Sparse representations and approximation theory
نویسندگان
چکیده
منابع مشابه
Sparse representations and approximation theory
This paper is an attempt to both expound and expand upon, from an approximation theorist’s point of view, some of the theoretical results that have been obtained in the sparse representation (compressed sensing) literature. In particular, we consider in detail l1 -approximation, which is fundamental in the theory of sparse representations, and the connection between the theory of sparse represe...
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We present some results obtained recently in signal processing in the so-called “sparse representations” domain and indicate how they can be applied to a very specific and limited problem in realization theory. This is mainly to bring these type of results to the knowledge of this community. Other applications in order estimation for instance are potentially feasible. The basic problem is the f...
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Cleaning of noise from signals is a classical and long-studied problem in signal processing. For signals that admit sparse representations over a known dictionary, MAP-based denoising seeks the sparsest representation that synthesizes a signal close to the corrupted one. While this task is NP-hard, it can usually be approximated quite well by a greedy method, such as the Orthogonal Matching Pur...
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Relation between a family of generalized Support Vector Machine (SVM) problems and the novel -sparse representation is provided. In defining -sparse representations, we use a natural generalization of the classical insensitive cost function for vectors. The insensitive parameter of the SVM problem is transformed into component-wise insensitivity and thus overall sparsification is replaced by co...
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Relation between a family of generalized Support Vector Machine (SVM) problems and the novel 2-sparse representation is provided. In defining 2-sparse representations, we use a natural generalization of the classical 2-insensitive cost function for vectors. The insensitive parameter of the SVM problem is transformed into component-wise insensitivity and thus overall sparsification is replaced b...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2011
ISSN: 0021-9045
DOI: 10.1016/j.jat.2010.10.007