CN112163611B - Feature tensor-based high-dimensional seismic data interpolation method - Google Patents
Feature tensor-based high-dimensional seismic data interpolation method Download PDFInfo
- Publication number
- CN112163611B CN112163611B CN202011014635.9A CN202011014635A CN112163611B CN 112163611 B CN112163611 B CN 112163611B CN 202011014635 A CN202011014635 A CN 202011014635A CN 112163611 B CN112163611 B CN 112163611B
- Authority
- CN
- China
- Prior art keywords
- training
- tensor
- data
- regression model
- interpolation
- 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
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F18/00—Pattern recognition
- G06F18/20—Analysing
- G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
- G06F18/213—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods
-
- 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
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F18/00—Pattern recognition
- G06F18/20—Analysing
- G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
- G06F18/214—Generating training patterns; Bootstrap methods, e.g. bagging or boosting
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N20/00—Machine learning
- G06N20/10—Machine learning using kernel methods, e.g. support vector machines [SVM]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N20/00—Machine learning
- G06N20/20—Ensemble learning
Abstract
The invention discloses a feature tensor-based high-dimensional seismic data interpolation method which comprises the steps of preprocessing data, extracting training feature tensors, training and learning a tensor regression model and carrying out interpolation reconstruction. The tensor regression model is applied to seismic data interpolation reconstruction, the tensor is used as the input feature for training, the original feature is directly input into the tensor regression model, the structural information of high-dimensional data is not damaged, the structural information in the original feature is effectively reserved, the structural information utilization rate of the high-dimensional seismic data is improved, the interpolation effect of a machine learning method is improved, the seismic data recovery quality is improved, the seismic data interpretation accuracy is improved, and the universality capacity of different types of different-dimension seismic data is realized.
Description
Technical Field
The invention relates to the field of seismic data processing, in particular to a feature tensor-based high-dimensional seismic data interpolation method.
Background
At present, the traditional energy sources such as natural gas, petroleum and the like which the national people rely on for survival are exploited without exploring physics, and the acquired data are called seismic data. High density complete seismic data is of great importance in subsequent steps such as offset imaging and multiple suppression. On one hand, the arrangement of the detectors is restricted by natural conditions, so that the phenomenon of column alignment loss of the acquired data is caused; on the other hand, in order to save mining cost, the distance between adjacent detectors is increased, so that data are too sparse, and the phenomenon of data loss of the acquired data is caused. The purpose of seismic data interpolation is to complement missing data completely or encrypt sparse data by a mathematical algorithm to densify the data. In recent years, the exploration industry has become more concerned with the acquisition of high dimensional seismic data. The high-dimensional seismic data refers to data acquired by multiple detectors and multiple shot points at different moments. Information among data space coordinate axes is closely connected under the constraint of complex physical wave characteristics, so that the high-dimensional seismic data can contain more structural information, and more basis is provided for the correct interpretation of the underground medium. However, due to the limitation of economic conditions and natural conditions, the problem of interpolation reconstruction of high-dimensional seismic data is particularly important.
When the traditional algorithm processes the interpolation problem of high-dimensional seismic data, such as sparse transformation, dictionary learning, tensor completion and the like, the high-dimensional seismic data are often converted into low-dimensional seismic data by depending on dimension reduction conversion in an unfolding mode, and the interpolation is carried out by adopting a low-dimensional interpolation algorithm, so that the physical correlation relationship of the seismic data among different dimensions is destroyed, and the interpolation effect needs to be further improved. The original machine learning method usually expands high-dimensional data into vectors according to a certain dimension, which destroys the rich multi-dimensional characteristics of high-dimensional seismic data, and as the dimension is increased, the training parameters are increased, which results in low efficiency and unsatisfactory interpolation effect in training the high-dimensional data. Emerging machine learning algorithms exhibit universality and powerful learning capabilities for different types of seismic data, but still do not achieve the capability of learning structural information. When solving the high dimensional data, the interpolation is still carried out by adopting a low dimensional algorithm after the expansion.
In recent years, tensor regression models such as a support tensor machine, a generalized tensor linear regression model, a low-rank sparse tensor regression model and the like are applied to the application fields such as the image field, neuroimaging, hyperspectral remote sensing imaging and the like. With the tensor decomposition, the model has significant advantages in the processing of high-dimensional data. In the seismic data interpolation technology, the existing algorithm lacks the universality capability of high-dimensional data, and the research of the universality interpolation algorithm suitable for the high-dimensional data is necessary.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a feature tensor-based high-dimensional seismic data interpolation method.
The technical scheme for solving the technical problem is to provide a feature tensor-based high-dimensional seismic data interpolation method, which is characterized by comprising the following steps of:
step one, preprocessing data: selecting original training data, and then carrying out deletion processing on the original training data to obtain deletion training data; performing pre-interpolation processing on the missing training data and the missing seismic data respectively by adopting an interpolation algorithm to obtain pre-interpolation training data and pre-interpolation reconstruction data;
step two, extracting a training feature tensor: selecting step length and scale, and respectively carrying out local cutting processing on pre-interpolation training data and pre-interpolation reconstruction data to obtain a training feature tensor and a predicted feature tensor;
step three, training and learning of a tensor regression model: determining a mapping point of a training feature tensor and original training data in the original training data, wherein the mapping point is a training label, and a training set consisting of the training label and the training feature tensor is obtained; each training feature tensor and the corresponding training label form a group of training point pairs in a training set; sequentially inputting each group of training point pairs to a tensor regression model, and training and learning the tensor regression model to obtain a trained tensor regression model;
step four, interpolation reconstruction: sequentially inputting the predicted feature tensors into a trained tensor regression model to obtain a predicted label set; and then according to the mapping relation between the training feature tensor determined in the third step and the original training data, performing interpolation operation on the missing seismic data by using the prediction labels in the prediction label set to obtain reconstructed seismic data.
Compared with the prior art, the invention has the beneficial effects that:
(1) the tensor regression model is applied to seismic data interpolation reconstruction, the tensor is used as the input feature for training, the original feature is directly input into the tensor regression model, the structural information of high-dimensional data is not damaged, the structural information in the original feature is effectively reserved, the structural information utilization rate of the high-dimensional seismic data is improved, the interpolation effect of a machine learning method is improved, the seismic data recovery quality is improved, the seismic data interpretation accuracy is improved, and the universality capacity of different types of different-dimension seismic data is realized.
(2) When high-dimensional data is interpolated, by means of CP decomposition, the high-dimensional data is decomposed into a plurality of matrixes on the premise of not destroying the structural information of the high-dimensional data, so that training parameters can be effectively reduced, and the interpolation efficiency is further improved.
(3) In the model parameter training process, the alternating least square method is adopted, each wheel retrains the correlation matrix of each dimension, the multi-dimensional structure correlation property of the seismic data is repeatedly considered, and the utilization capacity of the structure information is obviously improved.
Drawings
FIG. 1 is a complete seismic data plot of example 1 of the present invention;
FIG. 2 is 8 graphs of original training data according to example 1 of the present invention;
FIG. 3 is a graph of missing seismic data at a sampling rate of 50% for example 1 of the present invention;
fig. 4 is a pre-interpolation reconstruction data graph obtained through a Bicubic interpolation algorithm in embodiment 1 of the present invention;
FIG. 5 is a flow chart of data preprocessing of the present invention;
FIG. 6 is a flow chart of training learning of the tensor regression model of the present invention;
FIG. 7 is a flow chart of CP decomposition of the three-dimensional tensor;
FIG. 8 is a flow chart of an interpolation reconstruction of the present invention;
fig. 9 is a recovery result of the tensor regression algorithm of embodiment 1 of the present invention;
fig. 10 shows the recovery result of the support vector machine algorithm according to embodiment 1 of the present invention.
Detailed Description
Specific examples of the present invention are given below, and the specific examples are only for illustrating the present invention in further detail, and do not limit the scope of protection of the claims of the present application.
The invention provides a feature tensor-based high-dimensional seismic data interpolation method (short method), which is characterized by comprising the following steps of:
step one, preprocessing data: selecting original training data from the existing seismic database, and then performing missing processing on the original training data to obtain missing training data; performing pre-interpolation processing on the missing training data and the missing seismic data respectively by adopting an interpolation algorithm to obtain pre-interpolation training data and pre-interpolation reconstruction data;
selecting seismic data with proper scale and similar landform structure from the original training data, wherein the quality of the original training data is closely related to the interpolation recovery result; missing seismic data are obtained during actual exploration; the missing condition of the missing training data is consistent with the missing seismic data;
step two, extracting a training feature tensor: selecting step length and scale, and respectively carrying out local cutting processing on pre-interpolation training data and pre-interpolation reconstruction data to obtain a local feature tensor for training and learning, namely a training feature tensor, and a local feature tensor for interpolation reconstruction, namely a prediction feature tensor;
step three, training and learning of a tensor regression model: determining a mapping point of a training feature tensor and original training data, namely a training label, in the original training data to obtain a training set consisting of the training label and the training feature tensor; each training feature tensor and the corresponding training label form a group of training point pairs in a training set; sequentially inputting each group of training point pairs to a tensor regression model, and training and learning parameters of the tensor regression model, namely adjusting coefficient tensor and bias to obtain a trained tensor regression model;
step 3.1, determining a mapping point of the training feature tensor and the original training data in the original training data, wherein the mapping point is a training label, and further obtaining a training set consisting of the training label and the training feature tensorWhereinFor the ith training feature tensor, yiThe ith training label; each training feature tensor and its pairThe corresponding training labels form a group of training point pairs in a training set;
step 3.2: sequentially inputting each group of training point pairs to a tensor regression model, and training and learning parameters of the tensor regression model, namely adjusting coefficient tensor and bias to obtain a trained tensor regression model;
the training and learning method of the parameters of the tensor regression model comprises the following steps:
the tensor regression model is shown in equation 1):
in the formula 1), the reaction mixture is,is a tensor argument; operator, euclidean inner product of the representation tensor; the parameters of the tensor regression model are coefficient tensorsAnd an offset b;
tensor of coefficientPerforming CP decomposition to obtain(FIG. 6 shows the CP decomposition process of the three-dimensional tensor, which is a mature tensor decomposition technique, and the regression model is built on the basis of tensor decomposition), and the regression model is substituted into the formula 1) to obtain:
pass through pairTensor of coefficientsThe CP decomposition is performed so that the number of parameters of the tensor regression model is determined byIs reduced toR denotes the CP rank of the coefficient tensor W; p is a radical ofiThe variable number of the coefficient tensor in the ith dimension;
converting equation 2) to equation 3 by separability of the Khatri-Rao product):
in formula 3), X(n)N-mode expansion for χ; "" indicates the product of Khatri-Rao;
therefore, in each training and learning process, the coefficient tensor W does not need to be adjusted, and only each factor matrix W needs to be adjustednMaking adjustments, i.e. to the factor matrix WnAdjustment with offset b:
in formula 4), L (-) is a loss function, Xi(n)Is xiN-mode unfolding of (1);
solving n +1 optimization problems in the formula 4) by an alternating least square method to obtain an optimal estimation value of the coefficient tensorOptimal estimation of biasObtaining a trained tensor regression model:
preferably, the method for solving the n +1 optimization problems in equation 4) by the alternating least squares method is as follows:
giving error precision epsilon, inputting error precision epsilon and training set { chii,y i1, …, M; for bias b and factor matrix WnInitialization is performed according to equations 6) and 7), respectively:
in formulae 6) and 7), b(0)And Wn (0)Representing the bias and factor matrix obtained from the 0 th training turn, namely the initial bias and initial factor matrix; operator rand (p)nR) represents the generation of pnA random number matrix of x R;
in the training of the t-th round, a factor matrix W of the t-th round is obtained according to the following formulai (t)I is 1, …, N, and then the coefficient tensor W of the t round is obtained(t)Offset from round t b(t):
Calculating the loss of the t-th roundValue of loss function L (b)(t),W(t));
When L (b)(t),W(t))-L(b(t-1),W(t-1)) Stopping training when the error precision epsilon is less than or equal to the error precision epsilon; order toObtaining the optimal estimated value of the coefficient tensorAnd biasThe optimal estimated value of (a).
Step four, interpolation reconstruction: sequentially inputting the predicted feature tensors into a trained tensor regression model to obtain a predicted label set; and then according to the mapping relation between the training feature tensor determined in the third step and the original training data, performing interpolation operation on the missing seismic data by using the prediction labels in the prediction label set to obtain reconstructed seismic data.
Example 1
In this embodiment, a support vector machine algorithm (SVR algorithm) and the interpolation method (i.e., a tensor regression algorithm (TR algorithm)) are used to perform interpolation operation on missing seismic data, so as to obtain reconstructed seismic data respectively.
In the SVR algorithm, a piece of two-dimensional complete seismic data (as shown in fig. 1) is selected from the existing seismic database, and the missing seismic data is obtained by performing missing processing on the piece of two-dimensional complete seismic data. The missing seismic data size is 128 x 128. Selecting 8 pieces of seismic data which are 128 multiplied by 128 in size and have similar landform structures with missing seismic data from an existing seismic database as original training data (as shown in figure 2); as can be seen in fig. 2, the landform structure of the original training data is similar to the complete seismic data.
In the interpolation method, the selection of complete seismic data, missing seismic data and original training data is the same as that of the SVR algorithm.
In the first step of the interpolation method, as can be seen from fig. 3, the missing seismic data rule is missing, and the sampling rate is 1/a which is 50%;
the interpolation algorithm adopts Bicubic interpolation technology. It can be seen from fig. 4 that the pre-interpolated reconstructed data is only simply reconstructed and restored; the signal-to-noise ratio S/N of the pre-interpolation reconstruction data obtained in the step is 25.03dB, the reconstruction result is not ideal, and still needs to be further improved;
in the second step of the interpolation method, the step length is selected to be 1, the scale is 3 multiplied by 3, and the pre-interpolation training data and the pre-interpolation reconstruction data are subjected to local cutting processing to obtain 127008 training feature tensors and 15876 predicted feature tensors.
And quantifying the recovery quality according to the signal-to-noise ratio, wherein the signal-to-noise ratio is calculated according to the following formula:
wherein I is complete seismic data, InTo reconstruct seismic data;
the selected sampling rate was 50%, the recovery effects of the SVR algorithm and the TR algorithm of the present invention were compared, and the signal-to-noise ratio of the interpolation results is listed in table 1.
TABLE 1
In table 1, the percentage refers to the percentage ratio of the training set used in the process of training and learning the parameters of the model to the total training set. As can be seen from fig. 9, the recovery result of the TR algorithm at 100% is the signal-to-noise ratio S/N of 33.9dB, and as can be seen from fig. 10, the recovery result of the SVM algorithm at 100% is the signal-to-noise ratio S/N of 32.16 dB. As can be seen from the reconstruction results of fig. 9 and 10 and the signal-to-noise ratios in table 1, the reconstruction effect of the tensor regression algorithm using tensor as argument is better than the reconstruction effect of the support vector machine algorithm using vector as argument.
The embodiments are only for illustrating the invention and not for limiting the invention, and those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention, so all equivalent technical solutions also belong to the scope of the invention, and the scope of the invention should be defined by the claims.
Nothing in this specification is said to apply to the prior art.
Claims (2)
1. A feature tensor-based high-dimensional seismic data interpolation method is characterized by comprising the following steps:
step one, preprocessing data: selecting original training data, and then carrying out deletion processing on the original training data to obtain deletion training data; performing pre-interpolation processing on the missing training data and the missing seismic data respectively by adopting an interpolation algorithm to obtain pre-interpolation training data and pre-interpolation reconstruction data;
step two, extracting a training feature tensor: selecting step length and scale, and respectively carrying out local cutting processing on pre-interpolation training data and pre-interpolation reconstruction data to obtain a training feature tensor and a predicted feature tensor;
step three, training and learning of a tensor regression model: determining a mapping point of a training feature tensor and original training data in the original training data, wherein the mapping point is a training label, and a training set consisting of the training label and the training feature tensor is obtained; each training feature tensor and the corresponding training label form a group of training point pairs in a training set; sequentially inputting each group of training point pairs to a tensor regression model, and training and learning the tensor regression model to obtain a trained tensor regression model;
step 3.1, determining a mapping point of the training feature tensor and the original training data in the original training data, wherein the mapping point is a training label, and further obtaining a training set consisting of the training label and the training feature tensorWhereinFor the ith training feature tensor, yiThe ith training label; each training feature tensor and the corresponding training label form a group of training point pairs in a training set;
step 3.2: sequentially inputting each group of training point pairs to a tensor regression model, and training and learning parameters of the tensor regression model to obtain a trained tensor regression model;
the training learning process of the parameters of the tensor regression model is as follows:
the tensor regression model is shown in equation 1):
in the formula 1), the reaction mixture is,is a tensor argument; operator<>A euclidean inner product representing the tensor; the parameters of the tensor regression model are coefficient tensorsAnd an offset b;
tensor of coefficientPerforming CP decomposition to obtainAnd substituting it into formula 1) to obtain:
passing pair coefficient tensorThe CP decomposition is performed so that the number of parameters of the tensor regression model is determined byIs reduced toR denotes coefficient tensorCP rank of (d); p is a radical ofiThe variable number of the coefficient tensor in the ith dimension;
converting equation 2) to equation 3 by separability of the Khatri-Rao product):
therefore, in each training learning process, the tensor of the coefficient is not required to be processedThe adjustment is carried out only by each factor matrix WnMaking adjustments, i.e. to the factor matrix WnAdjustment with offset b:
solving n +1 optimization problems in the formula 4) by an alternating least square method to obtain an optimal estimation value of the coefficient tensorOptimal estimation of biasObtaining a trained tensor regression model:
step four, interpolation reconstruction: sequentially inputting the predicted feature tensors into a trained tensor regression model to obtain a predicted label set; and then according to the mapping relation between the training feature tensor determined in the third step and the original training data, performing interpolation operation on the missing seismic data by using the prediction labels in the prediction label set to obtain reconstructed seismic data.
2. The feature tensor-based high-dimensional seismic data interpolation method as recited in claim 1, wherein the method for solving n +1 optimization problems in the formula 4) by the alternating least square method is as follows:
giving error precision epsilon, inputting error precision epsilon and training setFor bias b and factor matrix WnInitialization is performed according to equations 6) and 7), respectively:
in formulae 6) and 7), b(0)Andrepresenting the bias and factor matrix obtained from the 0 th training turn, namely the initial bias and initial factor matrix; operator rand (p)nR) represents the generation of pnA random number matrix of x R;
in the training of the t-th round, a factor matrix W of the t-th round is obtained according to the following formulai (t)I is 1, …, N, and then the coefficient tensor of the t round is obtainedOffset from round t b(t):
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202011014635.9A CN112163611B (en) | 2020-09-24 | 2020-09-24 | Feature tensor-based high-dimensional seismic data interpolation method |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202011014635.9A CN112163611B (en) | 2020-09-24 | 2020-09-24 | Feature tensor-based high-dimensional seismic data interpolation method |
Publications (2)
Publication Number | Publication Date |
---|---|
CN112163611A CN112163611A (en) | 2021-01-01 |
CN112163611B true CN112163611B (en) | 2021-04-06 |
Family
ID=73863699
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN202011014635.9A Active CN112163611B (en) | 2020-09-24 | 2020-09-24 | Feature tensor-based high-dimensional seismic data interpolation method |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN112163611B (en) |
Families Citing this family (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN114066720B (en) * | 2021-11-01 | 2024-03-26 | 力度工业智能科技(苏州)有限公司 | Tensor regression-based three-dimensional surface morphology prediction method, device and readable medium |
Citations (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN105717547A (en) * | 2015-12-22 | 2016-06-29 | 吉林大学 | Anisotropy medium magnetotelluric meshless value simulation method |
CN109001802A (en) * | 2018-08-30 | 2018-12-14 | 电子科技大学 | Seismic signal reconstructing method based on Hankel tensor resolution |
CN110082823A (en) * | 2019-05-09 | 2019-08-02 | 中国石油大学(北京) | A kind of seismic data interpolation method and device |
CN110568486A (en) * | 2019-09-17 | 2019-12-13 | 电子科技大学 | Seismic signal completion method based on synchronous sparse low-rank tensor completion model |
Family Cites Families (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
AU2014201436A1 (en) * | 2013-03-22 | 2014-10-09 | Cgg Services Sa | System and method for interpolating seismic data |
WO2017019388A1 (en) * | 2015-07-28 | 2017-02-02 | Schlumberger Technology Corporation | Seismic constrained discrete fracture network |
CN107367759A (en) * | 2017-06-14 | 2017-11-21 | 中国石油化工股份有限公司 | A kind of geological data based on architectural feature protects side denoising method |
CN109242770B (en) * | 2017-07-10 | 2021-12-24 | 中国石油化工股份有限公司 | Image guided seismic velocity interpolation method and computer readable storage medium |
CN109765611B (en) * | 2019-03-11 | 2020-07-31 | 河北地质大学 | Seismic data interpolation method and device |
-
2020
- 2020-09-24 CN CN202011014635.9A patent/CN112163611B/en active Active
Patent Citations (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN105717547A (en) * | 2015-12-22 | 2016-06-29 | 吉林大学 | Anisotropy medium magnetotelluric meshless value simulation method |
CN109001802A (en) * | 2018-08-30 | 2018-12-14 | 电子科技大学 | Seismic signal reconstructing method based on Hankel tensor resolution |
CN110082823A (en) * | 2019-05-09 | 2019-08-02 | 中国石油大学(北京) | A kind of seismic data interpolation method and device |
CN110568486A (en) * | 2019-09-17 | 2019-12-13 | 电子科技大学 | Seismic signal completion method based on synchronous sparse low-rank tensor completion model |
Also Published As
Publication number | Publication date |
---|---|
CN112163611A (en) | 2021-01-01 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
Nishino et al. | Product wave function renormalization group | |
CN109784480B (en) | Power system state estimation method based on convolutional neural network | |
CN104867119B (en) | The structural missing image fill method rebuild based on low-rank matrix | |
CN107561576A (en) | Seismic signal method based on dictionary learning regularization rarefaction representation | |
CN109033030B (en) | Tensor decomposition and reconstruction method based on GPU | |
CN111667444B (en) | Image compressed sensing reconstruction method based on multi-channel residual error network | |
CN113204738B (en) | Mechanical fault feature extraction method based on wavelet transformation and topological data analysis | |
CN112163611B (en) | Feature tensor-based high-dimensional seismic data interpolation method | |
Pant et al. | Unconstrained regularized ℓ p-norm based algorithm for the reconstruction of sparse signals | |
CN109143151B (en) | Uniform area array tensor reconstruction method and information source positioning method for partial array element damage | |
CN114786018A (en) | Image reconstruction method based on greedy random sparse Kaczmarz | |
Ying | Tensor network skeletonization | |
CN103886050B (en) | Image feature storing method, image searching method and device based on compressive sensing | |
CN113225089B (en) | Industrial robot multichannel monitoring data compression method and system | |
Lüst et al. | A stringy massive double copy | |
Zheng et al. | On the application of principal component analysis to classification problems | |
CN106899305B (en) | Original signal reconstruction method based on second-generation wavelet | |
CN112749807A (en) | Quantum state chromatography method based on generative model | |
Long et al. | Low rank tensor completion for multiway visual data | |
Sun et al. | Spatial-temporal scientific data clustering via deep convolutional neural network | |
Sun et al. | Tensor completion using kronecker rank-1 tensor train with application to visual data inpainting | |
Le Magoarou et al. | FAμST: Speeding up linear transforms for tractable inverse problems | |
CN113052319B (en) | Quantum-computing Cramer-Schmitt orthogonalization method | |
Si et al. | An efficient tensor regression for high-dimensional data | |
CN112700372B (en) | Seismic data interpolation method combining Gabor feature extraction and support vector regression |
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 | ||
CB03 | Change of inventor or designer information |
Inventor after: Jia Yongna Inventor after: Chen Yao Inventor after: Gu Junhua Inventor after: Chang Guangyao Inventor after: Li Yifan Inventor before: Chen Yao Inventor before: Jia Yongna Inventor before: Gu Junhua Inventor before: Chang Guangyao Inventor before: Li Yifan |
|
CB03 | Change of inventor or designer information |