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Sparse approximation

About: Sparse approximation is a research topic. Over the lifetime, 18037 publications have been published within this topic receiving 497739 citations. The topic is also known as: Sparse approximation.


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Journal ArticleDOI
TL;DR: This paper finds a simple regularized version of Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of L1-minimization.
Abstract: This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements—L1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of L1-minimization. Our algorithm, ROMP, reconstructs a sparse signal in a number of iterations linear in the sparsity, and the reconstruction is exact provided the linear measurements satisfy the uniform uncertainty principle.

998 citations

Journal ArticleDOI
TL;DR: A novel inpainting algorithm that is capable of filling in holes in overlapping texture and cartoon image layers using a direct extension of a recently developed sparse-representation-based image decomposition method called MCA (morphological component analysis).

974 citations

01 Jan 2010
TL;DR: In this paper, a survey of the major practical algorithms for sparse approximation is presented, focusing on computational issues, circumstances in which individual methods tend to perform well, and theoretical guarantees available.
Abstract: The goal of the sparse approximation problem is to approximate a target signal using a linear combination of a few elementary signals drawn from a fixed collection. This paper surveys the major practical algorithms for sparse approximation. Specific attention is paid to computational issues, to the circumstances in which individual methods tend to perform well, and to the theoretical guarantees available. Many fundamental questions in electrical engineering, statis- tics, and applied mathematics can be posed as sparse approximation problems, making these algorithms versatile and relevant to a plethora of applications.

954 citations

Journal ArticleDOI
TL;DR: A general image fusion framework by combining MST and SR to simultaneously overcome the inherent defects of both the MST- and SR-based fusion methods is presented and experimental results demonstrate that the proposed fusion framework can obtain state-of-the-art performance.

952 citations

Journal ArticleDOI
TL;DR: A simple algorithm for selecting a subset of coordinates with largest sample variances is provided, and it is shown that if PCA is done on the selected subset, then consistency is recovered, even if p(n) ≫ n.
Abstract: Principal components analysis (PCA) is a classic method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. Contemporary datasets often have p comparable with or even much larger than n. Our main assertions, in such settings, are (a) that some initial reduction in dimensionality is desirable before applying any PCA-type search for principal modes, and (b) the initial reduction in dimensionality is best achieved by working in a basis in which the signals have a sparse representation. We describe a simple asymptotic model in which the estimate of the leading principal component vector via standard PCA is consistent if and only if p(n)/n → 0. We provide a simple algorithm for selecting a subset of coordinates with largest sample variances, and show that if PCA is done on the selected subset, then consistency is recovered, even if p(n) ≫ n.

937 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023193
2022454
2021641
2020924
20191,208
20181,371