CN108961181A - A kind of ground penetrating radar image denoising method based on shearlet transformation - Google Patents
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Abstract
The invention discloses a kind of ground penetrating radar image denoising methods based on shearlet transformation, frequency domain Fourier transformation is carried out to collected Coherent Noise in GPR Record first, then window adding in frequency domain processing is carried out, non-lower sampling shearlet transformation is carried out to the Coherent Noise in GPR Record after windowing process, then the two-varaible model based on maximum a-posteriori estimation is utilized, threshold shrink processing is carried out to the shearlet coefficient of the different directions of different scale, update coefficient, it carries out inverse shearlet to new shearlet coefficient to convert, the Ground Penetrating Radar frequency domain image after being denoised.This algorithm realizes that simply denoising works well, and has good engineering practical value.
Description
Technical field
The invention belongs to ground penetrating radar image noise-removed technology field, and in particular to a kind of spy based on shearlet transformation
Radar image denoising method.
Background technique
In geologic prospect, Ground Penetrating Radar is this since underground is there are the objective body of different physical property using more and more extensive
Discontinuity, which becomes Radar Technology, the foundation that underground objective body is effectively detected is compared with others geologic prospect,
Ground penetrating radar exploration has very big advantage in reconnoitring to underground shallow part objective body, not only has very high resolution ratio, but also
Will not be to damaging property of detection scene, detection efficient is high, and speed of detection is fast, these advantages make ground penetrating radar exploration in shallow-layer
Buried target body, which is reconnoitred, middle plays critically important effect.Its application field is related to the detection of the underground pollution in environmental project, builds
Build the environmental evaluation on ground and road surface, the fields such as archaeological investigation.Just because of the above-mentioned advantage of ground penetrating radar exploration, Ground Penetrating Radar
Using more and more extensive in the geologic prospect in China, the effect of performance is also increasing.Researchers at home and abroad increase simultaneously
Research to Radar Technology, produces a series of radar instruments applied to geologic prospect.
Although current Ground Penetrating Radar Instrument Development is rapid, there is very high resolution ratio, Gpr Signal processing software
Research and development speed do not catch up with the research and development speed of Ground Penetrating Radar instrument much.And the geological conditions of the underground detected is intricate,
In addition there are noises for instrument itself or system.The reflection of the interference such as communication cable, pipeline of earth's surface, aerial various human factors
Wave.The non-standard operation of operator, the back wave from the non-local non-homogeneous body for detecting purpose body in underground.These are uncertain
Factor can all influence us and obtain the true geological condition in underground.If the data that we are measured using Ground Penetrating Radar instrument are not
Can really corresponsively under geological condition, this will bring very big influence to the judgement of researcher.To obtain
Correct conclusion.The presence of these influence factors, so that being had to as far as possible when carrying out detection study using Ground Penetrating Radar
Eliminate these impact factors.
Currently, being concentrated mainly on noise suppressed (the main performance to signal to the research achievement of Gpr Signal processing
For to one-dimensional signal), carry out it is corresponding eliminate noise jamming, the deconvolution processing applied to channel balancing etc., time-varying increase
Benefit and be filtered by the way that signal is transformed into frequency domain from time-domain.The development of signal processing be unable to do without the hair of mathematics
Exhibition, mathematical theory provide solid theoretical basis for the development of signal processing.During studying Radar Signal Processing, Fu
In leaf transformation this mathematical tool played an important role.The signal typically resulted in exists in the form of Time Domain Spectrum, i.e., horizontal
Coordinate is the time, and ordinate is amplitude.When extracting signal, noise is inevitably adulterated, so that distorted signals.But
It is highly difficult that noise is removed in time-domain analysis.General signal can be equivalent to many simple single-frequencies just
String, the weighted sum of cosine amount and obtain.In order to solve noise problem, by Time Domain Spectrum be converted into frequency domain spectra (i.e. abscissa be frequency,
Ordinate is amplitude), the energy of signal is concentrated mainly in certain section of specific frequency section, and noise concentrates on another band frequency section
It is interior.Noise signal can be removed from original signal, achieve the effect that signal processing.
Fourier transformation also has the limitation of itself.The global feature for the only signal that it can reflect, and actually grinding
Study carefully middle care is the feature of signal subrange.And it may be only available for the analysis of stationary signal, pass through frequency spectrum function pair
The major harmonic ingredient of signal is characterized, to show the relationship of time-domain function and frequency-domain function.
Wavelet analysis is a breakthrough after Fourier analysis.Wavelet function shows good characterization
The ability of signal characteristic, reason is that small echo has preferable local characteristics in time domain and frequency domain, and wavelet transformation is for letter
Number energy has a kind of ability of aggregation, i.e., carries out wavelet transformation to noisy image, in obtained wavelet coefficient, low frequency coefficient and
Some big high frequency coefficients indicate the main energetic of image, and noise energy is then generally evenly distributed in low frequency coefficient and each high frequency system
On number.In this way, in wavelet transformed domain, what signal and noise were shown is different feature, therefore, can preferably distinguish signal
Coefficient and noise coefficient.Based on this thought, Mallat in 1992 carries out image denoising, then, Donoho using wavelet transformation
The Image denoising algorithm of hard -threshold and soft-threshold is proposed in wavelet field, wherein the soft-threshold algorithm based on small echo has obtained extensively
Application.However small echo hard -threshold and wavelet soft-threshold method use be all a kind of overall situation threshold value, there is no reflection images
Partial statistics characteristic, therefore denoise the effect is unsatisfactory.
Using the statistical information of wavelet coefficient in image, denoises effect and be greatly improved, such algorithm also gradually becomes figure
As the research hotspot and mainstream in noise suppressed field.But wavelet analysis itself is also limited.Small echo is to dotted
Unusual objective function is optimal base, and when analyzing this kind of target, wavelet coefficient is sparse, but wavelet analysis is being handled
The excellent characteristics shown when one-dimensional signal can not simply be generalized to two dimension or more higher-dimension.This is because by one-dimensional small echo
At two-dimentional separable wavelets only have horizontal, vertical and diagonal three limited directions cannot be made full use of in higher-dimension
Geometrical characteristic specific to data itself, expression that can not the be optimal high-dimension function unusual containing line or face.And in fact two
The directional information of dimension image is often presented as the singularity of straight line or curve, and is not only point singularity, this kind of analyzing
When signal, small echo cannot excavate directional information therein well.
Summary of the invention
It is based in view of the above-mentioned deficiencies in the prior art, the technical problem to be solved by the present invention is that providing one kind
The ground penetrating radar image denoising method of shearlet transformation realizes simple, excellent effect, can be good at removing around target
Target is clearly presented in noise jamming, has good practical implementation value.
The invention adopts the following technical scheme:
A kind of ground penetrating radar image denoising method based on shearlet transformation, first to collected Coherent Noise in GPR Record
Frequency domain Fourier transformation is carried out, window adding in frequency domain processing is then carried out, is adopted under non-to the Coherent Noise in GPR Record progress after windowing process
Sample shearlet transformation, then utilizes the two-varaible model based on maximum a-posteriori estimation, to the different directions of different scale
Shearlet coefficient carry out threshold shrink processing, update coefficient, inverse shearlet carried out to new shearlet coefficient and is converted,
Ground Penetrating Radar frequency domain image after being denoised.
Specifically, the following steps are included:
S1, orientation Fourier transformation, and windowing process are carried out to collected Coherent Noise in GPR Record, after the adding window
Frequency domain image is divided into image block；
S2, the image block for obtaining the first step carry out non-lower sampling shearlet transformation one by one, obtain transformed subband
Image；
S3, transformed sub-band images are denoised based on neighborhood two-varaible model threshold value；
S4, inverse shearlet transformation is carried out to the sub-band images after removing dryness, the image block after being denoised, and according to transformation
Gradually correspondence combines for preceding position, removes the position filled up, the Ground Penetrating Radar frequency domain figure after finally being denoised.
Further, in step S1, obtained frequency domain data piecemeal is filled, Fu only is carried out to the orientation of echo data
In leaf transformation, be one-dimensional Fourier transform, add rectangular window removal due to static background clutter bring direct current point in slow time-frequency domain
Amount, High-frequency Interference and intended vibratory higher harmonic components.
Further, the frequency domain image after adding window is divided into the image block that size is 256*256.
Further, in step S2, first input picture block chooses shearlet and converts wavelet basis, determines decomposition scale layer
Number constructs shearlet base, decomposes on shearlet base to noise image.
Further, be based on neighborhood two-varaible model threshold denoising the following steps are included:
S301, noise variance is determined to the sub-band images of different scale different directionsWith the observation mean-square value of estimationObtain the mean-square value estimation of shearlet coefficient
S302, it is treated with a certain discrimination according to the difference of direction number, is corresponded when direction number is identical, when direction number difference
When, the direction number of subband mostly with father and son with direction number, and the relationship of generally integral multiple numbered using subband and is divided by with multiple
As a result it corresponds to, determines the paternal number of each coefficient；
S303, the corresponding shrinkage value of each coefficient is determined according to two-varaible model；
S304, window is taken to coefficient centered on coefficient just to be processed, corresponding shrinkage value at each position in calculating window
To the shrinkage value of the center coefficient, then using the shrinkage value in Gaussian window weighting windows, obtain after the coefficient final process more
New value obtains the denoising result of area block image to convert using inverse shearlet.
Further, in step S301, the mean-square value of shearlet coefficient is estimatedIt calculates as follows:
Wherein,For the noise variance under the dimension of estimation,For the observation mean-square value of estimation.
Further, in step S303, the corresponding shrinkage value of each coefficient calculates as follows:
Wherein, y1、y2Pass through the transformed coefficient of shearlet, and y for noise image2It is y1It is paternal number, s1It is y1
Constriction coefficient.
Further, in step S304, Gaussian matrix is as follows:
。
Further, in step S4, the piecemeal frequency domain figure after denoising is reintegrated according to original corresponding position, is then gone
Fall the zero of filling, obtains denoising image with the frequency domain of original same size.
Compared with prior art, the present invention at least has the advantages that
A kind of ground penetrating radar image denoising method based on shearlet transformation of the present invention, first to collected spy land mine
Frequency domain Fourier transformation is carried out up to data, then carries out window adding in frequency domain processing, the Coherent Noise in GPR Record after windowing process is carried out
Non-lower sampling shearlet transformation, then utilizes the two-varaible model based on maximum a-posteriori estimation, not to different scale
Equidirectional shearlet coefficient carries out threshold shrink processing, updates coefficient, carries out to new shearlet coefficient inverse
Shearlet transformation, the Ground Penetrating Radar frequency domain image after being denoised.The present invention can be good at removing the noise around target
Target is clearly presented in signal, provides better method for the denoising of practical ground penetrating radar image, convenient and simple, actually to answer
Image preprocessing in provides technical support.
Further, the Fourier transformation of orientation is first carried out to Coherent Noise in GPR Record, then window adding in frequency domain, filtered out quiet
Only clutter and some High-frequency Interferences, then piecemeal is handled, and is improved speed, is reduced hardware load.
Further, in this way can be quite time-consuming in subsequent decomposition transform since ground penetrating radar image is bigger, therefore
It is the image block that size is 256*256, the zero padding filling of data deficiencies by the image block.
Further, frequency domain blocks image is converted using non-lower sampling shearlet, optimal sparse force is carried out to image
Closely, while spectral aliasing is avoided, enhances its direction selection and translation invariance.
Further, bivariate shrinkage function denoising has been carried out to transformed sub-band coefficients, fully considered father and son's coefficient it
Between correlation, while considering the correlation between neighborhood, and different according to the correlation between different distance adjacent coefficient, use
Gaussian window weighting processing, correlation is related in direction between sufficiently having excavated the scale of coefficient, to reach good denoising effect.
Further, there is good denoising effect to ground penetrating radar image, can be good at removing around image object
Noise, target is clearly presented.
In conclusion this algorithm realizes that simply denoising works well, there is good engineering practical value.
Below by drawings and examples, technical scheme of the present invention will be described in further detail.
Detailed description of the invention
Fig. 1 is general flow chart of the invention；
Fig. 2 is denoising effect picture of several algorithms of different to actual measurement ground penetrating radar image, wherein (a) is original echo figure
Picture is (b) image after Wavelet Denoising Method, is (c) image after non-local mean denoising, (d) after for inventive algorithm denoising
Image.
Specific embodiment
The present invention provides a kind of ground penetrating radar image denoising methods based on shearlet transformation, it is only necessary to actual acquisition
The Coherent Noise in GPR Record arrived has been mixed into additive noise or multiplicative noise without paying close attention on earth, has not needed to mention in the radar data
Before know the variance of noise；This rarefaction representation characteristic to Multi-dimension chaos is converted to Ground Penetrating Radar figure using shearlet
As being decomposed；Threshold value contraction is carried out using neighborhood two-varaible model；And Gauss is carried out to multiple estimated values of the same coefficient
Weighted average processing；Make the program to the denoising effect of ground penetrating radar image better than existing algorithm, can be good at removing target
The noise jamming of surrounding, is clearly presented target, has good practical implementation value.
Referring to Fig. 1, a kind of ground penetrating radar image denoising method based on shearlet transformation of the present invention, first to acquisition
The Coherent Noise in GPR Record arrived carries out frequency domain Fourier transformation, window adding in frequency domain processing is then carried out, to the spy land mine after windowing process
Non-lower sampling shearlet transformation is carried out up to data, the two-varaible model based on maximum a-posteriori estimation is then utilized, to not
With scale different directions shearlet coefficient carry out threshold shrink processing, update coefficient, to new shearlet coefficient into
The inverse shearlet of row is converted, the Ground Penetrating Radar frequency domain image after being denoised.Specific step is as follows:
S1, orientation Fourier transformation, and windowing process are carried out to collected Coherent Noise in GPR Record, after the adding window
Frequency domain image is divided into the image block that size is 256*256；
Frequency domain data piecemeal filling to obtaining, only carries out Fourier transformation to the orientation of echo data, is one-dimensional Fu
In leaf transformation, slow time-frequency domain add rectangular window removal due to static background clutter bring DC component, High-frequency Interference and mesh
Mark vibration higher harmonic components；Frequency domain data piecemeal is filled, since ground penetrating radar image is bigger, in this way in subsequent decomposition
Can be quite time-consuming when transformation, therefore be the image block that size is 256*256, the zero padding filling of data deficiencies by the image block.
S2, the image block for obtaining the first step carry out non-lower sampling shearlet transformation one by one, obtain transformed subband
Image；
Include: input picture block, chooses shearlet and convert wavelet basis, the decomposition scale number of plies is determined, to construct
Shearlet base decomposes noise image on shearlet base.
S3, it is based on neighborhood two-varaible model threshold denoising, specific as follows:
S301, noise variance is determined according to formula (1) and formula (3) to the sub-band images of different scale different directionsAnd estimation
Observation mean-square value
Wherein, yiFor the coefficient after shearlet is decomposed of the direction under the scale, median () is to take intermediate value,For the noise variance under the dimension of estimation；
Wherein, yiFor the coefficient after shearlet is decomposed of the direction under the scale,wIt (k) is estimating window, M is window
Size,For the observation mean-square value of estimation；
Convolution (1) and formula (2) can obtain the mean-square value estimation of shearlet coefficientAre as follows:
(g)+It is defined as follows:
S302, the paternal number for determining each coefficient: when looking for corresponding paternal number, treating with a certain discrimination according to the difference of direction number,
When direction number is identical correspond, when direction number difference, generally the direction number of subband mostly with father and son with direction
Number, and the relationship of generally integral multiple, so being numbered using subband corresponding with multiple division result；
S303, the corresponding shrinkage value of each coefficient is determined according to two-varaible model, as shown in formula (5):
Wherein, y1、y2Pass through the transformed coefficient of shearlet, and y for noise image2It is y1It is paternal number, s1It is y1
Constriction coefficient；
S304, window is taken to coefficient centered on coefficient just to be processed, corresponding shrinkage value at each position in calculating window
To the shrinkage value of the center coefficient, then using the shrinkage value in Gaussian window weighting windows, obtain after the coefficient final process more
New value obtains the denoising result of area block image to convert using inverse shearlet.
Gaussian matrix used is as follows:
S4, carry out inverse shearlet to treated subband and convert, the image block after being denoised, and according to transformation before
Gradually correspondence combines for position, removes the position filled up, the Ground Penetrating Radar frequency domain figure after finally being denoised.
Piecemeal frequency domain figure after denoising is reintegrated according to original corresponding position, then removes the zero of filling, obtain with
Originally the frequency domain of same size denoises image.
The present invention is based on the set membership between adjacent scale shearlet coefficient and the similitude between neighborhood territory pixel, with
Based on Bayes posterior probability, threshold value constriction coefficient is carried out using the strong correlation between father and son's coefficient and is determined, then according to phase
Influence between adjacent pixel, is weighted with Gaussian window, the coefficient that obtains that treated, to reconstruct denoising image.
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.The present invention being described and shown in usually here in attached drawing is real
The component for applying example can be arranged and be designed by a variety of different configurations.Therefore, below to the present invention provided in the accompanying drawings
The detailed description of embodiment be not intended to limit the range of claimed invention, but be merely representative of of the invention selected
Embodiment.Based on the embodiments of the present invention, those of ordinary skill in the art are obtained without creative efforts
The every other embodiment obtained, shall fall within the protection scope of the present invention.
A, experimental program:
The present invention is based on the ground penetrating radar image Denoising Algorithms of Shearlet transformation and wavelet method, non-local mean to denoise
Comparison of the method (NL-means) to ground penetrating radar image denoising effect.
B, experiment condition:
Here using data volume is the Ground Penetrating Radar measured data of 4096*3051 as test data.Experimentation intermediate frequency
Domain window ranges are 5-103, and coefficient estimating window size is 3 × 3.Gauss weighting windows size is 3 × 3.
The ground penetrating radar image Denoising Algorithm of proposition of the invention converted based on shearlet is given below and compares calculation
The denoising effect picture of method, is illustrated in fig. 2 shown below, respectively original echo frequency domain image, the image after Wavelet Denoising Method, non-local mean
It denoises image and inventive algorithm denoises image.
Compared by the analysis in dialog box, it can be seen that compared to Wavelet Denoising Method, non-local mean denoising for visiting ground
The denoising effect of radar image, denoising effect of the invention is more preferable, has not only eliminated the noise jamming around target, but also be clearly in
Reveal target, works well.
The above content is merely illustrative of the invention's technical idea, and this does not limit the scope of protection of the present invention, all to press
According to technical idea proposed by the present invention, any changes made on the basis of the technical scheme each falls within claims of the present invention
Protection scope within.
Claims (10)
1. a kind of ground penetrating radar image denoising method based on shearlet transformation, which is characterized in that first to collected spy
Ground radar data carries out frequency domain Fourier transformation, window adding in frequency domain processing is then carried out, to the Coherent Noise in GPR Record after windowing process
Non-lower sampling shearlet transformation is carried out, the two-varaible model based on maximum a-posteriori estimation is then utilized, to different scale
The shearlet coefficients of different directions carry out threshold shrink processing, update coefficient, new shearlet coefficient carried out inverse
Shearlet transformation, the Ground Penetrating Radar frequency domain image after being denoised.
2. a kind of ground penetrating radar image denoising method based on shearlet transformation according to claim 1, feature exist
In, comprising the following steps:
S1, orientation Fourier transformation, and windowing process are carried out to collected Coherent Noise in GPR Record, by the frequency domain after the adding window
Image is divided into image block；
S2, the image block for obtaining the first step carry out non-lower sampling shearlet transformation one by one, obtain transformed sub-band images；
S3, transformed sub-band images are denoised based on neighborhood two-varaible model threshold value；
S4, the sub-band images after denoising carried out with inverse shearlet convert, the image block after being denoised, and according to transformation before
Gradually correspondence combines for position, removes the position filled up, the Ground Penetrating Radar frequency domain figure after finally being denoised.
3. a kind of ground penetrating radar image denoising method based on shearlet transformation according to claim 2, feature exist
In in step S1, being filled to obtained frequency domain data piecemeal, only Fourier transformation carried out to the orientation of echo data, slow
Time-frequency domain adds rectangular window removal due to static background clutter bring DC component, High-frequency Interference and intended vibratory higher hamonic wave
Component.
4. a kind of ground penetrating radar image denoising method based on shearlet transformation according to claim 2 or 3, feature
It is, the frequency domain image after adding window is divided into the image block that size is 256*256.
5. a kind of ground penetrating radar image denoising method based on shearlet transformation according to claim 2, feature exist
In in step S2, first input picture block chooses shearlet and converts wavelet basis, determine the decomposition scale number of plies, constructs shearlet
Base decomposes noise image on shearlet base.
6. a kind of ground penetrating radar image denoising method based on shearlet transformation according to claim 2, feature exist
In, be based on neighborhood two-varaible model threshold denoising the following steps are included:
S301, noise variance is determined to the sub-band images of different scale different directionsWith the observation mean-square value of estimation?
Mean-square value to shearlet coefficient is estimated
S302, it is treated with a certain discrimination according to the difference of direction number, is corresponded when direction number is identical, when direction number difference, subband
Direction number mostly with father and son with direction number, and the relationship of generally integral multiple, using subband number and multiple division result pair
It answers, determines the paternal number of each coefficient；
S303, the corresponding shrinkage value of each coefficient is determined according to two-varaible model；
S304, window taken to coefficient centered on coefficient just to be processed, calculates in window at each position corresponding shrinkage value to this
The shrinkage value of center coefficient, then using the shrinkage value in Gaussian window weighting windows, the updated value after obtaining the coefficient final process,
To convert using inverse shearlet, the denoising result of area block image is obtained.
7. a kind of ground penetrating radar image denoising method based on shearlet transformation according to claim 6, feature exist
In in step S301, the mean-square value of shearlet coefficient is estimatedIt calculates as follows:
Wherein,For the noise variance under the dimension of estimation,For the observation mean-square value of estimation.
8. a kind of ground penetrating radar image denoising method based on shearlet transformation according to claim 6, feature exist
In in step S303, the corresponding shrinkage value of each coefficient calculates as follows:
Wherein, y1、y2Pass through the transformed coefficient of shearlet, and y for noise image2It is y1It is paternal number, s1It is y1Receipts
Contracting coefficient.
9. a kind of ground penetrating radar image denoising method based on shearlet transformation according to claim 6, feature exist
In in step S304, Gaussian matrix is as follows:
。
10. a kind of ground penetrating radar image denoising method based on shearlet transformation according to claim 2, feature exist
In the piecemeal frequency domain figure after denoising being reintegrated according to original corresponding position, then removes the zero of filling, obtains in step S4
Image is denoised to the frequency domain of original same size.
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| CN110646851A (en) * | 2019-10-17 | 2020-01-03 | 东北大学 | Adaptive threshold seismic random noise suppression method based on Shearlet transformation |
| CN111308197A (en) * | 2019-12-10 | 2020-06-19 | 国网江苏省电力有限公司扬州供电分公司 | Harmonic measurement method and device based on block FFT |
| CN112862888A (en) * | 2021-01-29 | 2021-05-28 | 广东电网有限责任公司 | Cable positioning method and device, computer equipment and storage medium |
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