The relationship analysis between variable selection and basis pursuit

Hongchao Zhou; Zhengming Wang

doi:10.1117/12.652300

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3 November 2005 The relationship analysis between variable selection and basis pursuit

Hongchao Zhou, Zhengming Wang

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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 C_p 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.

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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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