Seismic data reconstruction via matrix completion

Yang, Yi; Ma, Jianwei; Osher, Stanley

doi:10.3934/ipi.2013.7.1379

Cited by 73 publications

(41 citation statements)

References 25 publications

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“…In this paper, we work with the original data using the so-called texture transformation, which is defined as base texture [22] and applied to seismic data recovery in [9]. Below two are the motivations to use the texture transformation.…”

Section: Matrix Completion and Pre-transformationmentioning

confidence: 98%

“…[8] The low-rank matrix completion theory based on nuclear-norm minimization is becoming increasingly popular in practice, and has been applied to seismic data reconstruction with missing traces. Yang et al [9] discovered the connection between seismic data reconstruction and the general matrix completion problem, and first formulated the seismic data reconstruction as a nuclear-norm minimization problem through building a pre-transformation. Recently, Ma [10] extended the low-rank matrix completion with a designed texture-patch pre-transformation to three-dimensional seismic data reconstruction.…”

Section: Introductionmentioning

confidence: 99%

“…We follow Yang et al's method [9] that uses the texture-patch mapping, but consider the weighted nuclear-norm minimization model to complete the low-rank texturepatch matrix in order to obtain the high-quality reconstruction. However, the weighted nuclear-norm is generally non-convex.…”

Section: Introductionmentioning

confidence: 99%

“…This method is usually much faster than the singular value decomposition based methods. [9] From an algorithmic viewpoint, one central idea of the above mentioned most solution methods is the convex relaxation of the l 0 -functional (the function giving the number of non-zero elements of a vector) and of the rank function. A weak point of the nuclear-norm minimization algorithms is that it treats all singular values of the sampled matrix equally.…”

Section: Introductionmentioning

confidence: 99%

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Seismic data reconstruction via weighted nuclear-norm minimization

Wang

Han

et al. 2014

Inverse Problems in Science and Engineering

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The low-rank matrix completion theory based on nuclear-norm minimization is becoming increasingly popular in practice, and has been applied to seismic data reconstruction of missing traces. In this paper, we investigate the weighted nuclearnorm minimization model on low-rank seismic texture matrix which is obtained with a designed texture-patch pre-transformation. Unlike the previous nuclearnorm model that treats all singular values of the seismic data matrix equally, the weighted nuclear-norm model, based on the idea of iterative reweighting, makes a closer approximation to the 'counting rank function' and can promote the lowrank matrices. We apply weighted spectral soft-thresholding iterative scheme and weighted iterative supported detection method to solve the weighted model. Experimental study on synthetic and real seismic data shows that high-quality reconstruction can be obtained by the weighted low-rank methods.

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Section: Matrix Completion and Pre-transformationmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Seismic data reconstruction via weighted nuclear-norm minimization

Wang

Han

et al. 2014

Inverse Problems in Science and Engineering

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“…The most popular one, originally proposed for matrix completion problems, is the nuclear norm (cf. [102,317,86,87,367])…”

Section: Low Rank Regularizationmentioning

confidence: 99%

Modern regularization methods for inverse problems

2018

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Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from linear towards nonlinear regularization methods even for linear inverse problems. The aim of this paper is to provide a reasonably comprehensive overview of this development towards modern nonlinear regularization methods, including their analysis, applications, and issues for future research.In particular we will discuss variational methods and techniques derived from those, since they have attracted particular interest in the last years and link to other fields like image processing and compressed sensing. We further point to developments related to statistical inverse problems, multiscale decompositions, and learning theory.

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Spatial matrix completion for spatially misaligned and high‐dimensional air pollution data

Szpiro

Simon

2021

Environmetrics

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In health‐pollution cohort studies, accurate predictions of pollutant concentrations at new locations are needed, since the locations of fixed monitoring sites and study participants are often spatially misaligned. For multi‐pollution data, principal component analysis (PCA) is often incorporated to obtain low‐rank (LR) structure of the data prior to spatial prediction. Recently developed predictive PCA modifies the traditional algorithm to improve the overall predictive performance by leveraging both LR and spatial structures within the data. However, predictive PCA requires complete data or an initial imputation step. Nonparametric imputation techniques without accounting for spatial information may distort the underlying structure of the data, and thus further reduce the predictive performance. We propose a convex optimization problem inspired by the LR matrix completion framework and develop a proximal algorithm to solve it. Missing data are imputed and handled concurrently within the algorithm, which eliminates the necessity of a separate imputation step. We review the connections among those existing methods developed for spatially misaligned multivariate data, and show that our algorithm has lower computational burden and leads to reliable predictive performance as the severity of missing data increases.

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Seismic data reconstruction via matrix completion

Cited by 73 publications

References 25 publications

Seismic data reconstruction via weighted nuclear-norm minimization

Seismic data reconstruction via weighted nuclear-norm minimization

Modern regularization methods for inverse problems

Spatial matrix completion for spatially misaligned and high‐dimensional air pollution data

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