CN111934690A - New nuclear signal reconstruction method based on adaptive compressed sensing - Google Patents

New nuclear signal reconstruction method based on adaptive compressed sensing Download PDF

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CN111934690A
CN111934690A CN202010774814.6A CN202010774814A CN111934690A CN 111934690 A CN111934690 A CN 111934690A CN 202010774814 A CN202010774814 A CN 202010774814A CN 111934690 A CN111934690 A CN 111934690A
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adaptive
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coefficient
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李祥
刘用泽
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East China Institute of Technology
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Abstract

The new nuclear signal reconstruction method based on the adaptive compressed sensing comprises a Gaussian convolution adaptive threshold discrete wavelet conversion process and a compressed sensing adaptive sensing matrix construction process; the Gaussian convolution adaptive threshold discrete wavelet conversion process comprises the following steps: s1: inputting a neutron signal x; s2: sparse representation of neutron signal x; s4: selecting a threshold value; s5: making a threshold-sparsity curve, and taking a threshold on the maximum curvature node as an adaptive threshold; s6: obtaining Gaussian convolution; s7: designing and constructing a self-adaptive sparse coefficient contraction matrix, and determining a large coefficient position vector; s8: and constructing an adaptive effective sparse base. According to the invention, the neutron signal compression sparsity is higher, the transmission speed is higher, the sampling times are less, the reconstruction time is shorter, and the pulsed neutron uranium quantitative logging instrument system is effectively optimized.

Description

New nuclear signal reconstruction method based on adaptive compressed sensing
Technical Field
The invention relates to the technical field of compressed sensing, in particular to a new kernel signal reconstruction method based on adaptive compressed sensing.
Background
The acquisition of neutron logging signals relates to massive high-speed (ns-level) data acquisition, transmission, reconstruction and processing technologies, however, the neutron logging system under the traditional Nyquist-Shannon (Shannon) sampling theorem has high acquisition cost, and the real-time performance of the logging system is poor from the sampling compression to the transmission and storage to the reconstruction, analysis and processing processes.
According to the appearance of a compressive sensing theory, firstly, original signals can be reconstructed by a small number of observed values through compressive sampling, so that the data acquisition cost can be reduced, the time for transmitting the reconstructed signals in the well logging experiment process can be shortened, and the nuclear radiation hazard time can be reduced; secondly, the compressed sensing theory has robustness on the processing of noise signals, and signal reconstruction is also a signal noise reduction process; also, one of the characteristics of the compressed samples is: only useful information is collected, and the fact that the compressed sensing has certain data restoration capability, namely the data packet loss resistance capability, is determined; thirdly, the compressed sensing is directly analyzed and identified aiming at the observed value, so that the real-time property of the logging signal is expected to be improved, and a theoretical basis and a technical basis are provided for analyzing and processing the nuclear signal on site; finally, a better solution is provided for the field logging work system in the aspects of data acquisition, noise analysis, nuclear signal transmission reconstruction analysis processing real-time performance and the like.
The compressed sensing has very important innovation application prospect in on-site neutron logging.
Disclosure of Invention
Objects of the invention
In order to solve the technical problems in the background art, the invention provides a new method for reconstructing a nuclear signal based on self-adaptive compressed sensing.
(II) technical scheme
In order to solve the problems, the invention provides a new kernel signal reconstruction method based on adaptive compressed sensing, which comprises a Gaussian convolution adaptive threshold discrete wavelet conversion process and a compressed sensing adaptive sensing matrix construction process;
the Gaussian convolution adaptive threshold discrete wavelet conversion process comprises the following steps:
s1: inputting a neutron signal x, wherein x is non-sparse;
s2: for sparse representation of a neutron signal x, a sym4level6 wavelet transformation base is adopted; the variance is generated as sign m, mean mu, A, the value of the positive probability density function at k, as follows:
A＝normpdf(k,mu,sigma)；
s3: convolving the sparse coefficient with a gaussian to expand the resolution of the "size coefficient";
G＝conv(C,A)；
s4: by passing
Figure BDA0002618000470000022
The method comprises the steps of selecting a threshold value;
estimating and determining the matrix position corresponding to the large coefficient after Gaussian convolution through a threshold value so as to determine the position corresponding to the large coefficient of the sparse coefficient theta matrix;
s5: making a threshold-sparsity curve, and taking a threshold on the maximum curvature node as an adaptive threshold;
the node of the maximum curvature of the threshold-sparsity curve is a 'big and small coefficient inflection point', and the absolute distinguishing threshold of the big coefficient and the small coefficient is obtained by calculating the threshold of the maximum curve transformation rate node of the sparse coefficient;
s6: obtaining a gaussian convolution sym4level6, wherein the optimal threshold is sigma-14, and the optimal sparsity is sigma-109;
s7: designing and constructing a self-adaptive sparse coefficient contraction matrix, and determining a large coefficient position vector;
Figure BDA0002618000470000021
s8: an adaptive effective sparse base is constructed,
Figure BDA0002618000470000031
a compressed sensing adaptive sensing matrix construction process, comprising the steps of:
s21: generating random numbers uniformly distributed among obeys (0,1) by adopting a mixed congruence method;
Xi+1＝mod(λxi+c,M)，i＝xi/M；
i∈(0，1)；
s22: to the parameter1And2carrying out nonlinear transformation on a sampling algorithm to obtain a pair of random variables X and Y which obey standard normal distribution N (0, 1);
Figure BDA0002618000470000032
Figure BDA0002618000470000033
Xf＝(-2ln1)1/2cos(2π2)；
Yf＝(-2ln1)1/2sin(2π2)；
s23: constructing a deterministic Monte Carlo sampling pseudo-random number observation matrix, namely constructing an adaptive observation matrix, and generating an m x n-dimensional deterministic MC sampling pseudo-random number observation matrix which is called an original observation matrix psi;
Figure BDA0002618000470000034
then: the matrix psi is partitioned and paired
Figure BDA0002618000470000035
Carrying out normalization;
Figure BDA0002618000470000039
let θ be (θ)1θ2……θn)TS of0Each large coefficient being thetar1θr2……θrs0And their positions in theta are respectively gammar1，γr2……γrs0(ii) a Is recorded as: a ═ γ1，γ2……γs0}；
Order to
Figure BDA0002618000470000036
In (1) correspond to
Figure BDA0002618000470000037
Unchanged, remaining column vectors
Figure BDA0002618000470000038
Changed into the original 10qDoubling, q is less than 0;
thereby obtaining a new observation matrix
Figure BDA0002618000470000041
Namely:
Figure BDA0002618000470000042
Figure BDA0002618000470000043
an adaptive Monte Carlo observation matrix AMCOM;
wherein:
Figure BDA0002618000470000044
wherein, j corresponds to the position of the large coefficient, and then delta is equal to the diagonal matrix Lambda in the sparse coefficient contraction matrix;
i.e. Δi，j＝Λ(j，j)；
Wherein, adopt
Figure BDA0002618000470000045
After the monte carlo observation matrix AMCOM is adapted, the observation value vector can be obtained by the following formula:
Figure BDA0002618000470000046
and reconstructing the neutron signal by adopting a compressed sensing OMP reconstruction algorithm.
According to the invention, the neutron signal compression sparsity is higher, the transmission speed is higher, the sampling times are less, the reconstruction time is shorter, and the pulsed neutron uranium quantitative logging instrument system is effectively optimized.
Drawings
Fig. 1 is a flow chart of the gaussian convolution adaptive threshold discrete wavelet transform process in the present invention.
Fig. 2 is a threshold-sparseness graph in the present invention.
FIG. 3 is a flow chart of the compressed sensing adaptive sensing matrix construction process according to the present invention.
FIG. 4 is a diagram of the distribution of random variables in the present invention.
Fig. 5 is a schematic frequency histogram in the present invention.
FIG. 6 is a diagram showing the signal-to-noise ratio of sym4level6 transformation base and GCTDWT (sym4) base at different dilutions in the experimental analysis of the present invention by the CoSaMP algorithm.
Fig. 7 is a schematic diagram of results of obtaining an optimal threshold and an optimal sparsity after a sparse coefficient-threshold maximum curve transformation ratio in a sparsity-threshold curve of experimental analysis according to the present invention.
FIG. 8 is a schematic diagram of the coefficient vector dimension at the base of sym 4-DWT coefficients of neutron signals in an experimental analysis of the present invention.
FIG. 9 is a diagram of the GCTDWT coefficient of a neutron signal along the vector dimension of the coefficient based on GCTDWT (sym4) in an experimental analysis of the present invention.
Fig. 10 is a schematic diagram of the error of the DWT coefficient of the error-neutron signal with its best K term approximation for the sym4 basis coefficient with its best K term approximation in the experimental analysis of the present invention.
FIG. 11 is a schematic diagram of the error of the GCTDWT (sym4) basis coefficient and its best K term approximation-the error of the GCTDWT coefficient and its best K term approximation for the neutron signal in the experimental analysis of the present invention.
FIG. 12 is a schematic diagram of the signal-to-noise ratio of the observation matrix in the experimental analysis 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 will be described in further detail with reference to the accompanying drawings in conjunction with the following detailed description. It should be understood that the description is intended to be exemplary only, and is not intended to limit the scope of the present invention. Moreover, in the following description, descriptions of well-known structures and techniques are omitted so as to not unnecessarily obscure the concepts of the present invention.
As shown in fig. 1-12, the new kernel signal reconstruction method based on adaptive compressed sensing proposed by the present invention includes a gaussian convolution adaptive threshold discrete wavelet transform process and a compressed sensing adaptive sensing matrix construction process;
the Gaussian convolution adaptive threshold discrete wavelet conversion process comprises the following steps:
s1: inputting a neutron signal x, wherein x is non-sparse;
s2: for sparse representation of a neutron signal x, a sym4level6 wavelet transformation base is adopted; the variance is generated as sign m, mean mu, A, the value of the positive probability density function at k, as follows:
A＝normpdf(k,mu,sigma)；
s3: convolving the sparse coefficient with a gaussian to expand the resolution of the "size coefficient";
G＝conv(C,A)；
s4: by passing
Figure BDA0002618000470000061
The method comprises the steps of selecting a threshold value;
estimating and determining the matrix position corresponding to the large coefficient after Gaussian convolution through a threshold value so as to determine the position corresponding to the large coefficient of the sparse coefficient theta matrix;
s5: making a threshold-sparsity curve, and taking a threshold on the maximum curvature node as an adaptive threshold;
the node of the maximum curvature of the threshold-sparsity curve is a 'big and small coefficient inflection point', and the absolute distinguishing threshold of the big coefficient and the small coefficient is obtained by calculating the threshold of the maximum curve transformation rate node of the sparse coefficient;
s6: obtaining a gaussian convolution sym4level6, wherein the optimal threshold is sigma-14, and the optimal sparsity is sigma-109;
s7: designing and constructing a self-adaptive sparse coefficient contraction matrix, and determining a large coefficient position vector;
Figure BDA0002618000470000062
s8: an adaptive effective sparse base is constructed,
Figure BDA0002618000470000063
a compressed sensing adaptive sensing matrix construction process, comprising the steps of:
s21: generating random numbers uniformly distributed among obeys (0,1) by adopting a mixed congruence method;
Xi+1＝mod(λxi+c,M)，i＝xi/M；
i∈(0，1)；
s22: to the parameter1And2carrying out nonlinear transformation on a sampling algorithm to obtain a pair of random variables X and Y which obey standard normal distribution N (0, 1);
Figure BDA0002618000470000064
Figure BDA0002618000470000065
Xf＝(-2ln1)1/2cos(2π2)；
Yf＝(-2ln1)1/2sin(2π2)；
s23: constructing a deterministic Monte Carlo sampling pseudo-random number observation matrix, namely constructing an adaptive observation matrix, and generating an m x n-dimensional deterministic MC sampling pseudo-random number observation matrix which is called an original observation matrix psi;
Figure BDA0002618000470000071
then: the matrix psi is partitioned and paired
Figure BDA0002618000470000072
Carrying out normalization;
Figure BDA0002618000470000073
let θ be (θ)1θ2……θn)TS of0Each large coefficient being thetar1θr2……θrs0And their positions in theta are respectively gammar1，γr2……γrs0(ii) a Is recorded as: a ═ γ1，γ2……γs0}；
Order to
Figure BDA0002618000470000074
In (1) correspond to
Figure BDA0002618000470000075
Unchanged, remaining column vectors
Figure BDA0002618000470000076
Changed into the original 10qDoubling, q is less than 0;
thereby obtaining a new observation matrix
Figure BDA0002618000470000077
Namely:
Figure BDA0002618000470000078
Figure BDA0002618000470000079
an adaptive Monte Carlo observation matrix AMCOM;
wherein:
Figure BDA00026180004700000710
wherein, j corresponds to the position of the large coefficient, and then delta is equal to the diagonal matrix Lambda in the sparse coefficient contraction matrix;
i.e. Δi，j＝Λ(j，j)；
Wherein, adopt
Figure BDA00026180004700000711
After the monte carlo observation matrix AMCOM is adapted, the observation value vector can be obtained by the following formula:
Figure BDA00026180004700000712
and reconstructing the neutron signal by adopting a compressed sensing OMP reconstruction algorithm.
According to the invention, the neutron signal compression sparsity is higher, the transmission speed is higher, the sampling times are less, the reconstruction time is shorter, and the pulsed neutron uranium quantitative logging instrument system is effectively optimized.
Experimental analysis:
according to the new nuclear signal reconstruction method based on the adaptive compressed sensing, provided by the invention, the experimental test analysis of the communication transmission and reconstruction performance of the neutron signal under the adaptive compressed sensing system is as follows:
comparing the performances of the sym4 base, the level6 base and the GCTDWT (sym4 base and level6) base, and reconstructing by adopting a CoSaMP algorithm in a greedy algorithm;
the Ψ measurement matrix is a gaussian matrix M × N, where N is 1024, M is N/2 to obtain a better reconstruction effect, the Φ sparse matrix is a wavelet sym4 or level6 matrix, G is mu is 0, sigma is 1, k is 5 gaussian matrix, Λ is a diagonal matrix parameter q is 10, CNT is performed 100 times in the experiment, and the reconstructed signal-to-noise ratio is averaged.
As shown in fig. 6: the GCTDWT obviously improves the signal-to-noise ratio, and when the sparsity s belongs to [0, 70], the threshold value is selected to be larger, so that the low-frequency large coefficient of more useful signals is filtered, and the large coefficient is not selected sufficiently and is too sparse; with the increase of sparsity, the sparse coefficient existing in the interval of | (supp θ |) |(s) is mostly a low-frequency large coefficient, the number of the large coefficient is also increased, the number of the low frequencies of useful signals is also increased, the high-frequency small coefficient is still in a filtering state under the corresponding threshold value of the sparsity interval, the influence on the signal-to-noise ratio after reconstruction is small, the signal-to-noise ratio of the reconstruction of the two is in an increasing trend, the signal-to-noise ratio of the reconstruction of the two is similar in the interval, and the selection on the large coefficient is not different; when the sparsity s belongs to [0, 140], the signal-to-noise ratio of the sym4 base is in a fluctuating state, in the interval, along with the increase of the sparsity, the small coefficient in the low-frequency coefficient, the large coefficient in the medium-frequency coefficient and the large coefficient in the high-frequency coefficient are close in amplitude, so that the sparsity is doped with partial medium-high frequency sparse coefficients, and in the process of reconstructing the low, medium and high frequency coefficients, along with the change of input of useful signals and interference signals, the reconstructed signal-to-noise ratio also fluctuates, but the overall state is stable.
The sparsity s of the GCTDWT base is equal to [0, 14 ∈0]And when the sparsity is increased, the threshold value is reduced, the advantage that the difference value on the large and small sparse coefficients is large and the resolution is high is reflected, the small amplitude coefficient in the low-frequency large coefficient is larger than the large amplitude coefficient in the high-frequency small coefficient, the resolution on the coefficient selection is better, and the increased sparsity coefficient is mostly smaller in the low-frequency large coefficient of the useful signal. The first half signal-to-noise ratio can also continue to increase; in the latter half, similar to sym4level6, a part of small interference coefficient is doped in the dilution, and the signal-to-noise ratio after reconstruction fluctuates but tends to be in a stable state; when the sparsity s is more than 140, most of the sparsity of the sym4level6 base is small coefficient, the reconstruction signal to noise ratio is in a descending trend, and the small coefficient increased under the GCTDWT base passes through the contraction matrix Lambda to be 10-qThe filtering treatment plays a role in inhibiting the interference of the signal to noise ratio, and the signal to noise ratio tends to be in a larger and stable state.
As shown in fig. 7: the coefficient with the sparse coefficient amplitude of 0 is also regarded as the sparsity s and the sparsity after Gaussian convolution
Figure BDA0002618000470000091
And sparsity of GCTDWT
Figure BDA0002618000470000092
Similarly, the thresholds corresponding to the sparsity of sym4level6 and GCTDWT under the optimal snr are about σ -5 and σ -15, which verifies that the optimal threshold and the optimal sparsity result is obtained after calculating the maximum curve transformation ratio of the sparse coefficient and the threshold in fig. 7.
In the case of the figures 8-11,
Figure BDA0002618000470000093
the parameter σ is 14.
As can be seen from fig. 8, the sym4level6 coefficients have more small coefficients with non-zero amplitude.
As can be seen from fig. 9, the projection coefficients of the neutron signal under the GCTDWT basis, the GCTDWT transform mainly concentrates the useful information of the signal on the low-frequency coefficients to realize sparse representation of the signal, the sparse coefficients are approximately absolute sparse,
Figure BDA0002618000470000094
almost all the large coefficients are protected and all the small coefficients are scaled. Although the dilution of the GCTDWT maximum SNR point is less than the sym4 wavelet base, s contains a large number of positions 10-qThe small coefficients processed by filtering can be sampled and reconstructed only by transmitting the position amplitudes of the large coefficients (100) by neglecting the amplitudes of the small coefficients in the actual communication transmission channel of the subsystem, and the transmission speed is obviously higher than that of the coefficients of the traditional wavelet transform sparse coefficients (887), and the signal-to-noise ratio is higher than that of the sampling reconstruction of the wavelet coefficients (90) after the threshold. The complexity, the power consumption time and the transmission bandwidth are reduced on the compression transmission, and the signal-to-noise ratio can be improved on the reconstruction.
As can be seen from FIG. 10, sym4level6 is based on the sparse coefficient θ and the optimal K term approximation coefficient θkThe error of (2) is large.
As can be seen from the figure 11 of the drawings,
Figure BDA0002618000470000101
and thetakIn the residual after subtraction, the GCTDWT can keep the medium-frequency large coefficient after the sparsity K and has local analysis capability, while the optimal K term approximation of the 'one-knife-cut' type has no local analysis capability, so that the medium-frequency large coefficient is easy to filter, larger reconstruction error is caused, and the signal-to-noise ratio is reduced. Thus, the sparse coefficient
Figure BDA0002618000470000102
The sparsity performance of the method is obviously superior to the sparsity coefficient theta.
As can be seen from FIG. 12, the input signal is a neutron signal sequence x1024×1The transformation matrix is GCTDWT, the reconstruction algorithm is OMP, and the psi measurement matrix is Gaussian random matrix M multiplied by N and AMCOM, wherein N is 1024.
The neutron signal is in an optimal sparsity interval s epsilon [50, 123] of sym4level6 base, and the optimal sparsity is about 82 at s. The neutron signal is in the optimal sparsity interval s epsilon [82, 252] of the GCTDWT (sym4) base, and the optimal sparsity is 109.
Taking M as N/2 to obtain better reconstruction performance, and taking the optimal sparse interval and the optimal sparsity as sparsity for better testing and comparing the effects of the two observation matrixesIs equal to [51, 128 ]]Setting the ratio independent variable r of sparsity and observation vector length to be in the range of 0.1, 0.25]So that 8 points s in the sparsity of the intersection region can be taken as [51,62,73,94,95,106,117,128]The reconstructed SNR performances in these 8 points are compared, where Δ in AMCOMi，jΔ is the diagonal matrix parameter q 10 and the signal-to-noise ratio CNT is the average of 100 trials. It can be clearly seen that the signal-to-noise ratio of the reconstructed neutron signal obtained by the AMCOM is higher than that obtained by the gaussian random observation matrix under different sparsity degrees.
The operation experiment runs CNT (100 times) on a Dell Inspiron7420 notebook (6GB RAM memory, Inter (R) core (TM) i5-3230M CPU @2.60GHz 64-bit operating system), neutron signals take 13.316947 seconds under reconstruction of Gaussian random matrix maximum signal-to-noise ratio points (r is 0.16, M is 512, s is 84), neutron signals take 3.438698 seconds under reconstruction of AMCOM maximum signal-to-noise ratio points (r is 0.22, M is 512, s is 117), and the number of rows of the adaptive observation array is reduced from M512 to M-s in the compression, transmission and sampling reconstruction process of the adaptive observation matrix 0109, the number of required observation value vectors is reduced to 109 (coefficient amplitude is nonzero) from the original 512, the observation times are reduced to 109, the observation times are obviously reduced, and the adoption reconstruction speed is accelerated.
The method is characterized in that 700 pulse neutron counts obtained by a well and mine fault of a certain logging team on-site detection parameter at a cable ascending speed of 36m/h are subjected to compression transmission sampling reconstruction, the reconstruction algorithm is OMP, the sparse transformation base is sym4level6 wavelet transformation base, the time consumed by compression transmission sampling reconstruction of a Gaussian random observation matrix is 2639.783270 seconds, the reconstruction algorithm is OMP, the sparse transformation base is GCTDWT, and the observation matrix is AMCOM compression transmission sampling reconstruction is 675.581288 seconds.
In summary, it can be known from experiments that the experiments are to test the compressive sensing performance of the compressive sensing sparse transform basis GCTDWT and the compressive sensing observation matrix AMCOM, to test and compare the compressive sensing compressive transmission sampling reconstruction sparsity and the signal-to-noise ratio performance of a single pulse neutron signal in different sparse matrices and different observation matrices, and to test and compare 700 pulse neutron signal compressive transmission sampling reconstruction times of the field parameter well.
Test results show that the neutron signal compression sparsity is higher, the transmission speed is higher, the sampling times are fewer, the reconstruction time is shorter, and the pulsed neutron uranium quantitative logging instrument system is effectively optimized.
It is to be understood that the above-described embodiments of the present invention are merely illustrative of or explaining the principles of the invention and are not to be construed as limiting the invention. Therefore, any modification, equivalent replacement, improvement and the like made without departing from the spirit and scope of the present invention should be included in the protection scope of the present invention. Further, it is intended that the appended claims cover all such variations and modifications as fall within the scope and boundaries of the appended claims or the equivalents of such scope and boundaries.

Claims (1)

1. The new nuclear signal reconstruction method based on the adaptive compressed sensing is characterized by comprising a Gaussian convolution adaptive threshold discrete wavelet transform process and a compressed sensing adaptive sensing matrix construction process;
the Gaussian convolution adaptive threshold discrete wavelet conversion process comprises the following steps:
s1: inputting a neutron signal x, wherein x is non-sparse;
s2: for sparse representation of a neutron signal x, a sym4level6 wavelet transformation base is adopted; the variance is generated as sign m, mean mu, A, the value of the positive probability density function at k, as follows:
A＝normpdf(k,mu,sigma)；
s3: convolving the sparse coefficient with a gaussian to expand the resolution of the "size coefficient";
G＝conv(C,A)；
s4: by passing
Figure FDA0002618000460000011
The method comprises the steps of selecting a threshold value;
estimating and determining the matrix position corresponding to the large coefficient after Gaussian convolution through a threshold value so as to determine the position corresponding to the large coefficient of the sparse coefficient theta matrix;
s5: making a threshold-sparsity curve, and taking a threshold on the maximum curvature node as an adaptive threshold;
the node of the maximum curvature of the threshold-sparsity curve is a 'big and small coefficient inflection point', and the absolute distinguishing threshold of the big coefficient and the small coefficient is obtained by calculating the threshold of the maximum curve transformation rate node of the sparse coefficient;
s6: obtaining a gaussian convolution sym4level6, wherein the optimal threshold is sigma-14, and the optimal sparsity is sigma-109;
s7: designing and constructing a self-adaptive sparse coefficient contraction matrix, and determining a large coefficient position vector;
Figure FDA0002618000460000012
s8: an adaptive effective sparse base is constructed,
Figure FDA0002618000460000013
a compressed sensing adaptive sensing matrix construction process, comprising the steps of:
s21: generating random numbers uniformly distributed among obeys (0,1) by adopting a mixed congruence method;
Xi+1＝mod(λxi+c,M)，i＝xi/M；
i∈(0，1)；
s22: to the parameter1And2carrying out nonlinear transformation on a sampling algorithm to obtain a pair of random variables X and Y which obey standard normal distribution N (0, 1);
Figure FDA0002618000460000021
Figure FDA0002618000460000022
Xf＝(-2ln1)1/2cos(2π2)；
Yf＝(-2ln1)1/2sin(2π2)；
s23: constructing a deterministic Monte Carlo sampling pseudo-random number observation matrix, namely constructing an adaptive observation matrix, and generating an m x n-dimensional deterministic MC sampling pseudo-random number observation matrix which is called an original observation matrix psi;
Figure FDA0002618000460000023
then: the matrix psi is partitioned and paired
Figure FDA0002618000460000024
Carrying out normalization;
Figure FDA0002618000460000025
let θ be (θ)1θ2……θn)TS of0Each large coefficient being thetar1θr2……θrs0And their positions in theta are respectively gammar1，γr2……γrs0(ii) a Is recorded as: a ═ γ1，γ2……γs0}；
Order to
Figure FDA0002618000460000026
In (1) correspond to
Figure FDA0002618000460000027
Unchanged, remaining column vectors
Figure FDA0002618000460000028
Changed into the original 10qDoubling, q is less than 0;
thereby obtaining a new observation matrix
Figure FDA0002618000460000029
Namely:
Figure FDA00026180004600000210
Figure FDA0002618000460000031
an adaptive Monte Carlo observation matrix AMCOM;
wherein:
Figure FDA0002618000460000032
wherein, j corresponds to the position of the large coefficient, and then delta is equal to the diagonal matrix Lambda in the sparse coefficient contraction matrix;
i.e. Δi，j＝Λ(j，j)；
Wherein, adopt
Figure FDA0002618000460000033
After the monte carlo observation matrix AMCOM is adapted, the observation value vector can be obtained by the following formula:
Figure FDA0002618000460000034
and reconstructing the neutron signal by adopting a compressed sensing OMP reconstruction algorithm.
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Publication number Priority date Publication date Assignee Title
CN113515673A (en) * 2021-04-30 2021-10-19 山西大学 High-value object storage and transportation whole-process information compression and reconstruction method and system
CN113515673B (en) * 2021-04-30 2023-01-31 山西大学 High-value object storage and transportation whole-process information compression and reconstruction method and system
CN113670435A (en) * 2021-08-20 2021-11-19 西安石油大学 Underground vibration measuring device based on compressed sensing technology and measuring method thereof
CN113923723A (en) * 2021-10-15 2022-01-11 中国联合网络通信集团有限公司 Flow reconstruction method, device, equipment and storage medium
CN113923723B (en) * 2021-10-15 2023-05-09 中国联合网络通信集团有限公司 Flow reconstruction method, device, equipment and storage medium
CN114252899A (en) * 2022-03-02 2022-03-29 四川新先达测控技术有限公司 Cascade impulse convolution forming method and device for kernel signal
CN114252899B (en) * 2022-03-02 2022-05-20 四川新先达测控技术有限公司 Cascade impulse convolution forming method and device for kernel signal

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