The relationship analysis between variable selection and basis pursuit

Hongchao Zhou; Zhengming Wang

doi:10.1117/12.652300

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

Hongchao Zhou, Zhengming Wang

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.

Citation Download Citation

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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KEYWORDS

Feature selection

Associative arrays

Chemical elements

Superposition

Signal processing

Transform theory

Chemical species

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