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Proceedings Paper

The relationship analysis between variable selection and basis pursuit
Author(s): Hongchao Zhou; Zhengming Wang
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Paper 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.

Paper Details

Date Published: 3 November 2005
PDF: 9 pages
Proc. SPIE 6044, MIPPR 2005: Image Analysis Techniques, 604409 (3 November 2005); doi: 10.1117/12.652300
Show Author Affiliations
Hongchao Zhou, National Univ. of Defense Technology (China)
Zhengming Wang, National Univ. of Defense Technology (China)

Published in SPIE Proceedings Vol. 6044:
MIPPR 2005: Image Analysis Techniques
Deren Li; Hongchao Ma, Editor(s)

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