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Information theoretic bounds for lowrank matrix completion
 in 2010 IEEE International Symposium on Information Theory (ISIT 2010
, 2010
"... Abstract—This paper studies the lowrank matrix completion problem from an information theoretic perspective. The completion problem is rephrased as a communication problem of an (uncoded) lowrank matrix source over an erasure channel. The paper then uses achievability and converse arguments to pr ..."
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Cited by 7 (1 self)
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Abstract—This paper studies the lowrank matrix completion problem from an information theoretic perspective. The completion problem is rephrased as a communication problem of an (uncoded) lowrank matrix source over an erasure channel. The paper then uses achievability and converse arguments
A Singular Value Thresholding Algorithm for Matrix Completion
, 2008
"... This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task of reco ..."
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Cited by 539 (20 self)
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remarkable features making this attractive for lowrank matrix completion problems. The first is that the softthresholding operation is applied to a sparse matrix; the second is that the rank of the iterates {X k} is empirically nondecreasing. Both these facts allow the algorithm to make use of very minimal
Graph realization and lowrank . . .
, 2012
"... This thesis consists of five chapters, and focuses on two main problems: the graph realization problem with its applications to localization of sensor network and structural biology, and the lowrank matrix completion problem. Chapter 1 is a brief introduction to rigidity theory and supplies the bac ..."
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This thesis consists of five chapters, and focuses on two main problems: the graph realization problem with its applications to localization of sensor network and structural biology, and the lowrank matrix completion problem. Chapter 1 is a brief introduction to rigidity theory and supplies
Depth Enhancement via Lowrank Matrix Completion
"... Depth captured by consumer RGBD cameras is often noisy and misses values at some pixels, especially around object boundaries. Most existing methods complete the missing depth values guided by the corresponding color image. When the color image is noisy or the correlation between color and depth i ..."
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on this subspace constraint, our method formulates depth map enhancement as a lowrank matrix completion problem. Since the rank of a matrix changes over matrices, we develop a datadriven method to automatically determine the rank number for each matrix. The experiments on both public benchmarks and our own
Robust Matrix Completion via Joint Schatten
"... Abstract—The lowrank matrix completion problem is a fundamental machine learning problem with many important applications. The standard lowrank matrix completion methods relax the rank minimization problem by the trace norm minimization. However, this relaxation may make the solution seriously de ..."
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Cited by 3 (1 self)
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Abstract—The lowrank matrix completion problem is a fundamental machine learning problem with many important applications. The standard lowrank matrix completion methods relax the rank minimization problem by the trace norm minimization. However, this relaxation may make the solution seriously
Exact Matrix Completion via Convex Optimization
, 2008
"... We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can perfe ..."
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Cited by 860 (27 self)
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We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can
LowRank Matrix Completion
, 2013
"... While datasets are frequently represented as matrices, realword data is imperfect and entries are often missing. In many cases, the data are very sparse and the matrix must be filled in before any subsequent work can be done. This optimization problem, known as matrix completion, can be made welld ..."
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is convex and can be optimized efficiently, there has been a significant amount of research over the past few years to develop optimization algorithms that perform well. In this report, we review several methods for lowrank matrix completion. The first paper we review presents an iterative algorithm to
Robust video denoising using low rank matrix completion
"... Most existing video denoising algorithms assume a single statistical model of image noise, e.g. additive Gaussian white noise, which often is violated in practice. In this paper, we present a new patchbased video denoising algorithm capable of removing serious mixed noise from the video data. By gr ..."
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Cited by 40 (3 self)
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. By grouping similar patches in both spatial and temporal domain, we formulate the problem of removing mixed noise as a lowrank matrix completion problem, which leads to a denoising scheme without strong assumptions on the statistical properties of noise. The resulting nuclear norm related minimization
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