CN111399041A - Small-compact-frame self-adaptive sparse three-dimensional seismic data reconstruction method - Google Patents
Small-compact-frame self-adaptive sparse three-dimensional seismic data reconstruction method Download PDFInfo
- Publication number
- CN111399041A CN111399041A CN202010165607.0A CN202010165607A CN111399041A CN 111399041 A CN111399041 A CN 111399041A CN 202010165607 A CN202010165607 A CN 202010165607A CN 111399041 A CN111399041 A CN 111399041A
- Authority
- CN
- China
- Prior art keywords
- seismic data
- sparse
- dictionary
- small
- frame
- 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.)
- Pending
Links
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
Abstract
The invention discloses a small compact frame self-adaptive sparse three-dimensional seismic data reconstruction method, which is applied to the field of seismic data processing and aims at the problems of the limitation of the traditional fixed-base sparse transform and the insufficient stability of the existing self-adaptive sparse transform method; according to the method, the stability of dictionary learning is improved by utilizing the small wave tight frame, the optimal sparse representation of data is obtained by a stable dictionary learning method, the perfect reconstruction characteristic of the small wave tight frame is utilized, the reconstruction of three-dimensional seismic data with a complex structure is realized, and the noise reduction effect is good; the seismic data reconstructed by the method of the invention improves the reliability of the underground information acquired by three-dimensional seismic exploration, provides more accurate underground information for the next production work, and achieves the purposes of improving the production quality and reducing the economic cost.
Description
Technical Field
The invention belongs to the field of seismic data processing, and particularly relates to a seismic data reconstruction technology.
Background
Three-dimensional seismic exploration is a main technical method for oil and gas exploration, and the method mainly comprises the following three steps: and collecting, processing and explaining the seismic data. Seismic exploration aims to obtain reliable subsurface information, but requires high-precision seismic data as support. In the actual seismic data acquisition process, due to the influences of factors such as wind blowing, grass movement, transportation and the like, the acquired data generally contain noise and are limited by factors such as economic cost control, terrain and surface obstacles and the like, and the acquired data may have the defects of seismic channels. Such data will have a serious impact on subsequent processing and interpretation, and therefore reconstructing high-precision three-dimensional seismic data is a significant problem.
Seismic data reconstruction methods have numerous categories, which are mainly classified into five categories: predictive filtering, wave equation, coherent dip interpolation, matrix rank reduction, and mathematical transformation. The mathematical transformation method is a sparse transformation method based on the compressive sensing theory, and is a mainstream data reconstruction method at present. Such as fourier transform, Radon transform, wavelet transform, curvelet transform, etc.
The traditional sparse transformation data reconstruction methods are all used for carrying out certain specific transformation on original data, then obtaining corresponding sparse representation coefficients, and then carrying out threshold processing on the coefficients, thereby achieving the purpose of reconstructing data. In the traditional method, the basis functions of sparse transformation are generally fixed and invariable, and different sparse transformations are limited to processing data of a specific structure, so that the methods cannot adapt to seismic data with a complex structure. In order to obtain an adaptive sparse transform basis function, researchers working with signal processing have proposed many adaptive sparse transform methods that estimate basis functions through dictionary learning, which can adaptively derive a model from the data itself, thereby processing data with complex structures. Typical dictionary learning methods are commonly used as follows: MOD, K-SVD, online dictionary learning, G-PCA, group structure dictionary learning, and the like.
The methods do not pay attention to the problem of dictionary freedom degree, and the stability of dictionary learning is poor.
Introduction of the principle of adaptive sparse transformation:
the traditional sparse transformation method is reluctant to use fixed sparse bases to fit seismic data with complex structures, and the self-adaptive sparse transformation method breaks through the limitation and can effectively realize the reconstruction of three-dimensional seismic data with complex structures. The basic principle of this type of method is as follows:
suppose that the seismic data actually acquired in the field is Y ═ a (X + n), where X is clean and complete seismic data, n is random noise, and a is a sampling matrix with missing seismic trace information. Suppose X can be factored by ω under the complete dictionary { D }kApproximate sparse representation, solving the problem objective function of sparse approximate representation of X with respect to D can be expressed as:
when P is 0 or 1, the sparsity of omega is described by L0 norm, namely the number of nonzero elements in omega is minimum, when P is 1, the sparsity of omega is described by L1 norm, namely the sum of absolute values of all elements in constraint omega is minimum, the L0 norm optimization problem and the L1 norm optimization problem can be solved by a greedy algorithm and a convex optimization algorithm respectively.
The core of the adaptive sparse transformation method is the training of the dictionary D, and how to find an optimal domain or a group of bases is the key for determining whether the features of the seismic data can be effectively sparsely represented. Specifically, given a set of data block sets X ═ X1,x2,…xJ]Where J is the number of training blocks, usually a larger number. The goal of dictionary learning is to jointly optimize dictionary D and raritySparse representation coefficient Λ ═ ω1,ω2,…ωJ]So that x isk＝DωkAnd | ω |k||PL is less than or equal to, wherein P is 0 or 1, L is a constraint parameter of sparsity of the parameter, and the smaller the parameter is, the stronger the sparsity representation capability of a sparse coefficient is, therefore, the objective function of the optimization problem of jointly solving D and Λ is as follows:
obviously, the optimization problem needs to obtain a sparse representation with better data, the key point is the design of a dictionary learning method, and the process mainly comprises the construction of a dictionary and the updating training of the dictionary, which is also the key research content of the adaptive sparse transformation method.
Sparse transformation is a key step in a data reconstruction method, and a reconstruction algorithm is also an indispensable important link in the data reconstruction process. The basic idea of a general reconstruction algorithm is a threshold strategy, that is, a threshold process is performed on a sparse representation coefficient of data, and finally, inverse sparse transformation is performed to obtain reconstructed data, such as an Iterative Shrinkage Threshold (IST) algorithm, a convex set Projection (POCS) algorithm, and the like.
Disclosure of Invention
In order to solve the technical problems, the invention provides a small wave tight frame self-adaptive sparse three-dimensional seismic data reconstruction method, which further controls the degree of freedom of a dictionary, improves the stability of the method, and can obtain the optimal sparse representation of data by dictionary learning by utilizing the advantages of the perfect reconstruction characteristic of the small wave tight frame; and then carrying out threshold processing on the sparse representation coefficient by using an iterative shrinkage threshold method, thereby realizing the reconstruction of high-precision three-dimensional seismic data.
The technical scheme adopted by the invention is as follows: a method for reconstructing small-tight-frame adaptive sparse three-dimensional seismic data, as shown in fig. 1, includes:
s1, inputting data, wherein the input data are noisy and undersampled seismic data;
s2, initializing a dictionary by adopting a small compact frame;
s3, dividing the input data into blocks to generate training samples;
s4, training the initialized dictionary in the step S2 according to the training samples;
and S5, reconstructing the seismic data by adopting a sparse promotion method according to the dictionary trained in the step S4.
The step S2 specifically includes: the expression of the self-adaptive sparse transform objective function based on the wavelet tight frame is as follows:
where v is the sparse coefficient vector, DTIs a dictionary, D is DTG is a data vector, λ is a lagrange constant,
represents L2 norm square, |0Expressing L0 norm, I is an identity matrix, and lambda is used for balancing reconstruction error
And sparsity | | v | | non conducting phosphor0The weight parameter of (2).
Step S4 specifically includes: performing iterative solution on a self-adaptive sparse transformation target function based on a small wave tight frame to obtain a trained dictionary; specifically, the method comprises iteration in a sparse coding stage and iteration in a dictionary updating stage;
iteration of the sparse coding phase: fixed DTAnd solving the sparse coefficient v by a classical sparse approximation problem:
: is defined as;
iteration of the dictionary update phase: fix v and solve the following problem:
the above-mentioned
The solution is performed by a hard threshold method.
The above-mentioned
The solving process of (2) is as follows: firstly, deriving an explicit solution of the method based on principal component analysis theory:
(DT)(k+1)＝XUT
obtained by SVD decomposition method:
VGT＝USXT
wherein V ═ V1,v2,…,vN]G is in DTMatrix of combined down-conversion coefficients, G ═ G1,g2,…gN]Is a matrix formed by combining samples in a vector form.
The invention has the beneficial effects that: the invention provides a self-adaptive sparse transform three-dimensional seismic data reconstruction method based on a small wave tight frame theory, which improves the stability of dictionary learning by utilizing the small wave tight frame, obtains the optimal sparse representation of data by a stable dictionary learning method, realizes the reconstruction of three-dimensional seismic data with a complex structure and has good noise reduction effect by utilizing the perfect reconstruction characteristic of the small wave tight frame. By comparing the local detail features, it can be found that the fine features of the data themselves are well preserved. On one hand, the method breaks through the limitation of the traditional fixed base sparse transformation, and more importantly, the method solves the problem of insufficient stability of other self-adaptive sparse transformation methods. The seismic data reconstructed by the method improves the reliability of the underground information acquired by three-dimensional seismic exploration, provides more accurate underground information for the next production work, and achieves the purposes of improving the production quality and reducing the economic cost.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a diagram illustrating dictionary training performed by the method of the present invention according to an embodiment of the present invention;
wherein fig. 2(a) represents an initial dictionary, and fig. 2(b) represents a training dictionary;
FIG. 3 is raw actual three-dimensional seismic data provided by an embodiment of the invention;
FIG. 4 is a representation of actual three-dimensional seismic data including noisy and missing seismic traces according to an embodiment of the present invention;
FIG. 5 is a representation of reconstructed three-dimensional seismic data provided by an embodiment of the present invention;
FIG. 6 is a representation of local features of original actual three-dimensional seismic data and local features of reconstructed three-dimensional seismic data as provided by an embodiment of the present invention;
fig. 6(a) is a local feature i of the original actual three-dimensional seismic data, fig. 6(b) is a local feature i of the reconstructed three-dimensional seismic data, fig. 6(c) is a local feature ii of the original actual three-dimensional seismic data, and fig. 6(d) is a local feature ii of the reconstructed three-dimensional seismic data.
Detailed Description
In order to facilitate the understanding of the technical contents of the present invention by those skilled in the art, the present invention will be further explained with reference to fig. 1 to 6.
The three-dimensional seismic exploration aims to acquire underground structure information and provide effective construction dependence for production activities such as resource acquisition and engineering construction. However, in the actual exploration process, the acquired field seismic data cannot meet the exploration requirement, reliable and accurate underground structure information cannot be acquired from the field seismic data, and the reconstruction of the acquired incomplete field seismic data becomes a necessary link in the seismic data processing process.
Aiming at the problem, the invention designs a self-adaptive sparse transform three-dimensional seismic data reconstruction method based on a small wave tight frame theory. And finally, reconstructing the three-dimensional seismic data by combining an IST algorithm, and retaining fine features of the data. The method strives to obtain more reliable three-dimensional seismic data, provides more effective information for actual production work, improves production quality and saves production cost.
The realization process of the invention is as follows:
1 adaptive sparse transform method design
Definition 1: let { f }i}i∈N∈ H, wherein { fi}i∈NIs a sequence, denoted by N, a set of natural numbers or some subset of a set of natural numbers, h is Hilbert (Hilbert) space, if there are two normal numbers a, B, and a ≦ B such that the following holds:
then call { fi}i∈NIs a frame in Η. Wherein A and B represent the upper and lower boundaries of the frame. When a is B, the frame { f ═ Bi}i∈NReferred to as a tight frame. When each fiAre all divided by
Then a equals B equals 1, when frame f equals 1i}i∈NReferred to as normal tight frame, i.e.
Two operators are defined on a tight framework:
a. a synthesis operator D:
b. analysis operator DT：
Wherein D is a dictionary DTα, for reconstructing the processed sparse coefficients into seismic dataiDenotes the ith column vector in D, { αiBelong to
A space.
The original data can be transformed into coefficients by an analysis operator, and the processed coefficients can be reconstructed into data by a synthesis operator.
Definition 2: the wavelet tight framework is a product of combining wavelet theory and framework theory, and is a general transformation of orthogonal wavelet basis, namely, redundancy is introduced into a wavelet system. From finite mother wavelets
The sets are obtained by translating and magnifying
Wavelet framework in space:
wherein the content of the first and second substances,
a set of real numbers is represented as,
is that
One of the upper Hilbert spaces, t being represented in
Integers in space that construct the wavelet framework.
When X (Ψ) is a tight frame, it is referred to as a small tight frame. The invention uses a small compact frame to initialize the dictionary and limits the dictionary.
The adaptive sparse transform objective function based on the wavelet tight framework is as follows:
where v is the coefficient vector, DTIs a filter bank (dictionary) matrix, g is a data vector, and λ is a Lagrangian constant for balancing reconstruction errors
And sparsity | | v | | non conducting phosphor0I is an identity matrix.
The objective function (9) can be solved by an iterative method comprising two stages, thereby obtaining an optimal sparse representation of the trained dictionary and data:
first stage (sparse coding stage): fixed DTAnd solving the sparse coefficient v by a classical sparse approximation problem:
this optimization problem can be solved by a hard threshold method, specifically referring to: cai J F, Ji H, ShenZ, et al. data-drive light Frame Construction and Image rendering [ J ]. applied and comparative Harmonic Analysis,2014,37(1): 89-105.
Second stage (dictionary update stage): fix v and solve the following problems:
an explicit solution to the above problem can be derived based on Sparse Principal Component Analysis (SPCA) theory:
(DT)(k+1)＝XUT(12)
x and U can be obtained by SVD decomposition method:
VGT＝USXT(13)
wherein V is [ V ═ V1,v2,…,vN]G is in DTMatrix of combined down-conversion coefficients, G ═ G1,g2,…gN]Is a matrix formed by combining samples in a vector form.
Fig. 2 shows an example of an initial dictionary and a training dictionary in a three-dimensional seismic data reconstruction application according to the present invention, where fig. 2(a) corresponds to the initial dictionary, and a significant structural feature can be seen from the training dictionary shown in fig. 2(b), so that the trained dictionary can more sparsely represent original data.
2 data reconstruction method
Obtaining a trained dictionary D from the two-stage iteration of step 1TAnd reconstructing the seismic data by adopting a sparse promotion method. The following objective function is now optimized:
wherein g is the reconstructed data, g is the original data, g0To sample data, A is a sampling matrix.
For this reconstruction problem, an Iterative Shrinkage Threshold (IST) algorithm can be used to solve:
Dλ(g)＝DTλ(DTg) (15)
{Tλ(v)}i＝Tλ(vi),Tλ(vi)＝max(|vi|-λ,0) (16)
wherein, TλFor the soft threshold operator, the index i denotes the ith element of the coefficient vector v, and λ is the threshold parameter.
g′＝Dλ(g(k)),g(k+1)＝αkAT(g0-Ag′)+g′ (17)
Wherein the parameter αkStability of control algorithm, α in an iterative processkFrom 1 to 0.
The specific algorithm implementation flow is as follows:
data input: noisy and undersampled seismic data
(1) An initial dictionary:
initializing a dictionary with a small tight-framed
r×r × r is the dictionary size.
(2) Generating a sample:
blocking input data to generate training samples g1,g2,…gi}；i＝1,…r3。
(3) Training a dictionary:
for k＝0,1,…,K-1do
a. definition of
b. Let v(k)＝Tλ[(DT)(k)g]，TλA hard threshold operator;
c. constructing a matrix V, G;
d. for VGTSVD decomposition is carried out to obtain VGT＝USXT；
e. Order (D)T)(k+1)＝XUT。
(4) And (3) reconstruction:
a. data is divided into blocks;
b. sparse representation;
c. coefficient processing: an iterative shrinkage threshold algorithm;
d. and (4) block polymerization.
And (3) data output: reconstructed seismic data
As shown in FIGS. 2-4, the optimal sparse representation of the data is obtained by adopting the stable dictionary learning method, and the three-dimensional seismic data reconstruction with a complex structure is realized and the noise reduction effect is good by utilizing the perfect reconstruction characteristic of the small compact frame.
FIG. 3 shows the original actual three-dimensional seismic data, wherein two local features are labeled, namely a first local feature A and a second local feature B shown in FIG. 3; fig. 5 shows two local features corresponding to the two positions shown in fig. 3 in the reconstructed three-dimensional seismic data, namely, a first local feature C and a second local feature D shown in fig. 5; from the local detail features before and after the comparative reconstruction of fig. 6, it can be found that the fine features of the data itself are better preserved by the method of the present invention.
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 (9)
1. A small wave tight frame self-adaptive sparse three-dimensional seismic data reconstruction method is characterized in that a small wave tight frame initialization dictionary is adopted for training, and seismic data reconstruction is carried out according to the trained dictionary.
2. The small-compact-frame self-adaptive sparse three-dimensional seismic data reconstruction method according to claim 1, wherein a dictionary initialized by a small compact frame is adopted for training, and the method specifically comprises the following steps:
a1, inputting data, wherein the input data are noisy and undersampled seismic data;
a2, initializing a dictionary by adopting a small compact frame;
a3, dividing the input data into blocks to generate training samples;
and A4, training the initialized dictionary in the step A2 according to the training samples.
3. The small-compact-frame adaptive sparse three-dimensional seismic data reconstruction method according to claim 2, wherein the step a2 specifically comprises: the expression of the self-adaptive sparse transform objective function based on the wavelet tight frame is as follows:
where v is the sparse coefficient vector, DTIs a dictionary, D is DTG is the data vector and λ is LagrangeThe constant number is a constant number,
represents L2 norm square, |0Representing a L0 norm, I being the identity matrix.
4. The small-compact-frame adaptive sparse three-dimensional seismic data reconstruction method according to claim 3, wherein the step S4 specifically comprises: performing iterative solution on a self-adaptive sparse transformation target function based on a small wave tight frame to obtain a trained dictionary; the method specifically comprises iteration in a sparse coding stage and iteration in a dictionary updating stage.
5. The small-tight-frame adaptive sparse three-dimensional seismic data reconstruction method according to claim 4, wherein the iteration of the sparse coding stage specifically comprises:
fixed DTAnd solving the sparse coefficient v by a classical sparse approximation problem:
6. The small-compact-frame adaptive sparse three-dimensional seismic data reconstruction method according to claim 5, wherein the iteration of the dictionary update stage specifically comprises:
fix v and solve the following problem:
7. the small-tight-frame adaptive sparse three-dimensional seismic data reconstruction method according to claim 6Method characterized in that
The solution is performed by a hard threshold method.
8. The method of claim 7, wherein the method comprises reconstructing the sparse three-dimensional seismic data with the small compact frame adaptive method
The solving process of (2) is as follows: firstly, deriving an explicit solution of the method based on principal component analysis theory:
(DT)(k+1)＝XUT
obtained by SVD decomposition method:
VGT＝USXT
wherein V ═ V1,v2,…,vN]G is in DTMatrix of combined down-conversion coefficients, G ═ G1,g2,…gN]Is a matrix formed by combining samples in a vector form.
9. The small-compact-frame self-adaptive sparse three-dimensional seismic data reconstruction method according to claim 8, wherein seismic data reconstruction is performed according to a trained dictionary, and specifically comprises the following steps: and according to the trained dictionary, reconstructing the seismic data by adopting a sparse promotion method.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010165607.0A CN111399041A (en) | 2020-03-11 | 2020-03-11 | Small-compact-frame self-adaptive sparse three-dimensional seismic data reconstruction method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010165607.0A CN111399041A (en) | 2020-03-11 | 2020-03-11 | Small-compact-frame self-adaptive sparse three-dimensional seismic data reconstruction method |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN111399041A true CN111399041A (en) | 2020-07-10 |
Family
ID=71430654
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010165607.0A Pending CN111399041A (en) | 2020-03-11 | 2020-03-11 | Small-compact-frame self-adaptive sparse three-dimensional seismic data reconstruction method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111399041A (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114076986A (en) * | 2021-05-10 | 2022-02-22 | 中国矿业大学 | Multi-scale dictionary learning sparse denoising method |
| CN114460633A (en) * | 2022-01-19 | 2022-05-10 | 吉林大学 | Seismic denoising and interpolation method based on weighted frame transformation-low-dimensional manifold model |
| CN116522269A (en) * | 2023-06-28 | 2023-08-01 | 厦门炬研电子科技有限公司 | Fault diagnosis method based on Lp norm non-stationary signal sparse reconstruction |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104166161A (en) * | 2014-08-19 | 2014-11-26 | 成都理工大学 | Method and device for predicating fractures based on elliptical velocity inversion of anisotropism |
| US8923093B2 (en) * | 2009-08-25 | 2014-12-30 | Westerngeco L.L.C. | Determining the quality of a seismic inversion |
| CN104391326A (en) * | 2014-11-19 | 2015-03-04 | 中国海洋石油总公司 | Seismic attribute set combination selection method |
| CN107527371A (en) * | 2017-09-07 | 2017-12-29 | 中国科学院光电技术研究所 | One kind approaches smooth L in compressed sensing0The design constructing method of the image reconstruction algorithm of norm |
-
2020
- 2020-03-11 CN CN202010165607.0A patent/CN111399041A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8923093B2 (en) * | 2009-08-25 | 2014-12-30 | Westerngeco L.L.C. | Determining the quality of a seismic inversion |
| CN104166161A (en) * | 2014-08-19 | 2014-11-26 | 成都理工大学 | Method and device for predicating fractures based on elliptical velocity inversion of anisotropism |
| CN104391326A (en) * | 2014-11-19 | 2015-03-04 | 中国海洋石油总公司 | Seismic attribute set combination selection method |
| CN107527371A (en) * | 2017-09-07 | 2017-12-29 | 中国科学院光电技术研究所 | One kind approaches smooth L in compressed sensing0The design constructing method of the image reconstruction algorithm of norm |
Non-Patent Citations (4)
| Title |
|---|
| CAI J F, ET AL: "Data-driven tight frame construction and image denoising", 《APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS》 * |
| 刘文艺: "《风力发电机组振动监测与故障诊断技术》", 31 January 2016 * |
| 王一丁，等: "《数字图像处理》", 31 August 2015 * |
| 陈杰，等: "基于数据驱动紧框架的三维地震数据重建", 《中国地球科学联合学术年会 2019》 * |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114076986A (en) * | 2021-05-10 | 2022-02-22 | 中国矿业大学 | Multi-scale dictionary learning sparse denoising method |
| CN114460633A (en) * | 2022-01-19 | 2022-05-10 | 吉林大学 | Seismic denoising and interpolation method based on weighted frame transformation-low-dimensional manifold model |
| CN116522269A (en) * | 2023-06-28 | 2023-08-01 | 厦门炬研电子科技有限公司 | Fault diagnosis method based on Lp norm non-stationary signal sparse reconstruction |
| CN116522269B (en) * | 2023-06-28 | 2023-09-19 | 厦门炬研电子科技有限公司 | Fault diagnosis method based on Lp norm non-stationary signal sparse reconstruction |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Bioucas-Dias et al. | A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration | |
| CN111399041A (en) | Small-compact-frame self-adaptive sparse three-dimensional seismic data reconstruction method | |
| CN104199627B (en) | Gradable video encoding system based on multiple dimensioned online dictionary learning | |
| CN112150354B (en) | Single image super-resolution method combining contour enhancement and denoising statistical prior | |
| CN112257753B (en) | Image classification method of generalized equal-variation convolution network model based on partial differential operator | |
| CN103279932A (en) | Two-dimensional synthesis sparse model and dictionary training method based on two-dimensional synthesis sparse model | |
| CN112184547B (en) | Super resolution method of infrared image and computer readable storage medium | |
| Qi et al. | Two dimensional synthesis sparse model | |
| Xu et al. | Deep sparse representation based image restoration with denoising prior | |
| CN114545494A (en) | Non-supervision seismic data reconstruction method and device based on sparse constraint | |
| CN116777764A (en) | Diffusion model-based cloud and mist removing method and system for optical remote sensing image | |
| CN113176607A (en) | Sparse self-encoder seismic inversion method and system based on physical law fusion | |
| CN113869503B (en) | Data processing method and storage medium based on depth matrix decomposition completion | |
| CN109840888B (en) | Image super-resolution reconstruction method based on joint constraint | |
| CN114331853B (en) | Single image restoration iteration framework based on target vector updating module | |
| CN111932473B (en) | Multi-resolution sparse coding phase information noise reduction algorithm and storage medium | |
| CN112907456B (en) | Deep neural network image denoising method based on global smooth constraint prior model | |
| CN115131226A (en) | Image restoration method based on wavelet tensor low-rank regularization | |
| CN111352159B (en) | Nuclear norm and generalized total variation joint constraint seismic random noise suppression method | |
| Qiao et al. | Dcs-risr: Dynamic channel splitting for efficient real-world image super-resolution | |
| Jeon et al. | PDE-guided reservoir computing for image denoising with small data | |
| Gashnikov | Context interpolation of multidimensional digital signals in problem of compression | |
| CN112700372B (en) | Seismic data interpolation method combining Gabor feature extraction and support vector regression | |
| Zhang et al. | Salt‐and‐pepper denoising method for colour images based on tensor low‐rank prior and implicit regularization | |
| Zhao et al. | Variable-length image compression based on controllable learning network |
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 | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20200710 |
|
| RJ01 | Rejection of invention patent application after publication |