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

摘要

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