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Sharp recovery bounds for convex deconvolution, with applications
Michael B. McCoy,Joel A. Tropp +1 more
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This work introduces a randomized signal model which ensures that the two structures are incoherent, i.e., generically oriented, and describes and analyzes a framework, based on convex optimization, for solving deconvolution problems and many others.About:
The article was published on 2012-05-08 and is currently open access. It has received 44 citations till now. The article focuses on the topics: Deconvolution.read more
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Living on the edge: Phase transitions in convex programs with random data
TL;DR: This paper provides the first rigorous analysis that explains why phase transitions are ubiquitous in random convex optimization problems and introduces a summary parameter, called the statistical dimension, that canonically extends the dimension of a linear subspace to the class of convex cones.
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An Online Algorithm for Separating Sparse and Low-Dimensional Signal Sequences From Their Sum
TL;DR: In this article, a practical recursive projected compressive sensing (Prac-ReProCS) algorithm is proposed for real-time video layering, where the goal is to separate a video sequence into a slowly changing background sequence and a sparse foreground sequence that consists of one or more moving regions/objects on the fly.
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Living on the edge: A geometric theory of phase transitions in convex optimization
TL;DR: A new summary parameter, called the statistical dimension, is introduced that canonically extends the dimension of a linear subspace to the class of convex cones and leads to an approximate version of the conic kinematic formula that gives bounds on the probability that a randomly oriented cone shares a ray with a fixed cone.
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Recursive Robust PCA or Recursive Sparse Recovery in Large but Structured Noise
TL;DR: In this paper, a simple modification of the original ReProCS algorithm is proposed to recover the support set of a slowly changing background (Lt) from moving foreground objects (St) on-the-fly.
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Corrupted Sensing: Novel Guarantees for Separating Structured Signals
Rina Foygel,Lester Mackey +1 more
TL;DR: In this paper, a convex programming approach is used to disentangle signal and corruption, and conditions for exact signal recovery from structured corruption and stable signal recovery with added unstructured noise are provided.
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Compressed sensing
TL;DR: It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients, and a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing.
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Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
TL;DR: In this paper, the authors considered the model problem of reconstructing an object from incomplete frequency samples and showed that with probability at least 1-O(N/sup -M/), f can be reconstructed exactly as the solution to the lscr/sub 1/ minimization problem.
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Atomic Decomposition by Basis Pursuit
TL;DR: Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions.
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Robust principal component analysis
TL;DR: In this paper, the authors prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the e1 norm.
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Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
TL;DR: It is shown that if a certain restricted isometry property holds for the linear transformation defining the constraints, the minimum-rank solution can be recovered by solving a convex optimization problem, namely, the minimization of the nuclear norm over the given affine space.