steps:
s1, carrying out azimuth Fourier transform on the collected ground penetrating radar data, windowing, dividing the windowed frequency domain image into image blocks, filling the obtained frequency domain data in blocks, carrying out Fourier transform only on the azimuth of echo data, and adding a rectangular window in a slow time-frequency domain to remove direct current components, high-frequency interference and target vibration higher harmonic components caused by static background clutter;
s2, performing nonsubsampled shearlet transformation on the image blocks obtained in the first step one by one to obtain transformed sub-band images, inputting the image blocks, selecting shearlet transformation wavelet bases, determining the number of decomposition scale layers, constructing shearlet bases, and dividing the noise images on the shearlet bases;
s3, denoising the transformed sub-band image based on the neighborhood bivariate model threshold, specifically:
s301, determining noise variance for sub-band images with different scales and different directions
And the mean square value of the estimated observed value
Obtaining a mean square estimate of the shearlet coefficient
S302, the different treatment is carried out according to the different direction numbers, when the direction numbers are the same, the direction numbers of the sub-bands correspond to the direction numbers of the father sub-bands one by one, when the direction numbers are different, the direction numbers of the sub-bands are more than the direction numbers of the father sub-bands and are generally in an integral multiple relation, and the father coefficient of each coefficient is determined by adopting the correspondence of the division results of the sub-band numbers and the multiples;
s303, determining a contraction value corresponding to each coefficient according to the bivariate model;
s304, taking a window for the coefficient by taking the coefficient to be processed as a center, calculating a contraction value of the contraction value corresponding to each position in the window to the center coefficient, then obtaining an updated value of the coefficient after final processing by using the contraction value in the Gaussian window weighting window, and obtaining a denoising result of the frequency domain block image by adopting inverse shearlet transformation;
and S4, carrying out inverse shearlet transformation on the denoised sub-band image to obtain a denoised image block, successively and correspondingly combining the image block according to the position before transformation, and removing the filled position to obtain the final denoised ground penetrating radar frequency domain image.
2. The method as claimed in claim 1, wherein in step S1, the windowed frequency domain image is divided into 256 × 256 image blocks.
3. The method for denoising shearlet-transform-based ground penetrating radar image as claimed in claim 1, wherein in step S301, a mean square value of shearlet coefficients is estimated
The calculation is as follows:
wherein the content of the first and second substances,
to estimate the variance of the noise in this scale direction,
the estimated observation mean square value is obtained.
4. The method for denoising shearlet-transform-based ground penetrating radar image as claimed in claim 1, wherein in step S303, the shrinkage value corresponding to each coefficient is calculated as follows:
wherein, y1、y2Is subjected to shearlet transformation for noisy imagesTransformed coefficients, and y2Is y1Is the parent coefficient, s1Is y1The coefficient of contraction of (a).
5. The method for denoising shearlet-transform-based ground penetrating radar image as claimed in claim 1, wherein in step S304, the gaussian matrix is as follows:
6. the method for denoising shearlet-transform-based ground penetrating radar image as claimed in claim 1, wherein in step S4, the denoised partitioned frequency domain images are re-integrated according to the original corresponding positions, and then the filled zeros are removed to obtain the denoised image of the frequency domain with the same size as the original one.
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