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: A locality Weighted Sparse Representation based Classification (WSRC) method is proposed, which utilizes both data locality and linearity; it can be regarded as extensions of SRC, but the coding is local.
229 citations
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TL;DR: The audio inpainting framework that recovers portions of audio data distorted due to impairments such as impulsive noise, clipping, and packet loss is proposed and this approach is shown to outperform state-of-the-art and commercially available methods for audio declipping in terms of Signal-to-Noise Ratio.
Abstract: We propose the audio inpainting framework that recovers portions of audio data distorted due to impairments such as impulsive noise, clipping, and packet loss. In this framework, the distorted data are treated as missing and their location is assumed to be known. The signal is decomposed into overlapping time-domain frames and the restoration problem is then formulated as an inverse problem per audio frame. Sparse representation modeling is employed per frame, and each inverse problem is solved using the Orthogonal Matching Pursuit algorithm together with a discrete cosine or a Gabor dictionary. The Signal-to-Noise Ratio performance of this algorithm is shown to be comparable or better than state-of-the-art methods when blocks of samples of variable durations are missing. We also demonstrate that the size of the block of missing samples, rather than the overall number of missing samples, is a crucial parameter for high quality signal restoration. We further introduce a constrained Matching Pursuit approach for the special case of audio declipping that exploits the sign pattern of clipped audio samples and their maximal absolute value, as well as allowing the user to specify the maximum amplitude of the signal. This approach is shown to outperform state-of-the-art and commercially available methods for audio declipping in terms of Signal-to-Noise Ratio.
229 citations
Book•
01 Sep 2006
TL;DR: Direct Methods For Sparse Linear CSPARSE A Concise Sparse Matrix Package in C direct methods for sparse matrix solution.
Abstract: Iterative Methods for Sparse Linear Systems Direct methods for sparse linear systems IWR: Home Direct Methods for Sparse Linear Systems | Society for ... Direct Methods for Sparse Linear Systems: MATLAB sparse ... (PDF) Parallel Direct Methods For Sparse Linear Systems Direct Methods for Sparse Matrices Univerzita Karlova Iterative Methods for Sparse Linear Systems Second Edition Direct Methods for Sparse Linear Systems MATLAB ... Direct Methods for Sparse Linear Systems YouTube Direct Methods for Sparse Linear Systems by Timothy A ... A survey of direct methods for sparse linear systems Direct methods for sparse matrix solution Scholarpedia 01: direct methods for sparse linear systems (lecture 1 of 42) Direct Methods for Sparse Linear Systems (Fundamentals of ... Direct Methods For Sparse Linear CSPARSE A Concise Sparse Matrix Package in C [PDF] Download Direct Methods For Sparse Linear Systems ... Direct Methods for Sparse Linear Systems | Request PDF
229 citations
TL;DR: This work proposes a versatile convex variational formulation for optimization over orthonormal bases that covers a wide range of problems, and establishes the strong convergence of a proximal thresholding algorithm to solve it.
Abstract: The notion of soft thresholding plays a central role in problems from various areas of applied mathematics, in which the ideal solution is known to possess a sparse decomposition in some orthonormal basis. Using convex-analytical tools, we extend this notion to that of proximal thresholding and investigate its properties, providing, in particular, several characterizations of such thresholders. We then propose a versatile convex variational formulation for optimization over orthonormal bases that covers a wide range of problems, and we establish the strong convergence of a proximal thresholding algorithm to solve it. Numerical applications to signal recovery are demonstrated.
229 citations
TL;DR: This paper reviews the literature on sparse high dimensional models and discusses some applications in economics and finance, including variable selection methods that are proved to be effective in high dimensional sparse modeling.
Abstract: This article reviews the literature on sparse high-dimensional models and discusses some applications in economics and finance. Recent developments in theory, methods, and implementations in penalized least-squares and penalized likelihood methods are highlighted. These variable selection methods are effective in sparse high-dimensional modeling. The limits of dimensionality that regularization methods can handle, the role of penalty functions, and their statistical properties are detailed. Some recent advances in sparse ultra-high-dimensional modeling are also briefly discussed.
228 citations