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3 November 2005 The relationship analysis between variable selection and basis pursuit
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Proceedings Volume 6044, MIPPR 2005: Image Analysis Techniques; 604409 (2005) https://doi.org/10.1117/12.652300
Event: MIPPR 2005 SAR and Multispectral Image Processing, 2005, Wuhan, China
Abstract
In signal processing, great interest has been widely focused on the sparsest represent. Variable selection is a principle for decomposing a signal into "optimal" superposition bases, where optimal means having small value under some criterion among all such decomposition. Basis pursuit is a principle for decomposing a signal into "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients instead of l0 among all such decomposition. In this paper we present a relation between the variable selection and basis pursuit. After the most widely used Cp criterion is further discussed, variable selection is extended to the overcomplete dictionaries case. Based on the equivalence conditions of l1 norm and l0 in signal decomposing, the relationship between variable selection method and the basis pursuit is discussed. Finally, the example of spectrum estimation is given to demonstrate the equivalence of these two methods.
© (2005) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Hongchao Zhou and Zhengming Wang "The relationship analysis between variable selection and basis pursuit", Proc. SPIE 6044, MIPPR 2005: Image Analysis Techniques, 604409 (3 November 2005); https://doi.org/10.1117/12.652300
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