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ICASSP
2011
IEEE

Sparse decomposition of transformation-invariant signals with continuous basis pursuit

8 years 3 months ago
Sparse decomposition of transformation-invariant signals with continuous basis pursuit
Consider the decomposition of a signal into features that undergo transformations drawn from a continuous family. Current methods discretely sample the transformations and apply sparse recovery methods to the resulting finite dictionary. These methods do not exploit the underlying continuous structure, thereby limiting the ability to produce sparse solutions. Instead, we employ interpolation functions which linearly approximate the manifold of scaled and transformed features. Coefficients are interpreted as interpolation weights, and we formulate a convex optimization problem for obtaining them, enforcing both reconstruction accuracy and sparsity. We compare our method, which we call continuous basis pursuit (CBP) with the standard basis pursuit approach on a sparse deconvolution task. CBP yields substantially sparser solutions without sacrificing accuracy, and does so with a smaller dictionary. We conclude that for signals generated by transformation-invariant processes, a represe...
Chaitanya Ekanadham, Daniel Tranchina, Eero P. Sim
Added 21 Aug 2011
Updated 21 Aug 2011
Type Journal
Year 2011
Where ICASSP
Authors Chaitanya Ekanadham, Daniel Tranchina, Eero P. Simoncelli
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