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Basis pursuit

Shaobing Chen, David L. Donoho

Abstract

The time-frequency and time-scale communities have recently developed an enormous number of over-complete signal dictionaries, wavelets, wavelet packets, cosine packets, Wilson bases, chirplets, warped bases, and hyperbolic cross bases being a few examples. Basis pursuit is a technique for decomposing a signal into an optimal superposition of dictionary elements. The optimization criterion is the l/sup 1/ norm of coefficients. The method has several advantages over matching pursuit and best ortho basis, including super-resolution and stability. >

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Key concepts: Matching pursuit, Basis pursuit, Basis (linear algebra), Wavelet, Superposition principle, Computer science, Wavelet packet decomposition, Norm (philosophy)