CN109581516B - Denoising method and system for data of curvelet domain statistic adaptive threshold value ground penetrating radar - Google Patents
Denoising method and system for data of curvelet domain statistic adaptive threshold value ground penetrating radar Download PDFInfo
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Abstract
The invention belongs to the technical field of data denoising, and discloses a method and a system for denoising data of a curved-wave-domain statistic adaptive threshold value ground penetrating radar, wherein the method comprises the following steps: introducing a block complex field threshold function algorithm, analyzing the change rule of the traditional threshold function curvelet transform denoising effect along with a threshold function control coefficient, and using the change rule for self-adaptive threshold value comparison of subsequent curvelet field statistics; performing correlation superposition on the curvelet transform coefficients in the scale and direction by using a high-order statistic theory, and adaptively determining the distribution scale and the rotation direction of effective signals in the curvelet transform coefficients through correlation statistics; and determining the threshold range of the noise component to be removed, and constructing a statistical self-adaptive threshold function curvelet transform denoising algorithm. Compared with the prior art, the method has guiding significance for accurate inference and interpretation of complex ground penetrating radar data by comparing the processing results of the synthetic ground penetrating radar data containing random noise and related noise and the actually measured ground penetrating radar data.
Description
Technical Field
The invention belongs to the technical field of data denoising, and particularly relates to a method and a system for denoising data of a curved-wave-domain statistic adaptive threshold value ground penetrating radar.
Background
Currently, the current state of the art commonly used in the industry is such that:
the ground penetrating radar adopts an antenna to emit electromagnetic waves with different frequencies, utilizes the difference of electromagnetic properties of an underground medium, and infers the space and physical property distribution of a target medium according to the amplitude, waveform and other kinematic and dynamic characteristics of a received echo, and is widely applied to the fields of geological disaster monitoring, engineering and environmental geological exploration, hydrogeological exploration, military reconnaissance and the like. However, as the exploration environment of the ground penetrating radar is more complex and the target detection is more and more precise (Zhangwu et al, 2014; Raney et al,2015), how to extract weak target signals in various complex interference noise annihilation environments with strong energy is a difficult task (Baida et al, 2017; Zheng et al, 2017).
The conventional ground penetrating radar data denoising technology is mostly based on a simple optimization or orthogonal transformation algorithm, a fixed filtering window is formed, weak effective signal distortion of time-frequency domain overlapping is caused, and specific noise processing limitations are provided, such as a median filtering method (Wang Lei et al, 2009), S transformation denoising (Gao Jing et al, 2004; Jeng et al, 2009; Zhang Mr et al, 2013a) and an F-K filtering method (Zhang Mr et al, 2013 b; Wang and Zhang, 2015). Due to various noise source doping, georadar data is often a non-linear, non-stationary signal sequence (Wang and Liu, 2017). The signal processing technology developed based on the Fourier transform theory can effectively solve the problem of stable signal analysis and processing, and the non-adaptive time-frequency window limitation makes the denoising problem of the complex data of the ground penetrating radar unable to be solved. The premise of the wavelet transformation for denoising the ground penetrating radar data is that the frequency spectrum separation of effective signals and noise signals is assumed, and the goal of fidelity denoising is achieved by adopting the sparse representation of a basis function with the characteristics of expansion and contraction and translation in a specific frequency band and setting a noise frequency band threshold. For example, Wangbao and Shenfei (2015) utilize the high-frequency threshold function wavelet transform denoising theory to develop the research of extracting weak signals of the ground penetrating radar, and provide basis for deducing abnormal positions. The lifting wavelet transformation with the improved threshold is used for denoising the data of the concrete void ground penetrating radar (late epitation, winter storage, 2010; Ghozzi et al, 2017), so that the interpretation and inference precision is improved; the wavelet transformation of the harmonious direction threshold function is used for denoising and clutter suppression (Tzanis,2013 and 2015) of archaeology and geotechnical exploration ground penetrating radar data, and the signal-to-noise ratio of the data is improved. Therefore, the effective threshold function can effectively improve the denoising effect and achieve the purpose of fidelity denoising.
In order to break through the limitation of denoising by adopting a rectangular time-frequency window in wavelet transform, the curvelet transform adopts wavelet domain expansion and translation characteristics, and adds a direction parameter so as to have better direction identification capability (candes and Donoho, 2004; candes et al, 2006). The method is widely applied to the field of geophysical data processing, particularly to the fields of seismic data noise suppression, multiple separation and the like, and research results are continuously emerging (Zhanghua and Chengmuo, 2013; Dongqiqian and the like, 2016; Zhanghua and the like, 2017). Neelamandi et al (2008) apply curvelet transformation to the three-dimensional seismic data, and random noise and related noise are effectively eliminated by setting a threshold function, so that the signal-to-noise ratio of the seismic data is improved; zhang jin Liang et al (2013) SAR image denoising algorithm of fast curvelet transform domain, using a mean threshold filter to make visualization and interpretation of the image accurate; terlasse and the like (2017) clearly determine the information of the dimensions and the directions of clutter and noise sources to be removed by manually selecting the data curvelet transform domain coefficients of the ground penetrating radar, and add a hard threshold function to realize denoising. Therefore, the precondition of applying the curvelet transform to the data noise suppression of the ground penetrating radar is to acquire more accurate noise threshold parameters and the distribution range of the curvelet coefficients belonging to the noise threshold parameters on the scale and the direction.
However, the actually measured complex ground penetrating radar data often contains random noise, correlated noise and other unknown noise types, and the distribution ranges of the required threshold parameters and the affiliated curvelet coefficients on the scale and the direction are also different. If the Zhu-xi strength and the like (2014) set a direction factor as zero in a selected transformation domain under an angle window function, and simultaneously estimate a noise variance to determine a threshold function, the surface layer direct wave and a noise source are removed, and the reflection signals weakening a reinforcing steel bar layer and a crack water layer are extracted under the background of the direct wave with higher intensity. Bao et al (2014) consider that the main energy of background noise is concentrated near a 90-degree directional region, while random noise is relatively uniformly distributed in the whole curvelet domain, and design a two-dimensional filter to estimate the noise distribution. Tzanis (2017) artificially establishes different crack structures corresponding to the ground penetrating radar data curvelet transform domain size and azimuth distribution range through numerical simulation, and then realizes the extraction of the ground penetrating radar reflected wave signals of the specific direction development crack structure. Therefore, how to effectively determine the domain scale and the distribution range in the azimuth of the curvelet transform of the ground penetrating radar data caused by the target body is the key to achieve the purposes of efficient denoising and accurate offset imaging (rainlin et al, 2015). At present, a plurality of methods for calculating threshold values are developed for the configuration of the curvelet transform, such as a piecewise linear filtering method, an L2 standard deviation method, a curvelet positive transform method, a diagonal real number and complex threshold value method, and the like, and need to be selected according to the noise type of actual data, so that the purpose of adaptive fidelity denoising cannot be met on the whole. Therefore, the construction of curvelet domain adaptive thresholds is a research focus of attention of scholars.
In summary, the problems of the prior art are as follows:
(1) various complex noise sources are often doped in nonlinear and non-stationary ground penetrating radar data, the method has serious influence on accurately extracting weak reflected wave signals and identifying diffraction wave hyperbolic in-phase axis characteristics, and the influence of neglecting noise can cause great errors for full waveform offset imaging and subsequent interpretation of the ground penetrating radar detection data. The traditional threshold function curvelet transform denoising needs to give a reasonable threshold function control coefficient according to the noise level of the ground penetrating radar data.
(2) The precondition of applying curvelet transformation to ground penetrating radar data noise suppression is to acquire more accurate noise threshold parameters and the distribution range of the curvelet coefficients belonging to the noise threshold parameters on the scale and the direction. However, the actually measured complex ground penetrating radar data often contains random noise, correlated noise and other unknown noise types, and the distribution ranges of the required threshold parameters and the affiliated curvelet coefficients on the scale and the direction are also different.
(3) At present, a plurality of methods for calculating threshold values are developed for the configuration of the curvelet transform, such as a piecewise linear filtering method, an L2 standard deviation method, a curvelet positive transform method, a diagonal real number and complex threshold value method, and the like, and need to be selected according to the noise type of actual data, so that the purpose of adaptive fidelity denoising cannot be met on the whole.
The difficulty and significance for solving the technical problems are as follows:
the exploration environment of the ground penetrating radar is more and more complex, and the target detection is more and more delicate, so that the extraction of weak target signals in various complex interference noise annihilation environments with strong energy becomes a very challenging subject. How to break through the bottleneck of denoising by selecting a threshold function by a manual trial and error method and construct a denoising algorithm of a self-adaptive threshold function is the key point of the current research. By introducing the advantages of curvelet transformation and high-order correlation statistical analysis, the invention provides a self-adaptive threshold denoising algorithm constructed on the basis of the curvelet transformation multi-scale and multi-direction coefficient high-order correlation statistical analysis theory, and provides a technical means for self-adaptive threshold fidelity denoising of the ground penetrating radar data.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a method and a system for denoising wave domain statistic self-adaptive threshold value ground penetrating radar data. The invention combines the advantages of curvelet transform and high-order correlation statistical analysis, and provides a self-adaptive threshold algorithm constructed by adopting high-order correlation statistics on the basis of a multi-scale and multi-direction analysis theory of curvelet transform, and a self-adaptive fidelity denoising method technology for a curvelet domain of ground penetrating radar data is explored.
The invention is realized in such a way that a denoising method for the data of the curved-wave domain statistic adaptive threshold value ground penetrating radar comprises the following steps:
introducing a block complex field threshold function algorithm, analyzing the change rule of the traditional threshold function curvelet transform denoising effect along with the control coefficient of the threshold function by selecting various different block complex field thresholds, and determining a block complex field threshold which can be effectively used for noise removal and is used for the self-adaptive threshold value comparison of the subsequent curvelet field statistics;
performing relevance superposition on the curvelet transform coefficient in the scale and direction by utilizing a high-order relevance statistic theory, adaptively determining the distribution scale and the rotation direction of the effective signal in the curvelet transform coefficient through the relevance statistic, and constructing a subsequent adaptive threshold range;
based on random noise, different scales and rotation directions of related noise components and effective component distribution, the distribution scale and rotation direction of effective signals are determined, the threshold range of the noise components is eliminated, and a statistic self-adaptive threshold function curvelet transformation denoising algorithm is constructed.
Further, the distribution scale and the rotation direction of the effective signal in the curvelet transform coefficient are determined in a self-adaptive mode through the correlation statistics; the method comprises the following steps:
performing two-dimensional curvelet forward transformation on the ground penetrating radar data to obtain coefficient distribution of different scales and different rotation angles; calculating high-order correlation statistics of each piece of ground penetrating radar data under different scales and different angles, and defining threshold distribution weight according to the high-order correlation statistics to realize noise filtering; finally, reconstructing denoised ground penetrating radar data by adopting two-dimensional curvelet inverse transformation; wherein the third order correlation function without offset is represented as:
the normalized higher order correlation statistic is:
in the formula, i is a ground penetrating radar data receiving point, t is a time sampling point, q is a translation factor, the value is 1,
positive transformation coefficients of the kth scale and the theta direction of the ith channel ground penetrating radar data curved wave domain are obtained;
a second-order autocorrelation function value of the kth scale and the theta direction of the ith channel ground penetrating radar data curved wave domain;
a k-th scale and a theta-th direction second-order autocorrelation function value of the (i + 1) -th ground penetrating radar data curved wave domain are obtained;
the self-adaptive determination of the distribution scale and the rotation direction of the effective signal in the curvelet transform coefficient through the calculation of the high-order correlation statistics specifically comprises the following steps:
the method comprises the following steps: performing curvelet forward transformation on original ground penetrating radar data to obtain coefficient distribution of all scales j and rotation angles theta, and extracting curvelet coefficients of large scale and small scale
And
step two: determining a scale range participating in high-order related statistic calculation by adopting curvelet transform numerical analysis;
step three: for j ═ 1, …, Jdo;
for 1, …, M-1 do; the previous observation point data is used in each correlation calculation, so that only M-1 observation point data participate in the calculation.
I according to formula
Calculating a correlation coefficient
According to the formula
Normalization
According to the formula
Performing ground penetrating radar data superposition
To pair
Repeating the process I to obtain
The superimposed high order correlation statistic;
End；
i＝i+1；θ＝θ+1；j＝j+1；
End；
step four: superposition calculation of higher order related statistics passing through curvelet domain
Coefficient of original large-scale curvelet
And integrating into a complete curvelet coefficient, and adopting curvelet inverse transformation to obtain final noise suppressed ground penetrating radar data.
Another object of the present invention is to provide a computer program for implementing the denoising method of the curvelet domain statistic adaptive threshold value ground penetrating radar data.
The invention also aims to provide an information data processing terminal for realizing the denoising method of the curvelet domain statistic adaptive threshold value ground penetrating radar data.
It is another object of the present invention to provide a computer-readable storage medium comprising instructions which, when executed on a computer, cause the computer to perform the method for denoising curvelet domain statistic adaptive threshold georadar data.
Another objective of the present invention is to provide a denoising control system for data of a curved-wave domain statistic adaptive threshold value ground penetrating radar, comprising:
the complex field threshold function analysis unit is used for introducing a block complex field threshold function algorithm and analyzing the change rule of the traditional threshold function curvelet transform denoising effect along with a threshold function control coefficient;
the curvelet transform coefficient distribution scale unit is used for performing correlation superposition on the curvelet transform coefficients in the scale and the direction by utilizing a high-order correlation statistic theory, and adaptively determining the distribution scale and the rotation direction of the effective signals in the curvelet transform coefficients through the correlation statistic;
and the statistic self-adaptive threshold function curvelet transform denoising algorithm construction unit is used for determining the threshold range of the noise component to be eliminated and constructing a statistic calculation self-adaptive threshold function curvelet transform denoising algorithm.
The invention also aims to provide geological disaster monitoring equipment carrying the curvelet domain statistic self-adaptive threshold value ground penetrating radar data denoising control system.
The invention also aims to provide engineering and environmental geological exploration equipment carrying the curvelet domain statistic adaptive threshold value ground penetrating radar data denoising control system.
The invention also aims to provide hydrogeological exploration equipment carrying the curvelet domain statistic adaptive threshold value ground penetrating radar data denoising control system.
In summary, the advantages and positive effects of the invention are:
the invention introduces a block complex field threshold function algorithm, and analyzes the change rule of the traditional threshold function curvelet transformation denoising effect along with the threshold function control coefficient; and performing correlation superposition on the curvelet transform coefficient in the scale and direction by using a high-order correlation statistic theory, and calculating and adaptively determining the distribution scale and the rotation direction of the effective signal in the curvelet transform coefficient through correlation statistic so as to determine the threshold range of the noise component to be eliminated and construct a statistic adaptive threshold function curvelet transform denoising algorithm. The effectiveness and feasibility of the algorithm are verified by comparing the processing results of the traditional threshold function curvelet transform denoising and the denoising algorithm provided by the invention on the synthetic ground penetrating radar data containing random noise and related noise and the actually measured ground penetrating radar data. The research result has guiding significance for accurate inference and interpretation of the complex ground penetrating radar data.
The method is based on the problem that a threshold function needs to be estimated in the traditional ground penetrating radar data denoising process through curvelet transformation, and two-dimensional curvelet forward transformation is conducted on the ground penetrating radar data to obtain coefficient distribution of different scales and different rotation angles; the method comprises the steps of calculating high-order related statistics of each channel of ground penetrating radar data under different scales and different angles, determining threshold distribution weight according to the high-order related statistics, developing high-order related statistics adaptive function algorithm research, achieving the purpose that the scale and the rotation angle range of effective information of a target body ground penetrating radar are established through a statistical theory without estimating a curvelet transform threshold function and the coefficient range of the curvelet transform threshold function, and further constructing a statistics adaptive threshold function curvelet transform denoising algorithm.
Based on the theory of a block complex domain threshold function, a simple rectangular model and a double-rectangular model with different burial depths are designed, and the traditional threshold function curvelet transformation denoising analysis of the synthetic ground penetrating radar data containing random noise and related noise shows that: a threshold function control coefficient is required to be given in the threshold range of the block complex field, and the quality of the denoising effect depends on the threshold function control coefficient matched with the noise-containing data; the theoretically synthesized noisy data can accurately estimate a threshold function and realize high-efficiency denoising, but the actually measured noisy data is difficult to realize the high-efficiency fidelity denoising through threshold function denoising estimation. Aiming at ground penetrating radar measured data collected under a complex noise source environment, weak diffracted wave hyperbolic in-phase axis feature extraction, parallel discontinuous reflected wave group energy recovery of middle and deep strong amplitude and weak amplitude and scattered reflected wave group analysis processing of weak amplitude are carried out, and a corresponding denoising result is obtained. The corresponding result is compared with the traditional threshold function curvelet transform denoising result, the advantages that the high-order statistical quantity algorithm has high efficiency in fidelity weak reflected wave signals, effectively removes the complex noise, recovers strong reflected wave group in-phase axes and the like in the aspect of complex noise source weak signal extraction are analyzed, and reliable and accurate interpretation of the detection data of the ground penetrating radar is facilitated.
Drawings
Fig. 1 is a flowchart of a method for denoising curvelet domain statistic adaptive threshold value ground penetrating radar data according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of denoising a data curvelet transform threshold of a noise-containing simulated synthetic ground penetrating radar according to an embodiment of the present invention.
In fig. 2: (a) original synthetic data; (b) the PSNR is 17dB with random noise data; (c) PSNR 15.51dB with the associated noise data; (d) and the PSNR value of the de-noising data changes along with the value change curve of the threshold control coefficient.
Fig. 3 is a graph of denoising results of curvelet transform with threshold control coefficients of 0.08 for noisy data (fig. 2(b), (c)) provided in the embodiment of the present invention.
In fig. 3: (a) the PSNR is 20.23dB, and is improved by 3.23dB according to the denoising result of the random noise data; (b) and the PSNR (noise signal ratio) of the denoising result of the related noise data is 16.75dB, and is improved by 1.24 dB.
Fig. 4 is a graph of the denoising result of the statistical adaptive threshold curvelet transform of the noisy data (fig. 2(b), (c)) provided by the embodiment of the present invention.
In fig. 4: (a) the PSNR is 25.3dB, and the noise reduction result of the random noise data is improved by 8.3 dB; (b) and the PSNR is 21.92dB, which is the related noise data denoising result, and is improved by 6.41 dB.
Fig. 5 is a diagram of a denoising result of adaptive threshold curvelet transform of noisy data statistics of a dual-rectangular target model according to an embodiment of the present invention.
In fig. 5: (a) original synthetic data; (b) the PSNR is 16.04dB with random noise data; (c) PSNR 15.7dB with relevant noise data; (d) the PSNR is 23.97dB according to the denoising result of the random noise data; (e) and PSNR is 21.05d as a result of denoising the correlated noise data.
Fig. 6 is a graph of a 50 th statistical adaptive threshold curvelet transform denoising result of noisy data of a dual-rectangular target model according to an embodiment of the present invention.
In fig. 6: (a) denoising results of the random noise data; (b) and denoising the related noise data.
FIG. 7 is a graph of processing results of conventional curvelet transform denoising and the denoising algorithm of the present invention for a time profile of an actually measured ground penetrating radar provided by an embodiment of the present invention.
In fig. 7: (a) actually measuring a time profile; (b) estimating a threshold curvelet denoising result by adopting an L2 standard variance; (c) and the statistic self-adaptive threshold curvelet denoising result.
Fig. 8 is a graph of processing results of the conventional curvelet transform denoising and the denoising algorithm of the present invention for the 200 th channel of the actually measured ground penetrating radar time profile provided by the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
At present, a plurality of methods for calculating threshold values are developed for the configuration of the curvelet transform, such as a piecewise linear filtering method, an L2 standard deviation method, a curvelet positive transform method, a diagonal real number and complex threshold value method, and the like, and need to be selected according to the noise type of actual data, so that the purpose of adaptive fidelity denoising cannot be met on the whole.
As shown in fig. 1, the method for denoising curvelet domain statistic adaptive threshold value ground penetrating radar data provided by the embodiment of the present invention includes:
s101, introducing a block complex field threshold function algorithm, and analyzing the change rule of the traditional threshold function curvelet transformation denoising effect along with a threshold function control coefficient; adaptive threshold-to-threshold comparison for subsequent curvelet domain statistics;
s102, performing correlation superposition on a curvelet transform coefficient in the scale and direction by using curvelet domain statistics, namely using a high-order correlation statistic theory, and adaptively determining the distribution scale and the rotation direction of an effective signal in the curvelet transform coefficient through the correlation statistics;
s103, determining a threshold range for eliminating noise components, and constructing a statistical self-adaptive threshold function curvelet transform denoising algorithm.
The system for controlling denoising of the data of the curvelet domain statistic self-adaptive threshold value ground penetrating radar provided by the embodiment of the invention comprises:
the complex field threshold function analysis unit is used for introducing a block complex field threshold function algorithm and analyzing the change rule of the traditional threshold function curvelet transform denoising effect along with a threshold function control coefficient;
the curvelet transform coefficient distribution scale unit is used for performing correlation superposition on the curvelet transform coefficients in the scale and the direction by utilizing a high-order correlation statistic theory, and adaptively determining the distribution scale and the rotation direction of the effective signals in the curvelet transform coefficients through the correlation statistic;
and the statistic self-adaptive threshold function curvelet transform denoising algorithm construction unit is used for determining the threshold range of the noise component to be eliminated and constructing the statistic self-adaptive threshold function curvelet transform denoising algorithm.
The application of the present invention is further described below in conjunction with specific assays.
1 principle of the method
1.1 curvelet transform
The invention aims to adopt a second generation truncation dispersion curvelet transform algorithm (candes and dooho, 2004; candes et al, 2006) to carry out the research of the denoising algorithm. The curvelet transformation variables comprise frequency, scale and orientation (angle), and the transformation expression is as follows:
the frequency window U, the scale window W and the angle window V can be expressed as:
Uj(r,θ)＝2-3/4W(2-jr)V(2[j/2]·θ/2π) (2)
in the formula, j is a scale, m is a rotation direction, and r and t are space and time domain parameters respectively. The angle window V is a ring-shaped domain and satisfies | x | ∈ 2j,2j+1]And polar coordinate definition thetaj,m＝2πm·2-[j/2]. For the dimension j and the rotation angle thetaj,mAnd spatial position
For f (x) epsilon L2(R2) The coefficient of the curvelet is defined as:
the main idea of suppressing the curvelet domain noise is as follows: 1) performing two-dimensional fast Fourier transform on ground penetrating radar data to obtain coefficient distribution, 2) configuring frequency, scale and angle windows according to formulas (2) - (4), 3) performing truncation de-noising according to a given threshold function or setting a coefficient range of noise to be zero to realize noise suppression, and 4) obtaining a data processing result by using a two-dimensional fast Fourier inverse transform algorithm on the 3) partially processed residual curvelet coefficient. The key of the curvelet domain noise suppression technology is to obtain a more accurate threshold function and a coefficient range to which the threshold function belongs. For the synthetic ground penetrating radar data, an accurate threshold function can be given according to the type and the strength of the added noise, and the coefficient range of the threshold function is determined; for actually measured ground penetrating radar data, the conventional operation is to artificially select a proper estimation threshold function and an affiliated coefficient range according to the actual situation.
Second generation curvelet transformerConversion algorithms (candies et al, 2004; 2006) develop noisy data processing comparison studies in which the threshold window involved in the curvelet transform is set at all scales
The control coefficient is a threshold distribution range and can be set artificially; ecIs the norm of the curvelet transform coefficient L2. The larger the value, the larger the filter window, and the less the residual information; conversely, the smaller the value, the greater the amount of noise and useful information. For the estimation of the data filtering judgment range, there are various methods for reference, such as calculating the norm of data L2, block complex number threshold estimation, etc. (Saha et al, 2015). For complex data processing, the block complex threshold function is more advantageous, so that the block complex field threshold is introduced into the curvelet transform denoising process. The expression is shown in formula (6):
where Ψ is a complex domain threshold function for estimating the decision filtering range, specifically derived for reference (Saha et al,2015),1is the weighted value of the curvelet coefficient of the adjacent channel,2is the curvelet coefficient squared normalization and weight values.
1.2 curvelet domain statistics adaptive threshold denoising
Performing two-dimensional curvelet forward transformation on the ground penetrating radar data to obtain coefficient distribution of different scales and different rotation angles; calculating high-order correlation statistics of each piece of ground penetrating radar data under different scales and different angles, and defining threshold distribution weight according to the high-order correlation statistics to realize noise filtering; finally, reconstructing denoised ground penetrating radar data by adopting two-dimensional curvelet inverse transformation; wherein the third order correlation function without offset is represented as:
the normalized higher order correlation statistic is:
in the formula, i is a ground penetrating radar data receiving point, t is a time sampling point, q is a translation factor, the value is 1,
positive transformation coefficients of the kth scale and the theta direction of the ith channel ground penetrating radar data curved wave domain are obtained;
a second-order autocorrelation function value of the kth scale and the theta direction of the ith channel ground penetrating radar data curved wave domain;
a k-th scale and a theta-th direction second-order autocorrelation function value of the (i + 1) -th ground penetrating radar data curved wave domain are obtained;
the self-adaptive determination of the distribution scale and the rotation direction of the effective signal in the curvelet transform coefficient through the calculation of the high-order correlation statistics specifically comprises the following steps:
the method comprises the following steps: performing curvelet forward transformation on original ground penetrating radar data to obtain coefficient distribution of all scales j and rotation angles theta, and extracting curvelet coefficients of large scale and small scale
And
step two: determining a scale range participating in high-order related statistic calculation by adopting curvelet transform numerical analysis;
step three: for j ═ 1, …, Jdo;
for 1, …, M-1 do; the previous observation point data is used in each correlation calculation, so that only M-1 observation point data participate in the calculation.
I according to formula
Calculating a correlation coefficient
According to the formula
Normalization
According to the formula
Performing ground penetrating radar data superposition
To pair
Repeating the process I to obtain
The superimposed high order correlation statistic;
End；
i＝i+1；θ＝θ+1；j＝j+1；
End；
step four: superposition calculation of higher order related statistics passing through curvelet domain
Coefficient of original large-scale curvelet
Integrating into complete curvelet coefficient, and adopting curvelet inverse transformation to obtain final noise-suppressed land mineAnd the data is reached.
2 simulation test
2.1 conventional curvelet transform denoising
And establishing a theoretical model and calculating and synthesizing simulation data by adopting a two-dimensional finite difference program. The size of the rectangular target body is 2X 1m, the X-axis distribution is-1 m, and the Z-axis distribution is 2-3 m; the resistivity is 10 omega.m, and the dielectric constant is 30F/m; the resistivity of a background medium is 1000 omega, m, and the dielectric constant is 3F/m; the frequency of the ground penetrating radar observation system is 100MHz, the point distance is 0.1m, the number of measurement points is 101 in the X-axis direction, and the number of time-domain acquisition points is 241. Peak signal-to-noise ratio is defined herein as
Where MSE is the mean square error of the data, which represents the approximation degree of the original signal and the noise (or denoised) signal, and max(s) is the peak value of the original signal.
Fig. 2(a) shows the original time domain data of the noise-free simulated synthetic ground penetrating radar, and the reflected wave signals of the ground penetrating radar caused by setting the boundary of the target rectangular model in the visible space domain are distributed in different time domains. Fig. 2(b) and fig. 2(c) respectively show random noise (PSNR ═ 17dB) and correlated noise ground penetrating radar data (PSNR ═ 15.51dB), the random noise pepper salt type is irregularly distributed in the whole ground penetrating radar section, and the weak target reflection signal is completely submerged by noise; the correlated noise is distributed according to the range proportion of the effective reflection signal, and part of false reflection signals can be seen. The PSNR value of the denoised data transformed by the curvelet transform using the threshold function of the formula (6) is shown in fig. 2(d) along with the variation curve of the threshold control coefficient. With the increase of the value of the threshold control coefficient, the PSNR value of the denoised data gradually decreases to the level of the PSNR value of the original noise data after approaching to an extreme value, wherein the PSNR extreme value (27.33dB) is obtained by the denoising result PSNR value of the random noise data near the threshold control coefficient of 0.15 (consistent with the noise level of the original data), and the PSNR extreme value (23.27dB) is obtained by the corresponding related noise near the threshold control coefficient of 0.35. It can be seen that whether the denoising effect is good or not by adopting the threshold function curvelet transform depends on whether the value of the threshold control coefficient (the noise level of the original data) is reasonable or not. Meanwhile, the random noise and the related noise data are different in the law of reasonable threshold control coefficients for denoising by adopting threshold function curvelet transformation, wherein the threshold control coefficient is a noise level value (0.10-0.20), and the threshold control coefficient is slightly higher than the threshold control coefficient value (0.3-0.4).
Aiming at denoising through curvelet transformation of a threshold function of noisy analog data, the accurate threshold control coefficient range obtained in advance can be effectively used for processing noisy data. However, actually measured data are often polluted by noise sources of different types and different intensities, a reasonable threshold control coefficient range is difficult to determine, and in order to effectively use a threshold function curvelet transform denoising algorithm, the threshold control coefficient range needs to be artificially estimated through a specific mode, such as an L2 standard deviation algorithm. Fig. 3(a) - (b) show the denoising result of the curvelet transform when the noise-containing data (fig. 2(b), (c)) is determined to be 0.08 by using the estimation method. Compared with original noisy data (fig. 2(b) and (c)), the threshold function curvelet transform denoising eliminates partial noise component signals, but effective reflected wave signals caused by a target rectangular model are only sparse and can not be effectively used for full-waveform inversion imaging calculation and subsequent inference interpretation processes.
2.2 statistic adaptive threshold curvelet transform denoising
In order to avoid the need of estimating a reasonable threshold function range for the traditional curvelet transform denoising, a statistic adaptive threshold algorithm curvelet transform is introduced to denoise the random noise and the related noise data shown in fig. 2(a) - (d), as shown in fig. 4(a) - (b). According to the denoising result, the denoising method based on the statistic self-adaptive threshold curvelet transform not only can effectively attenuate random noise (the PSNR value is improved by 8.3dB) and related noise (the PSNR value is improved by 6.41dB), but also can better restore the space and time domain distribution of effective reflected wave signals in the profile. In the complete noise attenuation process, the threshold function range does not need to be estimated, and the self-adaptive threshold weight of the statistic is calculated by adopting a formula (8), so that the purpose of fidelity denoising is achieved. The noise removing effect of the random noise data is better than that of the related noise data, and the reason is that the noise-signal ratio of the related noise data is low (PSNR is 15.51dB), which causes the calculation error of the correlation statistic of the noise signal, and the noise signal with strong correlation of the residual part is remained. In general, the statistic adaptive threshold algorithm curvelet transform denoising result can be effectively used for the data full waveform offset imaging processing and the subsequent interpretation inference process.
The size of a double-rectangular target body is designed to be 1 x 1m, the horizontal positions are-2 to-3 m and 2 to 3m, and the buried depth ranges from 2 to 3m and 3 to 4 m; other physical parameters and the ground penetrating radar observation system are consistent with the model. The time profile of the numerically simulated double-rectangular target body ground penetrating radar is shown in fig. 5(a), and the data of random noise and correlated noise are shown in fig. 5(b) and (c). The random noise data (PSNR 16.04dB) and correlated noise data (PSNR 15.7dB) completely overwhelm the target-specific effective reflected wave signal and are not useful for target distribution inference.
FIGS. 5(d) and (e) are the processing results of the denoising algorithm proposed by the present invention, where the complex effective reflected wave signal caused by the double rectangular object in the random noise time profile is completely recovered, and the PSNR value is improved by 7.93dB compared with the original noisy data; the correlated noise data basically rebuilds the space-time distribution of the effective reflected wave signals of the target body, but the residual correlated noise components still exist, and the PSNR value is improved by 6.65dB compared with the original noisy data. The 50 th original noiseless data, noisy data and de-noising data signal detail comparison curves in fig. 5 are shown in fig. 5(a) - (e), the de-noising algorithm provided by the invention effectively eliminates global pepper salt random noise distribution (fig. 6(a)) and accurately distinguishes weak effective reflected wave signals (fig. 6(b)) in a related noise environment, the de-noising data curve is well matched with the original noiseless data curve, and the effectiveness and feasibility of the de-noising algorithm provided by the invention are verified.
The application of the present invention is further described below with reference to practical examples.
FIG. 7(a) is an original time profile of a measured line of a ground penetrating radar, which shows that the salt-pepper random noise is spread over the entire profile data under the influence of the field environment; the individual acquisition channel is affected by local inhomogeneity, and amplitude distortion of adjacent observation channels occurs. The energy of reflected waves of a medium in a shallow part (100-250 time sampling points) of an original data profile is very weak, several diffracted wave in-phase axes can be seen in a sparse way, but the diffracted wave in-phase axes is submerged by noise, and the hyperbolic characteristic is not obvious; strong energy similar to a parallel reflection wave group appears in the deep part in the sampling range of 250-300 times, and the in-phase axis is intermittent and discontinuous and is not continuous; under the strong reflected wave group (300-400 time sampling points), the weak scattered reflected wave group is difficult to identify the energy lower boundary of the strong reflected wave group.
The data processing is performed on fig. 7(a) by using the above-mentioned conventional curvelet transform denoising processing method, a threshold range is estimated by using the L2 standard deviation, and a radar profile obtained by denoising is shown in fig. 7 (b). As can be seen from 7(b), the signal energy of part of the underground reflected wave group is strengthened, and random noise sources are eliminated to a certain extent; but the hyperbolic characteristic of effective diffracted wave and the intermittent reflected wave group in the original data still can not be effectively identified, and the signal-to-noise ratio of the de-noised data is improved to a limited extent. The reason is that random noise, related noise and other types of noise sources are doped in the measured data, meanwhile, the original data comprise reflected wave groups with different amplitude intensities, and the estimated threshold range cannot effectively cover the characteristic data denoising range. The optimal threshold range is determined by a manual trial and error method or noise can be effectively eliminated, but the evaluation of the optimal denoising effect lacks scientific basis. Therefore, only the radar section processed by the traditional threshold function curvelet transformation denoising data is analyzed and explained, and the accuracy of data interpretation cannot be ensured.
The statistical quantity adaptive threshold curvelet transform denoising algorithm provided by the invention is adopted to process the original data in FIG. 7(a), and the denoising result is shown in FIG. 7 (c). The random noise source does not have statistical correlation characteristics in the scale and direction of the curvelet transform coefficient; although the conversion coefficient of the relevant noise source has certain correlation in the scale and direction, the correlation of the relative effective reflected wave group signal is still small, so that the statistic self-adaptive threshold can effectively distinguish the energy of the reflected wave group, remove the noise signal and achieve the purpose of fidelity denoising. As can be seen from FIG. 7(c), the energy of the underground reflected wave is obviously enhanced, especially the signal-to-noise ratio of the hyperbolic homophase axis characteristics of the plurality of diffracted waves in the shallow part is effectively improved, the homophase axes of the reflection groups of the medium-depth multilayer medium are continuous, the interface is obvious, and the energy of the reflected wave with weak amplitude from the strong reflection wave group is clearly visible. The radar profile processed by the statistic adaptive threshold curvelet transform data is analyzed and interpreted, which is helpful for the accuracy of data interpretation.
Fig. 7(a) - (c) are graphs showing details of the denoising result of the 200 th conventional curvelet transform denoising of the actually measured ground penetrating radar data according to the present invention, as shown in fig. 8. As can be seen from the comparison of the curves, the ground echo, the weak amplitude diffracted wave (100-150), the strong amplitude diffracted wave (150-230) and the strong reflected wave group (230-350) in the time sampling range of 0-100 are polluted by the random noise and the related noise with weak amplitude, and the weak reflected wave signal in the time sampling range of more than 350 is polluted by the drowning noise source with strong amplitude. Compared with the traditional curvelet transform denoising result, the denoising algorithm provided by the invention can effectively recover the homophasic axis characteristics of the weak amplitude diffracted wave (100-150), the strong amplitude diffracted wave (150-230) and the strong reflected wave group (230-350), and can clearly distinguish the weak reflected wave signals, thereby verifying the feasibility and effectiveness of the denoising algorithm provided by the invention.
The application of the present invention will be further described with reference to effects.
Based on the problem that a threshold function needs to be estimated in the traditional ground penetrating radar data denoising process by curvelet transformation, two-dimensional curvelet forward transformation is carried out on ground penetrating radar data to obtain coefficient distribution of different scales and different rotation angles; the method comprises the steps of calculating high-order related statistics of each piece of ground penetrating radar data under different scales and different angles, determining threshold distribution weight according to statistic distribution, developing statistic adaptive function algorithm research, and establishing the scale and the rotation angle range of effective information of a target body ground penetrating radar through a statistical theory without estimating a curvelet transform threshold function and the coefficient range of the curvelet transform threshold function, so that a statistic adaptive threshold function curvelet transform denoising algorithm is established.
Based on the theory of a block complex domain threshold function, a simple rectangular model and a double-rectangular model with different burial depths are designed, and the traditional threshold function curvelet transformation denoising analysis of the synthetic ground penetrating radar data containing random noise and related noise shows that: a threshold function control coefficient is required to be given in the threshold range of the block complex field, and the quality of the denoising effect depends on the threshold function control coefficient matched with the noise-containing data; the theoretically synthesized noisy data can accurately estimate a threshold function and realize high-efficiency denoising, but the actually measured noisy data is difficult to realize the high-efficiency fidelity denoising through threshold function denoising estimation.
Aiming at ground penetrating radar measured data collected under a complex noise source environment, weak diffracted wave hyperbolic in-phase axis feature extraction, parallel discontinuous reflected wave group energy recovery of middle and deep strong amplitude and weak amplitude and scattered reflected wave group analysis processing of weak amplitude are carried out, and a corresponding denoising result is obtained. The corresponding result is compared with the traditional threshold function curvelet transform denoising result, the advantages that the high-order statistical quantity algorithm has high efficiency in fidelity weak reflected wave signals, effectively removes the complex noise, recovers strong reflected wave group in-phase axes and the like in the aspect of complex noise source weak signal extraction are analyzed, and reliable and accurate interpretation of the detection data of the ground penetrating radar is facilitated.
In the above embodiments, the implementation may be wholly or partially realized by software, hardware, firmware, or any combination thereof. When used in whole or in part, can be implemented in a computer program product that includes one or more computer instructions. When loaded or executed on a computer, cause the flow or functions according to embodiments of the invention to occur, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device. The computer instructions may be stored in a computer readable storage medium or transmitted from one computer readable storage medium to another, for example, the computer instructions may be transmitted from one website site, computer, server, or data center to another website site, computer, server, or data center via wire (e.g., coaxial cable, fiber optic, Digital Subscriber Line (DSL), or wireless (e.g., infrared, wireless, microwave, etc.)). The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device, such as a server, a data center, etc., that includes one or more of the available media. The usable medium may be a magnetic medium (e.g., floppy Disk, hard Disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., Solid State Disk (SSD)), among others.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (8)
1. A denoising method for data of a curved wave domain statistic adaptive threshold value ground penetrating radar is characterized by comprising the following steps:
introducing a block complex field threshold function algorithm, analyzing the change rule of the traditional threshold function curvelet transform denoising effect along with a threshold function control coefficient, and using the change rule for self-adaptive threshold value comparison of subsequent curvelet field statistics;
performing relevance superposition on the curvelet transform coefficient in the scale and direction by utilizing a high-order relevant statistic theory, and calculating and adaptively determining the distribution scale and the rotation direction of the effective signal in the curvelet transform coefficient through the high-order relevant statistic;
determining a threshold range for eliminating noise components, and constructing a high-order related statistic self-adaptive threshold function curvelet transform denoising algorithm;
calculating and adaptively determining the distribution scale and the rotation direction of the effective signal in the curvelet transform coefficient through high-order related statistics; the method comprises the following steps:
performing two-dimensional curvelet forward transformation on the ground penetrating radar data to obtain coefficient distribution of different scales and different rotation angles; calculating high-order correlation statistics of each piece of ground penetrating radar data under different scales and different angles, and defining threshold distribution weight according to the high-order correlation statistics to realize noise filtering; finally, reconstructing denoised ground penetrating radar data by adopting two-dimensional curvelet inverse transformation; wherein the third order correlation function without offset is represented as:
the normalized higher order correlation statistic is:
in the formula, i is a ground penetrating radar data receiving point, t is a time sampling point, q is a translation factor, the value is 1, and Fi k,θPositive transformation coefficients of the kth scale and the theta direction of the ith channel ground penetrating radar data curved wave domain are obtained;
a second-order autocorrelation function value of the kth scale and the theta direction of the ith channel ground penetrating radar data curved wave domain;
a k-th scale and a theta-th direction second-order autocorrelation function value of the (i + 1) -th ground penetrating radar data curved wave domain are obtained;
the self-adaptive determination of the distribution scale and the rotation direction of the effective signal in the curvelet transform coefficient through the calculation of the high-order correlation statistics specifically comprises the following steps:
the method comprises the following steps: performing curvelet forward transformation on original ground penetrating radar data to obtain coefficient distribution of all scales j and rotation angles theta, and extracting curvelet coefficients of large scale and small scale
And
step two: determining a scale range participating in high-order related statistic calculation by adopting curvelet transform numerical analysis;
step three: for J ═ 1, …, J do;
for 1, …, M-1 do; the previous observation point data is used in each correlation calculation, so that only M-1 observation point data participate in the calculation;
the process I: according to the formula
Calculating to obtain correlation coefficient
According to the formula
Normalized correlation coefficient
Obtain the result of
According to the formula
Data superposition of ground penetrating radar is carried out on the change of subscript index i to obtain a result
To pair
Repeating the process I to obtain
The superimposed high order correlation statistic;
End；
i＝i+1；θ＝θ+1；j＝j+1；
End；
step four: superposition calculation of higher order related statistics passing through curvelet domain
Coefficient of original large-scale curvelet
Integrate into a complete curvelet coefficient and adoptAnd (4) performing inverse curvelet transformation to obtain final noise suppressed ground penetrating radar data.
2. A computer program for implementing the method for denoising curvelet domain statistic adaptive threshold georadar data of claim 1.
3. An information data processing terminal for implementing the method for denoising the curvelet domain statistic adaptive threshold value ground penetrating radar data as claimed in claim 1.
4. A computer-readable storage medium comprising instructions that when executed on a computer cause the computer to perform the method for denoising curvelet domain statistic adaptive threshold georadar data of claim 1.
5. A system for controlling denoising of data of a curved-wave domain statistic adaptive threshold value ground penetrating radar for implementing the method for denoising of data of a curved-wave domain statistic adaptive threshold value ground penetrating radar of claim 1, wherein the system for controlling denoising of data of a curved-wave domain statistic adaptive threshold value ground penetrating radar comprises:
the complex field threshold function analysis unit is used for introducing a block complex field threshold function algorithm, analyzing the change rule of the traditional threshold function curvelet transform denoising effect along with a threshold function control coefficient, and is used for the self-adaptive threshold value comparison of the subsequent curvelet field statistics;
the curvelet transform coefficient distribution scale unit is used for performing correlation superposition on the curvelet transform coefficients in the scale and the direction by utilizing a high-order statistic theory, and calculating and adaptively determining the distribution scale and the rotation direction of the effective signals in the curvelet transform coefficients through high-order correlation statistics;
and the statistic self-adaptive threshold function curvelet transform denoising algorithm construction unit is used for determining the threshold range of the noise component to be eliminated and constructing the statistic self-adaptive threshold function curvelet transform denoising algorithm.
6. A geological disaster monitoring device carrying the curvelet domain statistic adaptive threshold value ground penetrating radar data denoising control system of claim 5.
7. An engineering and environmental geological exploration device carrying the curvelet domain statistic adaptive threshold value ground penetrating radar data denoising control system of claim 5.
8. A hydrogeological exploration device carrying the curvelet domain statistic adaptive threshold value ground penetrating radar data denoising control system of claim 5.
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