A note on compressed sensing of structured sparse wavelet coefficients from subsampled Fourier measurements

2014/03/26 by Adcock, Ben, Hansen, Anders C., Roman, Bogdan
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1403.6541

Abstract

This note complements the paper "The quest for optimal sampling: Computationally efficient, structure-exploiting measurements for compressed sensing" [2]. Its purpose is to present a proof of a result stated therein concerning the recovery via compressed sensing of a signal that has structured sparsity in a Haar wavelet basis when sampled using a multilevel-subsampled discrete Fourier transform. In doing so, it provides a simple exposition of the proof in the case of Haar wavelets and discrete Fourier samples of more general result recently provided in the paper "Breaking the coherence barrier: A new theory for compressed sensing" [1].

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