Chapter

Scale Space and Variational Methods in Computer Vision

Volume 4485 of the series Lecture Notes in Computer Science pp 80-91

Best Basis Compressed Sensing

  • Gabriel PeyréAffiliated withCeremade, Université Paris Dauphine, Place du Maréchal De Lattre De Tassigny, 75775 Paris Cedex 16

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Abstract

This paper proposes an extension of compressed sensing that allows to express the sparsity prior in a dictionary of bases. This enables the use of the random sampling strategy of compressed sensing together with an adaptive recovery process that adapts the basis to the structure of the sensed signal. A fast greedy scheme is used during reconstruction to estimate the best basis using an iterative refinement. Numerical experiments on sounds and geometrical images show that adaptivity is indeed crucial to capture the structures of complex natural signals.