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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.


Papers
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Journal ArticleDOI
TL;DR: A recently emerged signal decomposition model known as convolutional sparse representation (CSR) is introduced into image fusion to address this problem, motivated by the observation that the CSR model can effectively overcome the above two drawbacks.
Abstract: As a popular signal modeling technique, sparse representation (SR) has achieved great success in image fusion over the last few years with a number of effective algorithms being proposed. However, due to the patch-based manner applied in sparse coding, most existing SR-based fusion methods suffer from two drawbacks, namely, limited ability in detail preservation and high sensitivity to misregistration, while these two issues are of great concern in image fusion. In this letter, we introduce a recently emerged signal decomposition model known as convolutional sparse representation (CSR) into image fusion to address this problem, which is motivated by the observation that the CSR model can effectively overcome the above two drawbacks. We propose a CSR-based image fusion framework, in which each source image is decomposed into a base layer and a detail layer, for multifocus image fusion and multimodal image fusion. Experimental results demonstrate that the proposed fusion methods clearly outperform the SR-based methods in terms of both objective assessment and visual quality.

615 citations

Journal ArticleDOI
TL;DR: The Harwell-Boeing sparse matrix collection is described, a set of standard test matrices for sparse matrix problems that comprises problems in linear systems, least squares, and eigenvalue calculations from a wide variety of scientific and engineering disciplines.
Abstract: We describe the Harwell-Boeing sparse matrix collection, a set of standard test matrices for sparse matrix problems. Our test set comprises problems in linear systems, least squares, and eigenvalue calculations from a wide variety of scientific and engineering disciplines. The problems range from small matrices, used as counter-examples to hypotheses in sparse matrix research, to large test cases arising in large-scale computation. We offer the collection to other researchers as a standard benchmark for comparative studies of algorithms. The procedures for obtaining and using the test collection are discussed. We also describe the guidelines for contributing further test problems to the collection.

614 citations

Journal ArticleDOI
TL;DR: The matrix computation language and environment MATLAB is extended to include sparse matrix storage and operations, and nearly all the operations of MATLAB now apply equally to full or sparse matrices, without any explicit action by the user.
Abstract: The matrix computation language and environment MATLAB is extended to include sparse matrix storage and operations. The only change to the outward appearance of the MATLAB language is a pair of commands to create full or sparse matrices. Nearly all the operations of MATLAB now apply equally to full or sparse matrices, without any explicit action by the user. The sparse data structure represents a matrix in space proportional to the number of nonzero entries, and most of the operations compute sparse results in time proportional to the number of arithmetic operations on nonzeros.

613 citations

Proceedings ArticleDOI
29 Jun 2000

609 citations

Proceedings Article
28 Jun 2011
TL;DR: This paper develops "Go Decomposition" (GoDec) to efficiently and robustly estimate the low-rank part L and the sparse part S of a matrix X = L + S + G with noise G to discover the robustness of GoDec.
Abstract: Low-rank and sparse structures have been profoundly studied in matrix completion and compressed sensing. In this paper, we develop "Go Decomposition" (GoDec) to efficiently and robustly estimate the low-rank part L and the sparse part S of a matrix X = L + S + G with noise G. GoDec alternatively assigns the low-rank approximation of X - S to L and the sparse approximation of X - L to S. The algorithm can be significantly accelerated by bilateral random projections (BRP). We also propose GoDec for matrix completion as an important variant. We prove that the objective value ||X - L - S||2F converges to a local minimum, while L and S linearly converge to local optimums. Theoretically, we analyze the influence of L, S and G to the asymptotic/convergence speeds in order to discover the robustness of GoDec. Empirical studies suggest the efficiency, robustness and effectiveness of GoDec comparing with representative matrix decomposition and completion tools, e.g., Robust PCA and OptSpace.

609 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