CN109657692A - Processing Seismic Data and system based on PCA dictionary and rarefaction representation - Google Patents
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Abstract
A kind of Processing Seismic Data based on PCA dictionary and rarefaction representation, comprising: step 1: adaptive PCA dictionary D is established；Step 2: inputting seismic data x to be processed(0), it is based on adaptive PCA dictionary D, obtains first time restored image x(1)；Step 3: with first time restored image x(1)It is iterated processing as seismic data to be processed, obtains final restored image x(k).By using adaptive PCA dictionary, in the main composition for acquiring image set, remaining extra dimension is omitted, achieve the purpose that dimensionality reduction, indirectly handled image is compressed, while the again more information for remaining original image, so as to improve the clarity of restored image.
Description
Technical field
The present invention relates to seismic data processing fields, and in particular to a kind of earthquake money based on PCA dictionary and rarefaction representation
Expect processing method and system.
Background technique
With oil-gas exploration and development gradually deeply, exploration targets is towards mid-deep strata Complex Fault Block Oil Reservoir, lithology concealment
The directions such as oil reservoir and stratigraphic oil pool are developed, and corresponding oil-gas exploration and development difficulty is increasing.Therefore in-depth oil-gas exploration is opened
Hair proposes higher demand to the precision of seismic imaging naturally.Seismic imaging data is to deepen the important money of oil-gas exploration and development
Material, it is most important to meet the needs of oilfield prospecting developing to improve the precision of seismic imaging.The resolution problem of seismic data
It is the key problem that seism processing needs to solve, improving seismic resolution using existing conventional Christmas data is current earthquake
The urgent need of data processing.
The existing method for improving seismic data resolution mainly has deconvolution processing method and inverse Q filtering processing method.Its
In, deconvolution processing method exist it is artificial it is assumed that and when opening up frequency and requiring high, envelope eapsulotomy is poor；Inverse Q filtering processing method needs
Will more accurately equivalent Q-value field, longitudinal attenuation by absorption can only be handled.
Therefore, expect a kind of better Processing Seismic Data of effect to obtain high-resolution seismic data image.
Summary of the invention
The present invention provides a kind of Processing Seismic Data based on PCA dictionary and rarefaction representation, comprising:
Step 1: establishing adaptive PCA dictionary D；
Step 2: inputting seismic data x to be processed(0), it is based on the adaptive PCA dictionary D, obtains first time restored image
x(1)；
Step 3: with first time restored image x(1)It is iterated processing as seismic data to be processed, obtains final answer
Original image x(k)。
Preferably, the step 1 includes:
Step 101: seismic data to be processed is divided by L cluster by K-means method；
Step 102: the matrix of the M image block composition in a cluster being subjected to the processing of data zero averaging, is obtained
Zero-mean result fmIt is expressed as row vector [fm(1),fm(2),...,fm(N)], wherein m=1,2 ..., M, each image
The size of block is n × n, and each image block is stored with column vector, N=n × n；
Step 103: define image block data matrix F:
Wherein, f(n)=[f1(n),f2(n),...,fM(n)]T, n=1,2 ..., N；
Step 104: establish image block covariance matrix C:
Step 105: calculating the orthogonal transform matrix A of image block data matrix F, and according to orthogonal transform matrix A to image
Block carries out orthogonal transformation:
The n-th column of orthogonal transform matrix A are shown below:
Transformed m-th of image block are as follows:
[am(1),am(2),...,am(N)]=uM TF
Wherein, U is the feature vector of covariance matrix C；
Step 106: being directed to each cluster, repeat above step 102-105；
Step 107: the square that the feature vector acquired for the image block covariance matrix C of each cluster calculation is constituted
Battle array carry out transposition processing, obtains adaptive PCA dictionary D.
Preferably, the step 2 includes:
Step 201: inputting seismic data x to be processed(0), by K-means method to seismic data x to be processed(0)It carries out
Cluster, judges seismic data x to be processed respectively(0)In the corresponding classification of each image block；
Step 202: being directed to an image block, operation Da is carried out according to its corresponding classification, wherein a indicates described image
Block；
Step 203: the image block after defining operation is ai 0, searching and a in seismic data to be processedi 0As Local Phase
Image block and global similar image block, pass through formulaAnd formula
Update μi (j)；
Wherein, ai,jIndicate j-th of image block similar with i-th of image block, wi,jIndicate weighting coefficient, SiIt indicates and the
The set of the similar image block composition of i image block, h is regulatory factor, wherein
Step 204: passing throughObtain initial prior modelWhereinFor energy
Function；
Step 205: passing through formulaCalculate initial regularization coefficient
Wherein, λiIndicate regularization coefficient, σnStandard deviation for the Gaussian noise added in degeneration system model, σiFor ai
Standard deviation；
Step 206: passing through formulaCalculate initial regularization coefficient γi (0)
Wherein, γiIndicate regularization coefficient, σnFor the standard deviation of the Gaussian noise of the addition in degeneration system model, δiFor
ξiStandard deviation,
Step 207: (1) calculates a according to the following formulay (1):
Wherein, τ indicates that regularization parameter, j=1,2 ..., k, k are the total degree of iteration, and i=1,2 ..., n, n are institute
The quantity of the image block divided, image block are all stored in a manner of column vector；
Step 208: according to formulaRestored image after obtaining first time iteration
Step 209: being directed to seismic data x to be processed(0)In each image block repeat step 202-208, obtain
Restored image x(1)。
Preferably, the step 3 includes:
Step 301: according to obtained x(j)And ai (j)As a result, in restored image x(j)Middle searching and ai (j)As Local Phase
Image block and global similar image block, pass through formulaAnd formula
Update μi (j)；Wherein, ai,jIndicate j-th of image block similar with i-th of image block, wi,jIndicate weighting coefficient, SiIt indicates and the
The set of the similar image block composition of i image block, h is regulatory factor；
Step 302: by passing throughThe available prior model based on AMRF
Step 303: by input picture x(0)After being clustered using K-means method, the image block in image is judged respectively
Which class belonged to；
Step 304: according to the adaptive PCA dictionary D of step 1, Da operation being carried out to all image blocks；
Step 305: passing through formulaCalculate initial regularization coefficient
Step 306: passing through formulaCalculate initial regularization coefficient γi (j-1)；
Step 307: (1) calculates a according to the following formulay (j):
Step 308: according to formulaIt obtains
Step 309: being directed to seismic data x to be processed(0)In each image block repeat step 301-308, obtain
The restored image x of j iteration(j)；
Step 310: repeating the k step 301-309, obtain final restored image x(k)。
Another aspect of the present invention provides a kind of seismic data processing system based on PCA dictionary and rarefaction representation, comprising:
Memory is stored with computer executable instructions；
Processor, the processor run the computer executable instructions in the memory, execute following steps:
Step 1: establishing adaptive PCA dictionary D；
Step 2: inputting seismic data x to be processed(0), it is based on the adaptive PCA dictionary D, obtains first time restored image
x(1)；
Step 3: with first time restored image x(1)It is iterated processing as seismic data to be processed, obtains final answer
Original image x(k)。
Preferably, the step 1 includes:
Step 101: seismic data to be processed is divided by L cluster by K-means method；
Step 102: the matrix of the M image block composition in a cluster being subjected to the processing of data zero averaging, is obtained
Zero-mean result fmIt is expressed as row vector [fm(1),fm(2),...,fm(N)], wherein m=1,2 ..., M, each image
The size of block is n × n, and each image block is stored with column vector, N=n × n；
Step 103: define image block data matrix F:
Wherein, f(n)=[f1(n),f2(n),...,fM(n)]T, n=1,2 ..., N；
Step 104: establish image block covariance matrix C:
Step 105: calculating the orthogonal transform matrix A of image block data matrix F, and according to orthogonal transform matrix A to image
Block carries out orthogonal transformation:
The n-th column of orthogonal transform matrix A are shown below:
Transformed m-th of image block are as follows:
[am(1),am(2),...,am(N)]=uM TF
Wherein, U is the feature vector of covariance matrix C；
Step 106: being directed to each cluster, repeat above step 102-105；
Step 107: the square that the feature vector acquired for the image block covariance matrix C of each cluster calculation is constituted
Battle array carry out transposition processing, obtains adaptive PCA dictionary D.
Preferably, the step 2 includes:
Step 201: inputting seismic data x to be processed(0), by K-means method to seismic data x to be processed(0)It carries out
Cluster, judges seismic data x to be processed respectively(0)In the corresponding classification of each image block；
Step 202: being directed to an image block, operation Da is carried out according to its corresponding classification, wherein a indicates described image
Block；
Step 203: the image block after defining operation is ai 0, searching and a in seismic data to be processedi 0As Local Phase
Image block and global similar image block, pass through formulaAnd formula
Update μi (j)；
Wherein, ai,jIndicate j-th of image block similar with i-th of image block, wi,jIndicate weighting coefficient, SiIt indicates and the
The set of the similar image block composition of i image block, h is regulatory factor, wherein
Step 204: passing throughObtain initial prior modelWhereinFor energy
Function；
Step 205: passing through formulaCalculate initial regularization coefficient
Wherein, λiIndicate regularization coefficient, σnStandard deviation for the Gaussian noise added in degeneration system model, σiFor ai
Standard deviation；
Step 206: passing through formulaCalculate initial regularization coefficient γi (0)
Wherein, γiIndicate regularization coefficient, σnFor the standard deviation of the Gaussian noise of the addition in degeneration system model, δiFor
ξiStandard deviation,
Step 207: (1) calculates a according to the following formulay (1):
Wherein, τ indicates that regularization parameter, j=1,2 ..., k, k are the total degree of iteration, and i=1,2 ..., n, n are institute
The quantity of the image block divided, image block are all stored in a manner of column vector；
Step 208: according to formulaRestored image after obtaining first time iteration
Step 209: being directed to seismic data x to be processed(0)In each image block repeat step 202-208, obtain
Restored image x(1)。
Preferably, the step 3 includes:
Step 301: according to obtained x(j)And ai (j)As a result, in restored image x(j)Middle searching and ai (j)As Local Phase
Image block and global similar image block, pass through formulaAnd formula
Update μi (j)；Wherein, ai,jIndicate j-th of image block similar with i-th of image block, wi,jIndicate weighting coefficient, SiIt indicates and the
The set of the similar image block composition of i image block, h is regulatory factor；
Step 302: by passing throughThe available prior model based on AMRF
Step 303: by input picture x(0)After being clustered using K-means method, the image block in image is judged respectively
Which class belonged to；
Step 304: according to the adaptive PCA dictionary D of step 1, Da operation being carried out to all image blocks；
Step 305: passing through formulaCalculate initial regularization coefficient
Step 306: passing through formulaCalculate initial regularization coefficient γi (j-1)；
Step 307: (1) calculates a according to the following formulay (j):
Step 308: according to formulaIt obtains
Step 309: being directed to seismic data x to be processed(0)In each image block repeat step 301-308, obtain
The restored image x of j iteration(j)；
Step 310: repeating the k step 301-309, obtain final restored image x(k)。
Compared with prior art, the beneficial effects of the present invention are: by using adaptive PCA dictionary, acquire image
When the main composition of collection, remaining extra dimension is omitted, achievees the purpose that dimensionality reduction, indirectly handled image is pressed
Contracting, while the again more information for remaining original image, so as to improve the clarity of restored image.
Method of the invention has other characteristics and advantages, these characteristics and advantages from the attached drawing being incorporated herein and with
Will be apparent in specific embodiment afterwards, or by the attached drawing and subsequent specific embodiment being incorporated herein into
Row statement, these the drawings and specific embodiments in detail are used together to explain specific principle of the invention.
Detailed description of the invention
Exemplary embodiment of the present is described in more detail in conjunction with the accompanying drawings, of the invention is above-mentioned and other
Purpose, feature and advantage will be apparent.
Fig. 1 shows the seism processing side according to an exemplary embodiment of the present invention based on PCA dictionary and rarefaction representation
The flow chart of method.
Specific embodiment
The present invention will be described in more detail below with reference to accompanying drawings.Although showing the preferred embodiment of the present invention in attached drawing,
However, it is to be appreciated that may be realized in various forms the present invention and should not be limited by the embodiments set forth herein.On the contrary, providing
These embodiments are of the invention more thorough and complete in order to make, and can will fully convey the scope of the invention to ability
The technical staff in domain.
In seismic image collection process, since instrument performance is not perfect, and by image imaging, transmission, storage etc.
The interference of different type noise in treatment process affects seismic image quality so as to cause image resolution ratio decline.Seismic chart
As recovery problem can be expressed as mathematical model:
Y=SHx+ σ
Wherein, x indicates original high-definition picture；S indicates image down sampling matrix；H indicates degenrate function；σ is indicated
Noise；Y indicates low-resolution image.
In the case where ignoring influence of noise, seismic image, which restores problem, to be indicated are as follows:
Y=Sx
Since the image in nature includes many duplicate parts, i.e., the same image block is in same scale and different rulers
Degree can find the same or similar image block, therefore Super-Resolution is carried out based on image block mostly.With this
Based on thought, the invention proposes a kind of Super-Resolution algorithm based on image self-similarity and sparse representation model.
In the method for the invention, using s multistage down-sampled images Y-1, the Y-2 of the low-resolution image Y of input ... Y-s is as instruction
Practice collection, train recovery dictionary D and be expressed as Super-Resolution model in conjunction with sparse representation theory:
X=D α
Wherein, λ is regularization parameter；X is super-resolution image to be estimated.
Fig. 1 shows the seism processing according to an exemplary embodiment of the present invention based on PCA dictionary and rarefaction representation
The flow chart of method comprising following steps:
Step 1: establishing adaptive PCA dictionary D.
In order to establish adaptive PCA dictionary, seismic data to be processed is divided into L by K-means method first and is gathered
Class establishes dictionary for each cluster, obtains L different dictionaries.Specific step is as follows:
Step 101: seismic data to be processed is divided by L cluster by K-means method；
Step 102: the matrix of the M image block composition in a cluster being subjected to the processing of data zero averaging, is obtained
Zero-mean result fmIt is expressed as row vector [fm(1),fm(2),...,fm(N)], wherein m=1,2 ..., M, each image
The size of block is n × n, and each image block is stored with column vector, N=n × n；
Step 103: define image block data matrix F:
Wherein, f(n)=[f1(n),f2(n),...,fM(n)]T, n=1,2 ..., N；
Step 104: establishing image block covariance matrix C
Covariance matrix C is nonnegative definite matrix, and the i-th column of feature vector U are by characteristic value ηiIt obtains；
Step 105: calculating the orthogonal transform matrix A of image block data matrix F, and according to orthogonal transform matrix A to image
Block carries out orthogonal transformation
Assuming that image block data matrix F obtains a new image block data matrix A after orthogonal transformation, order is newly obtained
The row vector of image block data matrix A (i.e. orthogonal transform matrix A) meet orthogonality, it may be assumed that
A=VTF
Wherein, V=(vmn)m×n, A=[am(n)]M×N, new image block data matrix A is indicated with row vector, it may be assumed that
Since the row vector of new image block data matrix A meets orthogonality, then:
Wherein,Then:
According to the uniqueness of matrix solution, then V=U,Wherein m=1,2 ..., M；
Then: A=UTF
Write above formula as vector form, the n-th column of orthogonal transform matrix A can be shown below:
Then transformed m-th of image block are as follows:
[am(1),am(2),...,am(N)]=uM TF
Step 106: being directed to each cluster, repeat above step 102-105；
Step 107: establishing adaptive PCA dictionary
The matrix that the feature vector acquired for the image block covariance matrix C of each cluster calculation is constituted is turned
Processing is set, adaptive PCA dictionary D is obtained.
Step 2: inputting seismic data x to be processed(0), it is based on adaptive PCA dictionary D, obtains first time restored image x(1)。
Step 2 includes following sub-step:
Step 201: inputting seismic data x to be processed(0), by K-means method to seismic data x to be processed(0)It carries out
Cluster, judges seismic data x to be processed respectively(0)In the corresponding classification of each image block；
Step 202: being directed to an image block, operation Da is carried out according to its corresponding classification, wherein a indicates described image
Block；
Step 203: the image block after defining operation is ai 0, searching and a in seismic data to be processedi 0As Local Phase
Image block and global similar image block, pass through formulaAnd formula
Update μi (j)；
Wherein, ai,jIndicate j-th of image block similar with i-th of image block, wi,jIndicate weighting coefficient, SiIt indicates and the
The set of the similar image block composition of i image block, h is regulatory factor, wherein
Step 204: passing throughObtain initial prior modelWhereinFor energy
Function,Vc(x) be connection group c potential-energy function；
Step 205: passing through formulaCalculate initial regularization coefficient
Wherein, λiIndicate regularization coefficient, σnStandard deviation for the Gaussian noise added in degeneration system model, σiFor ai
Standard deviation；
Step 206: passing through formulaCalculate initial regularization coefficient γi (0)
Wherein, γiIndicate regularization coefficient, σnFor the standard deviation of the Gaussian noise of the addition in degeneration system model, δiFor
ξiStandard deviation,
Step 207: (1) calculates a according to the following formulay (1):
Wherein, τ indicates that regularization parameter, j=1,2 ..., k, k are the total degree of iteration, and i=1,2 ..., n, n are institute
The quantity of the image block divided, image block are all stored in a manner of column vector；
Step 208: according to formulaRestored image after obtaining first time iteration
Step 209: being directed to seismic data x to be processed(0)In each image block repeat step 202-208, obtain
Restored image x(1)。
Step 3: with first time restored image x(1)It is iterated processing as seismic data to be processed, obtains final answer
Original image x(k)。
Step 3 includes following sub-step:
Step 301: according to obtained x(j)And ai (j)As a result, in restored image x(j)Middle searching and ai (j)As Local Phase
Image block and global similar image block, pass through formulaAnd formula
Update μi (j)；Wherein, ai,jIndicate j-th of image block similar with i-th of image block, wi,jIndicate weighting coefficient, SiIt indicates and the
The set of the similar image block composition of i image block, h is regulatory factor；
Step 302: by passing throughThe available prior model based on AMRF
Step 303: by input picture x(0)After being clustered using K-means method, the image block in image is judged respectively
Which classification belonged to；
Step 304: according to the adaptive PCA dictionary D of step 1, Da operation being carried out to all image blocks；
Step 305: passing through formulaCalculate initial regularization coefficient
Step 306: passing through formulaCalculate initial regularization coefficient γi (j-1)；
Step 307: (1) calculates a according to the following formulay (j):
Wherein, τ indicates that regularization parameter, j=1,2 ..., k, k are the total degree of iteration, and i=1,2 ..., n, n are institute
The quantity of the image block divided, image block are all stored in a manner of column vector；
Step 308: according to formulaIt obtains
Step 309: being directed to seismic data x to be processed(0)In each image block repeat step 301-308, obtain
The restored image x of j iteration(j)；
Step 310: repeating the k step 301-309, obtain final restored image x(k)。
The embodiment of the present invention also provides a kind of seismic data processing system based on PCA dictionary and rarefaction representation, comprising:
Memory is stored with computer executable instructions；
Processor, the processor run the computer executable instructions in the memory, execute following steps:
Step 1: establishing adaptive PCA dictionary D；
Step 2: inputting seismic data x to be processed(0), it is based on the adaptive PCA dictionary D, obtains first time restored image
x(1)；
Step 3: with first time restored image x(1)It is iterated processing as seismic data to be processed, obtains final answer
Original image x(k)。
Preferably, the step 1 includes:
Step 101: seismic data to be processed is divided by L cluster by K-means method；
Step 102: the matrix of the M image block composition in a cluster being subjected to the processing of data zero averaging, is obtained
Zero-mean result fmIt is expressed as row vector [fm(1),fm(2),...,fm(N)], wherein m=1,2 ..., M, each image
The size of block is n × n, and each image block is stored with column vector, N=n × n；
Step 103: define image block data matrix F:
Wherein, f(n)=[f1(n),f2(n),...,fM(n)]T, n=1,2 ..., N；
Step 104: establish image block covariance matrix C:
Step 105: calculating the orthogonal transform matrix A of image block data matrix F, and according to orthogonal transform matrix A to image
Block carries out orthogonal transformation:
The n-th column of orthogonal transform matrix A are shown below:
Transformed m-th of image block are as follows:
[am(1),am(2),...,am(N)]=uM TF
Wherein, U is the feature vector of covariance matrix C；
Step 106: being directed to each cluster, repeat above step 102-105；
Step 107: the square that the feature vector acquired for the image block covariance matrix C of each cluster calculation is constituted
Battle array carry out transposition processing, obtains adaptive PCA dictionary D.
Preferably, the step 2 includes:
Step 201: inputting seismic data x to be processed(0), by K-means method to seismic data x to be processed(0)It carries out
Cluster, judges seismic data x to be processed respectively(0)In the corresponding classification of each image block；
Step 202: being directed to an image block, operation Da is carried out according to its corresponding classification, wherein a indicates described image
Block；
Step 203: the image block after defining operation is ai 0, searching and a in seismic data to be processedi 0As Local Phase
Image block and global similar image block, pass through formulaAnd formula
Update μi (j)；
Wherein, ai,jIndicate j-th of image block similar with i-th of image block, wi,jIndicate weighting coefficient, SiIt indicates and the
The set of the similar image block composition of i image block, h is regulatory factor, wherein
Step 204: passing throughObtain initial prior modelWhereinFor energy
Function；
Step 205: passing through formulaCalculate initial regularization coefficient
Wherein, λiIndicate regularization coefficient, σnStandard deviation for the Gaussian noise added in degeneration system model, σiFor ai
Standard deviation；
Step 206: passing through formulaCalculate initial regularization coefficient
Wherein, γiIndicate regularization coefficient, σnFor the standard deviation of the Gaussian noise of the addition in degeneration system model, δiFor
ξiStandard deviation,
Step 207: (1) calculates a according to the following formulay (1):
Wherein, τ indicates that regularization parameter, j=1,2 ..., k, k are the total degree of iteration, and i=1,2 ..., n, n are institute
The quantity of the image block divided, image block are all stored in a manner of column vector；
Step 208: according to formulaRestored image after obtaining first time iteration
Step 209: being directed to seismic data x to be processed(0)In each image block repeat step 202-208, obtain
Restored image x(1)。
Preferably, the step 3 includes:
Step 301: according to obtained x(j)And ai (j)As a result, in restored image x(j)Middle searching and ai (j)As Local Phase
Image block and global similar image block, pass through formulaAnd formula
Update μi (j)；Wherein, ai,jIndicate j-th of image block similar with i-th of image block, wi,jIndicate weighting coefficient, SiIt indicates and the
The set of the similar image block composition of i image block, h is regulatory factor；
Step 302: by passing throughThe available prior model based on AMRF
Step 303: by input picture x(0)After being clustered using K-means method, the image block in image is judged respectively
Which class belonged to；
Step 304: according to the adaptive PCA dictionary D of step 1, Da operation being carried out to all image blocks；
Step 305: passing through formulaCalculate initial regularization coefficient
Step 306: passing through formulaCalculate initial regularization coefficient γi (j-1)；
Step 307: (1) calculates a according to the following formulay (j):
Step 308: according to formulaIt obtains
Step 309: being directed to seismic data x to be processed(0)In each image block repeat step 301-308, obtain
The restored image x of j iteration(j)；
Step 310: repeating the k step 301-309, obtain final restored image x(k)。
Embodiment
50000 pairs of different high-resolution and low-resolution images pair are randomly selected from training image concentration, and seek feature vector
It is trained, establishes adaptive PCA dictionary.In order to effectively compare processing after image and input picture, and EQUILIBRIUM CALCULATION FOR PROCESS efficiency and
The size of sparse dictionary is fixed as 1024 by outcome quality, and sample rate takes 0.5.Table 1 is the result pair of the present invention with conventional method
Than.As it can be seen from table 1 treated that seismic image root-mean-square error is substantially reduced for the method for the present invention, Y-PSNR is obvious
It improves.
The Comparative result of table 1 present invention and conventional method
The embodiment of the present invention is described above, above description is exemplary, and non-exclusive, and also not
It is limited to disclosed each embodiment.Without departing from the scope and spirit of illustrated each embodiment, for this technology
Many modifications and changes are obvious for the those of ordinary skill in field.The selection of term used herein, it is intended to
Best explain the principle, practical application or the improvement to the technology in market of each embodiment, or make the art its
Its those of ordinary skill can understand each embodiment disclosed herein.
Claims (8)
1. a kind of Processing Seismic Data based on PCA dictionary and rarefaction representation, comprising:
Step 1: establishing adaptive PCA dictionary D；
Step 2: inputting seismic data x to be processed(0), it is based on the adaptive PCA dictionary D, obtains first time restored image x(1)；
Step 3: with first time restored image x(1)It is iterated processing as seismic data to be processed, obtains final restored map
As x(k)。
2. the Processing Seismic Data according to claim 1 based on PCA dictionary and rarefaction representation, wherein the step
Rapid 1 includes:
Step 101: seismic data to be processed is divided by L cluster by K-means method；
Step 102: the matrix of the M image block composition in a cluster being subjected to the processing of data zero averaging, zero obtained is
It is worth result fmIt is expressed as row vector [fm(1),fm(2),...,fm(N)], wherein m=1,2 ..., M, each image block
Size is n × n, and each image block is stored with column vector, N=n × n；
Step 103: define image block data matrix F:
Wherein, f(n)=[f1(n),f2(n),...,fM(n)]T, n=1,2 ..., N；
Step 104: establish image block covariance matrix C:
Step 105: calculate image block data matrix F orthogonal transform matrix A, and according to orthogonal transform matrix A to image block into
Row orthogonal transformation:
The n-th column of orthogonal transform matrix A are shown below:
Transformed m-th of image block are as follows:
[am(1),am(2),...,am(N)]=uM TF
Wherein, U is the feature vector of covariance matrix C；
Step 106: being directed to each cluster, repeat above step 102-105；
Step 107: by the matrix constituted for the feature vector that acquires of image block covariance matrix C of each cluster calculation into
The processing of row transposition, obtains adaptive PCA dictionary D.
3. the Processing Seismic Data according to claim 2 based on PCA dictionary and rarefaction representation, wherein the step
Rapid 2 include:
Step 201: inputting seismic data x to be processed(0), by K-means method to seismic data x to be processed(0)It is clustered,
Seismic data x to be processed is judged respectively(0)In the corresponding classification of each image block；
Step 202: being directed to an image block, operation Da is carried out according to its corresponding classification, wherein a indicates described image block；
Step 203: the image block after defining operation is ai 0, searching and a in seismic data to be processedi 0Image block as Local Phase
With global similar image block, pass through formulaAnd formulaIt updates
μi (j)；
Wherein, ai,jIndicate j-th of image block similar with i-th of image block, wi,jIndicate weighting coefficient, SiIt indicates and i-th of figure
As the set that the similar image block of block forms, h is regulatory factor, wherein
Step 204: passing throughObtain initial prior modelWhereinFor energy function；
Step 205: passing through formulaCalculate initial regularization coefficient
Wherein, λiIndicate regularization coefficient, σnStandard deviation for the Gaussian noise added in degeneration system model, σiFor aiStandard
Difference；
Step 206: passing through formulaCalculate initial regularization coefficient γi (0)
Wherein, γiIndicate regularization coefficient, σnFor the standard deviation of the Gaussian noise of the addition in degeneration system model, δiFor ξi's
Standard deviation,
Step 207: (1) calculates a according to the following formulay (1):
Wherein, τ indicates that regularization parameter, j=1,2 ..., k, k are the total degree of iteration, and i=1,2 ..., n, n are divided
The quantity of image block, image block are all stored in a manner of column vector；
Step 208: according to formulaRestored image after obtaining first time iteration
Step 209: being directed to seismic data x to be processed(0)In each image block repeat step 202-208, obtain for the first time
Restored image x(1)。
4. the Processing Seismic Data according to claim 3 based on PCA dictionary and rarefaction representation, wherein the step
Rapid 3 include:
Step 301: according to obtained x(j)And ai (j)As a result, in restored image x(j)Middle searching and ai (j)Image as Local Phase
Block and global similar image block, pass through formulaAnd formulaIt updates
μi (j)；Wherein, ai,jIndicate j-th of image block similar with i-th of image block, wi,jIndicate weighting coefficient, SiIt indicates and i-th
The set of the similar image block composition of image block, h is regulatory factor；
Step 302: by passing throughThe available prior model based on AMRF
Step 303: by input picture x(0)After being clustered using K-means method, judge that the image block in image belongs to respectively
Which class；
Step 304: according to the adaptive PCA dictionary D of step 1, Da operation being carried out to all image blocks；
Step 305: passing through formulaCalculate initial regularization coefficient
Step 306: passing through formulaCalculate initial regularization coefficient γi (j-1)；
Step 307: (1) calculates a according to the following formulay (j):
Step 308: according to formulaIt obtains
Step 309: being directed to seismic data x to be processed(0)In each image block repeat step 301-308, obtain jth time
The restored image x of iteration(j)；
Step 310: repeating the k step 301-309, obtain final restored image x(k)。
5. a kind of seismic data processing system based on PCA dictionary and rarefaction representation, comprising:
Memory is stored with computer executable instructions；
Processor, the processor run the computer executable instructions in the memory, execute following steps:
Step 1: establishing adaptive PCA dictionary D；
Step 2: inputting seismic data x to be processed(0), it is based on the adaptive PCA dictionary D, obtains first time restored image x(1)；
Step 3: with first time restored image x(1)It is iterated processing as seismic data to be processed, obtains final restored map
As x(k)。
6. the seismic data processing system according to claim 5 based on PCA dictionary and rarefaction representation, wherein the step
Rapid 1 includes:
Step 101: seismic data to be processed is divided by L cluster by K-means method；
Step 102: the matrix of the M image block composition in a cluster being subjected to the processing of data zero averaging, zero obtained is
It is worth result fmIt is expressed as row vector [fm(1),fm(2),...,fm(N)], wherein m=1,2 ..., M, each image block
Size is n × n, and each image block is stored with column vector, N=n × n；
Step 103: define image block data matrix F:
Wherein, f(n)=[f1(n),f2(n),...,fM(n)]T, n=1,2 ..., N；
Step 104: establish image block covariance matrix C:
Step 105: calculate image block data matrix F orthogonal transform matrix A, and according to orthogonal transform matrix A to image block into
Row orthogonal transformation:
The n-th column of orthogonal transform matrix A are shown below:
Transformed m-th of image block are as follows:
[am(1),am(2),...,am(N)]=uM TF
Wherein, U is the feature vector of covariance matrix C；
Step 106: being directed to each cluster, repeat above step 102-105；
Step 107: by the matrix constituted for the feature vector that acquires of image block covariance matrix C of each cluster calculation into
The processing of row transposition, obtains adaptive PCA dictionary D.
7. the seismic data processing system according to claim 6 based on PCA dictionary and rarefaction representation, wherein the step
Rapid 2 include:
Step 201: inputting seismic data x to be processed(0), by K-means method to seismic data x to be processed(0)It is clustered,
Seismic data x to be processed is judged respectively(0)In the corresponding classification of each image block；
Step 202: being directed to an image block, operation Da is carried out according to its corresponding classification, wherein a indicates described image block；
Step 203: the image block after defining operation is ai 0, searching and a in seismic data to be processedi 0Image block as Local Phase
With global similar image block, pass through formulaAnd formulaIt updates
μi (j)；
Wherein, ai,jIndicate j-th of image block similar with i-th of image block, wi,jIndicate weighting coefficient, SiIt indicates and i-th of figure
As the set that the similar image block of block forms, h is regulatory factor, wherein
Step 204: passing throughObtain initial prior modelWhereinFor energy function；
Step 205: passing through formulaCalculate initial regularization coefficient
Wherein, λiIndicate regularization coefficient, σnStandard deviation for the Gaussian noise added in degeneration system model, σiFor aiStandard
Difference；
Step 206: passing through formulaCalculate initial regularization coefficient γi (0)
Wherein, γiIndicate regularization coefficient, σnFor the standard deviation of the Gaussian noise of the addition in degeneration system model, δiFor ξi's
Standard deviation,
Step 207: (1) calculates a according to the following formulay (1):
Wherein, τ indicates that regularization parameter, j=1,2 ..., k, k are the total degree of iteration, and i=1,2 ..., n, n are divided
The quantity of image block, image block are all stored in a manner of column vector；
Step 208: according to formulaRestored image after obtaining first time iteration
Step 209: being directed to seismic data x to be processed(0)In each image block repeat step 202-208, obtain for the first time
Restored image x(1)。
8. the seismic data processing system according to claim 7 based on PCA dictionary and rarefaction representation, wherein the step
Rapid 3 include:
Step 301: according to obtained x(j)And ai (j)As a result, in restored image x(j)Middle searching and ai (j)Image as Local Phase
Block and global similar image block, pass through formulaAnd formulaIt updates
μi (j)；Wherein, ai,jIndicate j-th of image block similar with i-th of image block, wi,jIndicate weighting coefficient, SiIt indicates and i-th
The set of the similar image block composition of image block, h is regulatory factor；
Step 302: by passing throughThe available prior model based on AMRF
Step 303: by input picture x(0)After being clustered using K-means method, judge that the image block in image belongs to respectively
Which class；
Step 304: according to the adaptive PCA dictionary D of step 1, Da operation being carried out to all image blocks；
Step 305: passing through formulaCalculate initial regularization coefficient
Step 306: passing through formulaCalculate initial regularization coefficient γi (j-1)；
Step 307: (1) calculates a according to the following formulay (j):
Step 308: according to formulaIt obtains
Step 309: being directed to seismic data x to be processed(0)In each image block repeat step 301-308, obtain jth time
The restored image x of iteration(j)；
Step 310: repeating the k step 301-309, obtain final restored image x(k)。
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| US20150154766A1 (en) * | 2012-08-06 | 2015-06-04 | Koninklijke Philips N.V. | Image noise reduction and/or image resolution improvement |
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