CN110838096B - Seismic image completion method based on information entropy norm - Google Patents

Seismic image completion method based on information entropy norm Download PDF

Info

Publication number
CN110838096B
CN110838096B CN201911112524.9A CN201911112524A CN110838096B CN 110838096 B CN110838096 B CN 110838096B CN 201911112524 A CN201911112524 A CN 201911112524A CN 110838096 B CN110838096 B CN 110838096B
Authority
CN
China
Prior art keywords
norm
information entropy
matrix
rank
image completion
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201911112524.9A
Other languages
Chinese (zh)
Other versions
CN110838096A (en
Inventor
李勇
陈力鑫
李雪梅
郝思宇
马泽川
陈杰
王鹏飞
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Chengdu Univeristy of Technology
Original Assignee
Chengdu Univeristy of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Chengdu Univeristy of Technology filed Critical Chengdu Univeristy of Technology
Priority to CN201911112524.9A priority Critical patent/CN110838096B/en
Publication of CN110838096A publication Critical patent/CN110838096A/en
Application granted granted Critical
Publication of CN110838096B publication Critical patent/CN110838096B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00—Image enhancement or restoration
    • G06T5/77—Retouching; Inpainting; Scratch removal

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Geophysics And Detection Of Objects (AREA)

Abstract

The invention discloses a seismic image completion method based on an information entropy norm, which is applied to the field of geophysical seismic data processing, aims at the problem that the low-rank matrix obtained by recovery based on a matrix rank reduction method is not really low-rank due to limitation of the existing L1 norm, replaces the nuclear norm adopted by the original SVD by an objective function based on the information entropy norm, then normalizes the rank minimization term of the objective function by the information entropy norm, and finally obtains the low-rank matrix by an iterative ADMM estimation method for approximate solution, thereby obtaining the steady recovery of a missing image.

Description

Seismic image completion method based on information entropy norm
Technical Field
The invention belongs to the field of geophysical seismic data processing, and particularly relates to a seismic data completion technology.
Background
In the actual geophysical seismic exploration and acquisition, the phenomenon of seismic data channel shortage is mainly caused by the following two reasons: (1) the arrangement of the geophones is often irregular due to the influence of the surface environment (such as rivers, ponds, lakes and the like), surface obstacles (roads, houses, bridges and the like) and the like of a work area; (2) due to poor coupling effect of the detector and the earth surface, a waste channel and a waste cannon can be generated due to environmental interference or the instrument. With the technical development of seismic exploration, the quantity of acquired data is larger and larger, on one hand, densely sampled data is expected to obtain more accurate underground structures, and on the other hand, in consideration of exploration cost, sparse sampling is needed in the spatial direction, so that the obtained data is often sparse and irregular. Therefore, reconstructing complete seismic data from sparse and irregular seismic data to obtain accurate subsurface structures is an important solution to solve the above contradictions.
The method for reconstructing the seismic data has various methods, such as methods based on prediction filtering, dip interpolation and the like, and the method mainly focuses on a matrix rank reduction method. The principle of such methods is that seismic data can be represented in the frequency domain by a low rank matrix, assuming that the seismic data consists of a finite number of linear in-phase axes. Irregular seismic data can increase the rank of the frequency domain matrix, and by reducing the rank, reconstruction of the data can be achieved. By utilizing the structural characteristics of the Toeplitz matrix in the rank reduction algorithm, the direct multiplication of the Toeplitz matrix and the vector can be avoided by adopting a multi-dimensional FFT algorithm, the calculated amount is greatly reduced, and the process of the rank reduction algorithm is accelerated.
The core of the matrix rank reduction-based method is that the low rank of seismic data is described by using the L1 norm of a matrix singular value vector, but the L1 norm description has the problem of insufficient sparsity: for example, for two singular value vectors, i.e., [4,4,4,0,0] and b ═ 10,1,1,0,0], the definition according to the norm of L1 cannot be accurately distinguished, and actually, the sparsity of the singular value b vector is much higher than that of the singular value a vector, so that the L1 norm limitation causes that the low rank matrix recovered by the matrix rank reduction method is not really low rank.
Disclosure of Invention
In order to solve the technical problem, the invention provides a seismic image completion method based on an information entropy norm, and the robustness and the correctness of a low-rank matrix in the seismic image completion problem are improved by using a low-rank approximation method based on information entropy norm combination.
The technical scheme adopted by the invention is as follows: a seismic image completion method based on an information entropy norm comprises the following steps:
s1, replacing the traditional kernel norm adopted by the existing seismic image completion model truncation SVD with the kernel norm based on the information entropy norm to obtain an objective function based on the information entropy norm;
s2, regularizing a rank minimization term of the target function by adopting an information entropy norm;
and S3, carrying out iterative solution on the target function which is normalized in the step S2 and is based on the information entropy norm, thereby obtaining the robust estimation of the low-rank matrix.
Further, step S1 specifically includes the following sub-steps:
s11, the seismic image completion model expression of the seismic data matrix X is as follows:
Figure BDA0002273144940000021
wherein R represents the rank of the seismic data, | | · |. non-calculationFIs Frobenius norm, BΩRepresenting the actual miss matrix, XΩRepresents the observed noise-free missing matrix, and BΩ＝XΩ+ E, E is additive random noise, rank (·) represents the rank of the matrix;
s12, converting the expression in the step S11 into a regular term objective function form:
Figure BDA0002273144940000022
wherein λ is regularized sparsity | X |*Representing a nuclear norm;
s13, introducing a robust norm to the error item of the regular item target function in the step S12 to obtain a matrix decomposition mode based on the information entropy norm:
Figure BDA0002273144940000023
wherein h (-) is an information entropy norm, X represents a seismic data matrix, argmin (-) represents an independent variable value when a function value is minimum, gamma represents a regular term parameter, and sigma (X) represents a singular value.
Further, step S13 is to introduce a robust norm to the error term of the regular term objective function in step S12, specifically to introduce an information entropy function
Figure BDA0002273144940000024
Instead of the nuclear norm:
Figure BDA0002273144940000025
wherein h (·) is an information entropy norm, xiRepresenting the i-th element, | x |)1Representing the L1 norm.
Further, step S3 is specifically:
s31, expressing the matrix decomposition mode based on the information entropy norm obtained in the step S13 as follows:
Figure BDA0002273144940000031
s.tX＝M
s32, solving X, M, Y by adopting an ADMM algorithm;
s33, obtaining a robust estimate of the low rank matrix according to X, M, Y of step S32.
Further, the step S32 of solving for X includes the following substeps:
a1, knowing M and Y, when solving for X, the objective function is:
Figure BDA0002273144940000032
a2, solving the objective function in the step A1 by utilizing a maximum likelihood criterion to obtain an analytic solution:
Figure BDA0002273144940000033
further, the step S32 of solving M includes the following sub-steps:
b1, knowing X and Y, when solving for M, the objective function is:
Figure BDA0002273144940000036
b2, solving the objective function in the step B1 by utilizing a maximum likelihood criterion to obtain an analytic solution:
Figure BDA0002273144940000034
wherein w represents a weight, U, Σ, and V are SVD decompositions of the following data:
Figure BDA0002273144940000035
further, step S32 solves for Y, the expression is: y + μ (X-M), μ denotes a regularization term parameter.
Further, the update expression of μ is: μ ═ ρ μ.
The invention has the beneficial effects that: according to the method, a target function based on an information entropy norm replaces a nuclear norm adopted by an original SVD, then the information entropy norm regularizes a rank minimization term of the target function, and finally an iterative ADMM estimation method is used for approximately solving to obtain a low-rank matrix, so that the steady recovery of a missing image is obtained; the method adopts the information entropy function to replace the L1 norm, not only can measure the sparse value, but also can use the information entropy to count the content of the singular value, and is more in line with the essence of sparse measurement or sparsity measurement; the method combines the excellent performance of the information entropy norm, has more stable performance than the traditional rank reduction method, obviously improves the actual seismic image recovery effect, and accords with the theoretical assumption.
Drawings
Fig. 1 is a schematic diagram of low rank matrix completion according to an embodiment of the present invention;
wherein, fig. 1(a) is missing seismic data, fig. 1(b) is a low rank matrix, and fig. 1(c) is noise;
FIG. 2 is a flow chart of an embodiment of the present invention;
FIG. 3 is an exploded view of an SVD according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of seismic data recovery provided by an embodiment of the present invention;
wherein, fig. 4(a) is an original seismic data slice, fig. 4(b) is a missing seismic data slice, and fig. 4(c) is a recovered seismic data slice;
FIG. 5 is a diagram illustrating an information entropy function provided by an embodiment of the present invention;
fig. 6 is a schematic diagram of a kernel norm (abbreviated as information entropy norm) based on an information entropy function according to an embodiment of the present invention;
wherein fig. 6(a) is low entropy, fig. 6(b) is high entropy, fig. 6(c) is sparse signal, and fig. 6(d) is dense signal;
FIG. 7 is a first original post-stack seismic slice provided by an embodiment of the present invention;
FIG. 8 is a first missing post-stack seismic section provided by an embodiment of the present invention;
FIG. 9 is a recovered post-stack seismic slice one provided by embodiments of the present invention;
FIG. 10 is a second original post-stack seismic section provided by an embodiment of the present invention;
FIG. 11 is a second missing post-stack seismic section provided by embodiments of the present invention;
FIG. 12 is a second recovered post-stack seismic slice provided by an embodiment of the present invention.
Detailed Description
To facilitate understanding of the present invention by those skilled in the art, the following techniques will now be explained:
matrix completion
In 2006, Donoho proposed a well-known compressive sensing Theory in "DONOHO D L.compressive sensing [ J ] Information Theory, IEEE Transactions on, 200652 (4): 1289-. The core idea of the compressed sensing theory is as follows: and accurately recovering the original high-dimensional sparse signal by using a small amount of sampling data, namely realizing the perception of the high-dimensional sparse signal. But suffer from a number of practical problems such as: text analysis, image restoration, recommendation systems and the like, data needing to be restored are often presented in a matrix. Naturally, the research object of compressed sensing extends from the research of vectors to the research of matrixes, and the low rank of the matrixes can be used for describing the sparse characteristic of singular values of the matrixes. The so-called low-rank Completion (MC) technique refers to recovering the original complete Matrix by sampling some elements in the Matrix, as shown in fig. 1, where fig. 1(a) is missing seismic data, fig. 1(b) is a low-rank Matrix, and fig. 1(c) is noise, and the standard form is as follows:
Figure BDA0002273144940000051
wherein M is an observation matrix, X is a low rank matrix,
Figure BDA0002273144940000055
[m]1,2, …, m is a set of sample matrix indices, PΩ(. represents an orthogonal projection operator, MijRepresents the sampling elements, namely:
Figure BDA0002273144940000052
the rank function rank () of the matrix is inherently non-smooth and non-convex, so the matrix completion problem is an NP-hard problem. As the size of the matrix to be solved increases, the time complexity for solving the problem is exponentially multiplied. And the kernel function of the matrix is used for replacing the rank function of the matrix, so that the low rank of the matrix is well characterized. The definition of the matrix kernel is as follows:
Figure BDA0002273144940000053
σiis the ith singular value arranged from large to small. As can be seen from equation (3), the kernel function of the matrix is actually equal to the sum of the singular values of the matrix. The L1 norm of the matrix singular value vector is used for replacing the L0 norm of the matrix singular value vector, namely, the matrix kernel function is used for replacing the L0 norm of the matrix singular value vectorThe nature of matrix ranks, Recht et al in the article "Recht B.A Simpler Aproach to matrix Assembly [ J]Journal of Machine Learning Research,2011,12(Dec): 3413-:
Figure BDA0002273144940000054
the problem is actually a convex optimization model, also called the Lasso model of the matrix.
As shown in fig. 2, which is a flowchart of the solution of the present invention, the seismic image completion method based on the information entropy norm of the present invention includes the following steps:
s1, replacing the traditional kernel norm adopted by the existing seismic image completion model truncation SVD with the kernel norm based on the information entropy norm to obtain an objective function based on the information entropy norm;
after SVD decomposition, the clean seismic data are found to be: most of the energy of the seismic signals is concentrated on a few eigenvalues, and most of the energy is concentrated on the first 4 eigenvalues, which is called the low rank characteristic of the seismic data. Further generalizing, the energy of the effective seismic data is distributed on a part of low-rank components, and the noise is distributed on components except the low-rank components. Therefore, seismic data can be completed by using the truncated SVD method shown in fig. 3, specifically, as shown in fig. 4, fig. 4(a) is an original seismic data slice, fig. 4(b) is a missing seismic data slice, and fig. 4(c) is a recovered seismic data slice.
More specifically, the seismic image completion model for seismic data matrix X may be expressed as follows:
Figure BDA0002273144940000061
wherein R represents the rank of the seismic data, | | · |. non-calculationFIs the Frobenius norm,
Figure BDA0002273144940000062
is a matrix
Figure BDA0002273144940000063
i is 1,2, …, m, j is 1,2, …, n. The optimization problem in equation (1) is essentially a convex optimization based on the Frobenius norm. Wherein in the presence of noise, BΩAnd XΩThe following conditions are satisfied:
BΩ＝XΩ+E
where E is additive random noise.
Converting equation (5) into a canonical term objective function form:
Figure BDA0002273144940000064
where λ is regularized sparsity. The robust norm is introduced into an error term to improve the sparse representation capability of singular value vectors, and then the formula (6) is converted into a matrix decomposition mode based on the information entropy norm:
Figure BDA0002273144940000065
wherein h (·) is an information entropy norm, which is specifically defined as formula (8) below. The information entropy norm is also a convex function as shown in fig. 5, so the introduction of the information entropy norm does not change the properties of the objective function (7), which is still a convex function.
S2, regularizing a rank minimization term of the target function by adopting an information entropy norm;
since the sparse eigenvalue statistics related to the kernel norm of the SVD in the prior art mainly adopts the L1 norm, and the actual statistical characteristics of the eigenvalue cannot be obtained, the distribution of the eigenvalue is counted by using the information entropy norm instead of the L1 norm, so that the method has better performance, as shown in fig. 6. The information entropy norm can be better approximated by low rank than the ordinary rank minimization method, and is stable to outliers. The information entropy norm of the matrix is a kernel norm optimization model described by formula (7), and the kernel norm optimization model is expanded to the information entropy norm:
the invention imports an information entropy function
Figure BDA0002273144940000066
Instead of the nuclear norm:
Figure BDA0002273144940000067
wherein,
Figure BDA0002273144940000071
xiindicating that the ith element is taken. 0log 0-0 and h (0) -0 since we need to iteratively solve the objective function of equation (3), it is necessary to make equation (8) continuously derivable to solve equation (7). Therefore, we need to first derive equation (8), and the derivative of the information entropy function is:
Figure BDA0002273144940000072
and S3, carrying out iterative solution on the target function which is normalized in the step S2 and is based on the information entropy norm, thereby obtaining the robust estimation of the low-rank matrix.
The core of the invention is to design a method based on the combination of a Huber function and a schattern p-norm to synchronously suppress random and regular noises, and simultaneously, the design of a robust inverse problem solving algorithm is also very important. To solve the problem of equation (7), the present invention chooses to use a new Alternating Direction Method of Multipliers (ADMM, alternative Direction multiplier Method). For ADMM solution convenience, equation (7) is expressed as:
Figure BDA0002273144940000073
s.tX＝M
according to the ADMM algorithm, equation (10) can be decomposed into the following several sub-problem solutions. Lagrange augmentation is performed on the formula (10) to obtain the following formula:
Figure BDA0002273144940000074
1) knowing M and Y, solving for X: in this case, we have the objective function:
Figure BDA0002273144940000075
using the maximum likelihood criterion to solve equation (12), we can get the following analytical solution
Figure BDA0002273144940000076
Wherein,
Figure BDA0002273144940000077
represents XΩThe (k + 1) th iteration result.
Knowing X and Y, solving for M: in this case, the objective function (6) becomes as follows
Figure BDA0002273144940000079
Solving the maximum likelihood solution for equation (14) as well, the following analytical solution can be obtained:
Figure BDA0002273144940000078
wherein, U, Σ, and V are SVD decompositions of the following data, and the specific formula thereof is as follows:
Figure BDA0002273144940000081
in addition, the weight w is determined by formula (4), which is specifically defined as follows:
Figure BDA0002273144940000082
3) knowing M and X, solving for Y:
Y＝Y+μ(X-M) (17)
the iterative equations (13), (15) and (17) belong to the convergence up to the end, which convergence is guaranteed by the ADMM framework.
As shown in fig. 7 and 10 for real seismic data without deletion, fig. 8 and 11 for seismic data after deletion, and fig. 9 and 12 for seismic data after final recovery using the method of the present invention, it can be seen from fig. 9 and 12 that the missing data is effectively recovered, and the recovered data and the missing data are very consistent, and the noise is further attenuated.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Various modifications and alterations to this invention will become apparent to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims (6)

1. A seismic image completion method based on an information entropy norm is characterized by comprising the following steps:
s1, replacing the traditional kernel norm adopted by the existing seismic image completion model truncation SVD with the kernel norm based on the information entropy norm to obtain an objective function based on the information entropy norm; step S1 specifically includes the following substeps:
s11, the seismic image completion model expression of the seismic data matrix X is as follows:
Figure FDA0003562369620000011
wherein R representsRank of seismic data, | · | | sweet windFIs Frobenius norm, BΩRepresenting the actual miss matrix, XΩRepresents the observed noise-free missing matrix, and BΩ＝XΩ+ E, E is additive random noise, rank (·) represents the rank of the matrix;
s12, converting the expression in the step S11 into a regular term objective function form:
Figure FDA0003562369620000012
wherein λ is regularized sparsity | X |*Representing the traditional nuclear norm adopted by the truncation SVD of the existing seismic image completion model;
s13, introducing a robust norm to the error item of the regular item target function in the step S12 to obtain a matrix decomposition mode based on the information entropy norm:
Figure FDA0003562369620000013
wherein h (-) is an information entropy norm, X represents a seismic data matrix, argmin (-) represents an independent variable value when a function value is minimum, gamma represents a regular term parameter, and sigma (X) represents a singular value;
step S13, introducing a robust norm to the error term of the regular term objective function in step S12, specifically importing an information entropy function h:
Figure FDA0003562369620000014
instead of the nuclear norm:
Figure FDA0003562369620000015
wherein h (·) is an information entropy norm, xiRepresenting the i-th element, | x |)1Represents the L1 norm;
s2, regularizing a rank minimization term of the target function by adopting an information entropy norm;
and S3, carrying out iterative solution on the target function which is normalized in the step S2 and is based on the information entropy norm, thereby obtaining the robust estimation of the low-rank matrix.
2. The seismic image completion method based on the information entropy norm as claimed in claim 1, wherein step S3 specifically includes:
s31, expressing the matrix decomposition mode based on the information entropy norm obtained in the step S13 as follows:
Figure FDA0003562369620000021
s.t X＝M
where M is an observation matrix, PΩ(. h) represents an orthogonal projection operator;
s32, solving X, M, Y by adopting an ADMM algorithm;
s33, obtaining a robust estimate of the low rank matrix according to X, M, Y of step S32.
3. The seismic image completion method based on the information entropy norm as claimed in claim 2, wherein the step S32 of solving X comprises the following substeps:
a1, knowing M and Y, when solving for X, the objective function is:
Figure FDA0003562369620000022
a2, solving the objective function in the step A1 by utilizing a maximum likelihood criterion to obtain an analytic solution:
Figure FDA0003562369620000023
4. the seismic image completion method based on the information entropy norm as claimed in claim 2, wherein the step S32 of solving M comprises the following substeps:
b1, knowing X and Y, when solving for M, the objective function is:
Figure FDA0003562369620000024
b2, solving the objective function in the step B1 by utilizing a maximum likelihood criterion to obtain an analytic solution:
Figure FDA0003562369620000025
wherein w represents a weight, U, Σ, and V are SVD decompositions of the following data:
Figure FDA0003562369620000026
5. the seismic image completion method based on the information entropy norm as claimed in claim 2, wherein step S32 solves for Y, and the expression is: y + μ (X-M), μ denotes a regularization term parameter.
6. The seismic image completion method based on the information entropy norm as claimed in claim 5, wherein the updating expression of μ is as follows: μ ═ ρ μ.
CN201911112524.9A 2019-11-14 2019-11-14 Seismic image completion method based on information entropy norm Active CN110838096B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201911112524.9A CN110838096B (en) 2019-11-14 2019-11-14 Seismic image completion method based on information entropy norm

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201911112524.9A CN110838096B (en) 2019-11-14 2019-11-14 Seismic image completion method based on information entropy norm

Publications (2)

Publication Number Publication Date
CN110838096A CN110838096A (en) 2020-02-25
CN110838096B true CN110838096B (en) 2022-05-10

Family

ID=69574985

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201911112524.9A Active CN110838096B (en) 2019-11-14 2019-11-14 Seismic image completion method based on information entropy norm

Country Status (1)

Country Link
CN (1) CN110838096B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111830560B (en) * 2020-07-24 2022-06-28 河北工业大学 Seismic data reconstruction method based on rank reduction algorithm

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108537738A (en) * 2018-02-02 2018-09-14 厦门大学 A kind of matrix complementing method
CN108828670A (en) * 2018-08-20 2018-11-16 成都理工大学 A kind of seismic data noise-reduction method
CN109671030A (en) * 2018-12-10 2019-04-23 西安交通大学 A kind of image completion method based on the optimization of adaptive rand estination Riemann manifold
CN109886884A (en) * 2019-01-21 2019-06-14 长沙理工大学 A kind of vision data complementing method based on the low-rank tensor estimation for limiting nuclear norm
CN110045321A (en) * 2019-04-12 2019-07-23 大连大学 The steady DOA estimation method restored based on sparse and low-rank

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8935308B2 (en) * 2012-01-20 2015-01-13 Mitsubishi Electric Research Laboratories, Inc. Method for recovering low-rank matrices and subspaces from data in high-dimensional matrices

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108537738A (en) * 2018-02-02 2018-09-14 厦门大学 A kind of matrix complementing method
CN108828670A (en) * 2018-08-20 2018-11-16 成都理工大学 A kind of seismic data noise-reduction method
CN109671030A (en) * 2018-12-10 2019-04-23 西安交通大学 A kind of image completion method based on the optimization of adaptive rand estination Riemann manifold
CN109886884A (en) * 2019-01-21 2019-06-14 长沙理工大学 A kind of vision data complementing method based on the low-rank tensor estimation for limiting nuclear norm
CN110045321A (en) * 2019-04-12 2019-07-23 大连大学 The steady DOA estimation method restored based on sparse and low-rank

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
Compressive sensing and entropy in seismic signals;Eberton S.Marinho 等;《Physica A: Statistical Mechanics and its Applications》;20170930;全文 *
L1 - 2 minimization for exact and stable seismic attenuation compensation;Yufeng Wang 等;《Geophysical Journal International》;20180430;全文 *
基于文本信息的归纳矩阵补全算法研究及应用;耿静静;《中国优秀博硕士学位论文全文数据库(硕士)信息科技辑》;20190215;全文 *

Also Published As

Publication number Publication date
CN110838096A (en) 2020-02-25

Similar Documents

Publication Publication Date Title
CN107728211B (en) Seismic signal recovery algorithm based on tensor nuclear norm regularization
CN110568486B (en) Seismic signal completion method based on synchronous sparse low-rank tensor completion model
Zhu et al. Seismic data denoising through multiscale and sparsity-promoting dictionary learning
Jia et al. Intelligent interpolation by Monte Carlo machine learning
Oropeza et al. Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis
Beckouche et al. Simultaneous dictionary learning and denoising for seismic data
Yang et al. Deep learning seismic random noise attenuation via improved residual convolutional neural network
CN110361778B (en) Seismic data reconstruction method based on generation countermeasure network
Yang et al. Curvelet-based POCS interpolation of nonuniformly sampled seismic records
Gao et al. Five-dimensional seismic reconstruction using parallel square matrix factorization
Jafarpour et al. Compressed history matching: exploiting transform-domain sparsity for regularization of nonlinear dynamic data integration problems
Jafarpour et al. Transform-domain sparsity regularization for inverse problems in geosciences
Liu et al. Sparse graph-regularized dictionary learning for suppressing random seismic noise
Sternfels et al. Multidimensional simultaneous random plus erratic noise attenuation and interpolation for seismic data by joint low-rank and sparse inversion
Dong et al. Multiscale spatial attention network for seismic data denoising
CN105931264B (en) A kind of sea infrared small target detection method
Zhu et al. Sparse-promoting full-waveform inversion based on online orthonormal dictionary learning
CN114418886B (en) Robust denoising method based on depth convolution self-encoder
Yang et al. Seislet-based morphological component analysis using scale-dependent exponential shrinkage
CN111046737A (en) Efficient intelligent sensing acquisition method for microseism signal detection
CN108828658A (en) A kind of ocean bottom seismic data reconstructing method
CN110838096B (en) Seismic image completion method based on information entropy norm
Wang et al. Data-driven pre-stack AVO inversion method based on fast orthogonal dictionary
Wang et al. Denoising with weak signal preservation by group-sparsity transform learning
Gao et al. Deep learning vertical resolution enhancement considering features of seismic data

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant