CN105403867A - Compression-sensing-based signal reconstruction and de-noising method of ground penetrating radar - Google Patents

Abstract

The invention discloses a compression-sensing-based signal reconstruction and de-noising method of a ground penetrating radar. The method comprises the following steps: establishing a complete dictionary for input signal sparse expression; constructing a sampling matrix based on a correspondence relation between missing ground penetrating radar data and complete data; according to a measurement matrix, the complete dictionary, and measurement data, reconstructing a sparse coefficient by using an orthogonal matching tracking algorithm; and carrying out inverse transformation by using the reconstructed sparse coefficient to construct a complete signal. The provided method is a novel ground penetrating radar data processing method. With the method, the missing ground penetrating radar data can be recovered correctly and noises in the ground penetrating radar can be eliminated effectively. Therefore, the provided method is a multi-purpose processing method.

Description

Gpr Signal based on compressed sensing is rebuild and denoising method

Technical field

The invention belongs to and belong to Geodetection and Information Technology field, particularly relate to a kind of Gpr Signal based on compressed sensing and rebuild and denoising method.

Background technology

Compressed sensing is a kind of new sampling theory, and it utilizes the sparse characteristic of signal, much smaller than under Nyquist sampling rate condition, draws source signal by stochastic sampling and restructing algorithm.It is that a kind of novel signal be based upon on the bases such as matrix analysis, statistical probability theory and optimum theory disposes theory.This theory avoids high-speed sampling, low rate can sample to signal and process, and significantly can reduce data and store and transmission cost, bring new impact to signal transacting field.This theory is shown great attention at numerous areas such as information theory, imaging of medical, wireless telecommunications and seismic prospectings after proposing, and brings new inspiration to commercial production innovation.

Ground penetrating radar has the advantages such as efficiency is high, precision is good, is used widely in geologic prospect and engineering detecting.Along with the raising of ground penetrating radar detection standard, make to propose higher requirement to the systematicness of data and integrality.But in the engineer applied of reality, the impact of geologic condition, factor such as collection environment and acquisition cost etc., often there is irregular and incomplete situation in the data of field acquisition, if the data of disappearance can not get rational process, finally can affect Effect on Detecting.In real work, process irregular employing data relatively simple, normally utilize the contiguous track data of linear interpolation, the obvious this practice has weak point, the Coherent Noise in GPR Record reconstructing method of reasonable, carries out recovery significant to missing data.And ground penetrating radar is as a kind of electromagnetic signal, be usually subject to noise, be difficult to correctly differentiate target echo at strong noise background, need to carry out denoising to signal, to improve signal to noise ratio (S/N ratio).Denoising common methods has frequency filtering, Wavelet Denoising Method etc., and these methods have certain effect in actual applications, but these method denoisings have respective applicability, especially under strong noise background or under low sampling rate data cases, effect is general.So, need to seek more a kind of more efficiently method, to strengthen Coherent Noise in GPR Record noise removal capability.

Summary of the invention

Goal of the invention: the object of the invention is the deficiency in order to solve existing Coherent Noise in GPR Record reconstructing method, improve the recovery precision to missing data, strengthen practicality and the reliability of algorithm, propose a kind of Gpr Signal based on compressed sensing and rebuild and denoising method.

Technical scheme: a kind of Gpr Signal based on compressed sensing is rebuild and denoising method, comprises the steps:

(1) the complete dictionary of the rarefaction representation of input signal is set up;

(2) Coherent Noise in GPR Record of disappearance and the corresponding relation structure sampling matrix R of partial data is utilized;

(3) by calculation matrix, complete dictionary and measurement data, orthogonal matching pursuit algorithm is utilized to reconstruct sparse coefficient α;

(4) utilize the sparse coefficient α rebuild to carry out inverse transformation and construct complete signal x.

In described step (1), complete dictionary adopts DCT dictionary.

Described DCT dictionary adopts fixed DCT dictionary, and its form of expression is:

$\mathrm{\Ψ}\left(k\right)=\mathrm{\α}\left(k\right)\underset{i=0}{\overset{n-1}{\Σ}}x\left(i\right)cos\left(\frac{(2i+1)k\mathrm{\π}}{2n}\right)---\left(8\right)$

Wherein, Ψ (k) is dictionary atom, $\mathrm{\α}\left(k\right)=\left\{\begin{array}{cc}\sqrt{1/n}& k=0\\ \sqrt{2/n}& 1\≤k\≤n-1\end{array}\right..$

In the sampling of described step (2), sampled data infects noise, and its formula is expressed as:

y＝Rx+e(9)

Wherein, y is measurement data, and R is calculation matrix, and e is noise;

The reconstruction formula of described step (3) is expressed as:

$\left\{\begin{array}{c}\begin{array}{cc}min\left|\right|{\mathrm{\Ψ}}^{T}x\left|\right|& sub\mathrm{jec}\mathrm{tto}\left|\right|{\mathrm{R\Ψ}}^{T}x-y\left|\right|\≤\mathrm{\ϵ}\end{array}\\ \mathrm{mi}n\left|\right|\mathrm{\α}|{|}_0\end{array}\right.---\left(10\right)$

Wherein, Ψ is complete dictionary, and α is sparse coefficient, and ε is constant.

The orthogonal matching pursuit algorithm of described step (3) is realized by following steps:

1) calculate residual error ε (j), formula is

$\mathrm{\ϵ}\left(j\right)=\left|\right|r^{t-1}|{|}_2^2-\frac{{\left({\mathrm{\Ψ}}_j^T{r}^{t-1}\right)}^2}{\left|\right|{\mathrm{\Ψ}}_j|{|}_2^2}---\left(11\right)$

2) vector in regeneration function set active set;

3) signal is estimated

${\hat{x}}^t=\arg \min \left|\right|y-\mathrm{\Φ}u|{|}_2^2---\left(12\right);$

4) residual error vector is upgraded

$r^t=y-{\hat{y}}^t---\left(13\right)$

In formula for approximate measure;

5) residual error is checked

$\left|\right|r^t|{|}_2^2<\mathrm{\&epsiv;}$

(14)

Satisfy condition, iteration terminates, otherwise repeats 1)-5) circulation step, until meet.

Complete dictionary small echo dictionary, lid the primary (Gabor) dictionary or K svd (K-SVD) dictionary in described step (1).

Beneficial effect: the present invention rebuilds disappearance Coherent Noise in GPR Record by compressive sensing theory, recovers the Coherent Noise in GPR Record in complete road.On the other hand, according to compressive sensing theory, for the Gpr Signal had containing strong noise background, utilize noise not have sparse features at transform domain, the data reconstructed so not Noise, thus realize signal denoising.Based on the Coherent Noise in GPR Record that compressive sensing theory is rebuild, can not only obtain complete Coherent Noise in GPR Record, and can remove the noise in data, be a kind of multiduty method for processing ground penetrating radar data.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention.

Embodiment

Below in conjunction with accompanying drawing, case study on implementation of the present invention is described in detail;

As shown in Figure 1, the Gpr Signal based on compressed sensing is rebuild and denoising method, is to be realized by following four key steps:

(1) set up the complete dictionary of the rarefaction representation of input signal, adopt modal DCT dictionary here;

(2) Coherent Noise in GPR Record of disappearance and the corresponding relation structure sampling matrix R of partial data is utilized;

(3) by calculation matrix, complete dictionary and measurement data, restructing algorithm is utilized---orthogonal matching pursuit algorithm (ROMP algorithm) reconstructs sparse coefficient α;

(4) utilize the sparse coefficient α rebuild to carry out inverse transformation and construct complete signal x.

Complete dictionary for rarefaction representation has fixed and self-adaptation two kinds, adopts fixed DCT dictionary, its form of expression:

$\mathrm{\&Psi;}\left(k\right)=\mathrm{\&alpha;}\left(k\right)\underset{i=0}{\overset{n-1}{\mathrm{\&Sigma;}}}x\left(i\right)\cos \left(\frac{(2i+1)\mathrm{k\&pi;}}{2n}\right)---\left(15\right)$

Wherein, $\mathrm{\&alpha;}\left(k\right)=\left\{\begin{array}{cc}\sqrt{1/n}& k=0\\ \sqrt{2/n}& 1\&le;k\&le;n-1\end{array}\right..$

Based on compressed sensing denoising, the method is different from traditional denoising method, and its prerequisite is having under a conversion, and source signal has rarefaction representation and noise signal does not have this feature.In lack sampling process, sampled data infects noise, and its formula is expressed as:

y＝Rx+e(16)

Wherein, y is measurement data, and R is calculation matrix, and e is noise.So reconstruction formula can be expressed as:

$\left\{\begin{array}{c}\begin{array}{cc}min\left|\right|{\mathrm{\&Psi;}}^{T}x\left|\right|& subjectto\left|\right|{\mathrm{R\&Psi;}}^{T}x-y\left|\right|\&le;\mathrm{\&epsiv;}\end{array}\\ min\left|\right|\mathrm{\&alpha;}|{|}_0\end{array}\right.$

(17)

Wherein, Ψ is complete dictionary, and α is sparse coefficient, and ε is constant.In the noisy situation of measured value, the signal reconstruction algorithm based on compressed sensing can rebuild source signal equally.

ROMP algorithm realization step:

Calculate residual error ε (j), formula is

1) vector in regeneration function set active set;

2) signal is estimated

${\hat{x}}^t=\arg \min {\left|\right|y-\mathrm{\&Phi;u}\left|\right|}_2^2---\left(19\right);$

3) residual error vector is upgraded

$r^t=y-{\hat{y}}^t---\left(20\right)$

In formula for approximate measure;

4) residual error is checked

${\left|\right|r^t\left|\right|}_2^2<\mathrm{\&epsiv;}---\left(21\right)$

Satisfy condition, iteration terminates, otherwise repeats 1)-5) circulation step, until meet.

The present invention realizes reconstruct and the denoising of Gpr Signal missing data by compressed sensing; Cross complete dictionary by DCT method, be not limited to and propose DCT method herein, comprise other fixing complete dictionary and adaptive learning dictionary, such as small echo, Gabor dictionary and K-SVD dictionaries etc.; Utilize the sampling matrix of the Coherent Noise in GPR Record of disappearance and the corresponding relation structure of partial data; Described signal reconfiguring method, is not limited to orthogonal matching pursuit algorithm, comprises other signal reconfiguring methods such as base tracing algorithm, Homotopy etc.; In the present invention, range of application is not limited to the recovery of Gpr Signal, comprises the denoising to signal.The present invention is a kind of novel method for processing ground penetrating radar data, and correctly can not only recover the Coherent Noise in GPR Record lacked, and effectively can remove the noise of Gpr Signal, be a kind of multiduty disposal route.The present invention is by DCT sparse dictionary, and sampling matrix and measurement data, utilize ROMP algorithm to reconstruct sparse coefficient, then DCT inverse transformation constructs complete Gpr Signal.

Claims (7)

1. the Gpr Signal based on compressed sensing is rebuild and a denoising method, it is characterized in that, comprises the steps:

(1) the complete dictionary of the rarefaction representation of input signal is set up;

(2) Coherent Noise in GPR Record of disappearance and the corresponding relation structure sampling matrix R of partial data is utilized;

(3) by calculation matrix, complete dictionary and measurement data, orthogonal matching pursuit algorithm is utilized to reconstruct sparse coefficient α;

(4) utilize the sparse coefficient α of reconstruct to carry out inverse transformation and construct complete signal x.

2. the Gpr Signal based on compressed sensing according to claim 1 is rebuild and denoising method, it is characterized in that, in described step (1), complete dictionary adopts DCT dictionary.

3. the Gpr Signal based on compressed sensing according to claim 2 is rebuild and denoising method, and it is characterized in that, described DCT dictionary adopts fixed DCT dictionary, and its form of expression is:

Wherein, Ψ (k) is dictionary atom,

4. the Gpr Signal based on compressed sensing according to claim 1 is rebuild and denoising method, it is characterized in that, in the sampling of described step (2), sampled data infects noise, and its formula is expressed as:

y＝Rx+e(2)

Wherein, y is measurement data, and x is complete signal, and R is sampling matrix, and e is noise.

5. the Gpr Signal based on compressed sensing according to claim 1 is rebuild and denoising method, and it is characterized in that, the reconstruct of described step (3) is expressed as:

Wherein, Ψ is complete dictionary, and α is sparse coefficient, and ε is constant.

6. the Gpr Signal based on compressed sensing according to claim 1 is rebuild and denoising method, and it is characterized in that, the orthogonal matching pursuit algorithm of described step (3) is realized by following steps:

1) calculate residual error ε (j), formula is

2) vector in regeneration function set active set;

3) signal is estimated

4) residual error vector is upgraded

In formula for approximate measure;

5) residual error is checked

Satisfy condition, iteration terminates, otherwise repeats 1)-5) circulation step, until meet.

7. the Gpr Signal based on compressed sensing according to claim 1 is rebuild and denoising method, it is characterized in that, in described step (1), complete dictionary adopts small echo dictionary, lid the primary (Gabor) dictionary or K svd (K-SVD) dictionary.