Topic
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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TL;DR: KLU is the default sparse direct solver in the XyceTMcircuit simulation package developed by Sandia National Laboratories and contains Gilbert/Peierls’ sparse left-looking LU factorization algorithm to factorize each block.
Abstract: KLU is a software package for solving sparse unsymmetric linear systems of equations that arise in circuit simulation applications. It relies on a permutation to Block Triangular Form (BTF), several methods for finding a fill-reducing ordering (variants of approximate minimum degree and nested dissection), and Gilbert/Peierls’ sparse left-looking LU factorization algorithm to factorize each block. The package is written in C and includes a MATLAB interface. Performance results comparing KLU with SuperLU, Sparse 1.3, and UMFPACK on circuit simulation matrices are presented. KLU is the default sparse direct solver in the XyceTMcircuit simulation package developed by Sandia National Laboratories.
290 citations
TL;DR: A novel image fusion scheme based on image cartoon-texture decomposition and sparse representation is proposed, which outperforms the state-of-art methods, in terms of visual and quantitative evaluations.
287 citations
20 Jun 2009
TL;DR: Without requiring any prior information of the blur kernel as the input, the proposed approach is able to recover high-quality images from given blurred images and the new sparsity constraints under tight frame systems enable the application of a fast algorithm called linearized Bregman iteration to efficiently solve the proposed minimization problem.
Abstract: Restoring a clear image from a single motion-blurred image due to camera shake has long been a challenging problem in digital imaging. Existing blind deblurring techniques either only remove simple motion blurring, or need user interactions to work on more complex cases. In this paper, we present an approach to remove motion blurring from a single image by formulating the blind blurring as a new joint optimization problem, which simultaneously maximizes the sparsity of the blur kernel and the sparsity of the clear image under certain suitable redundant tight frame systems (curvelet system for kernels and framelet system for images). Without requiring any prior information of the blur kernel as the input, our proposed approach is able to recover high-quality images from given blurred images. Furthermore, the new sparsity constraints under tight frame systems enable the application of a fast algorithm called linearized Bregman iteration to efficiently solve the proposed minimization problem. The experiments on both simulated images and real images showed that our algorithm can effectively removing complex motion blurring from nature images.
285 citations
TL;DR: Experimental results on multi-focus and multi-modal image sets demonstrate that the ASR-based fusion method can outperform the conventional SR-based method in terms of both visual quality and objective assessment.
Abstract: In this study, a novel adaptive sparse representation (ASR) model is presented for simultaneous image fusion and denoising. As a powerful signal modelling technique, sparse representation (SR) has been successfully employed in many image processing applications such as denoising and fusion. In traditional SR-based applications, a highly redundant dictionary is always needed to satisfy signal reconstruction requirement since the structures vary significantly across different image patches. However, it may result in potential visual artefacts as well as high computational cost. In the proposed ASR model, instead of learning a single redundant dictionary, a set of more compact sub-dictionaries are learned from numerous high-quality image patches which have been pre-classified into several corresponding categories based on their gradient information. At the fusion and denoising processes, one of the sub-dictionaries is adaptively selected for a given set of source image patches. Experimental results on multi-focus and multi-modal image sets demonstrate that the ASR-based fusion method can outperform the conventional SR-based method in terms of both visual quality and objective assessment.
284 citations
TL;DR: This work demonstrates how the direction-of-arrival (DOA) estimation problem can be cast as the problem of recovering a joint-sparse representation and proposes to minimize a mixed ℓ2,0 norm approximation to deal with the joint-Sparse recovery problem.
Abstract: A set of vectors is called jointly sparse when its elements share a common sparsity pattern. We demonstrate how the direction-of-arrival (DOA) estimation problem can be cast as the problem of recovering a joint-sparse representation. We consider both narrowband and broadband scenarios. We propose to minimize a mixed l2,0 norm approximation to deal with the joint-sparse recovery problem. Our algorithm can resolve closely spaced and highly correlated sources using a small number of noisy snapshots. Furthermore, the number of sources need not be known a priori. In addition, our algorithm can handle more sources than other state-of-the-art algorithms. For the broadband DOA estimation problem, our algorithm allows relaxing the half-wavelength spacing restriction, which leads to a significant improvement in the resolution limit.
283 citations