A note on compressed sensing of structured sparse wavelet coefficients from subsampled Fourier measurements
Functional Analysis
2014-06-17 v2
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].
Cite
@article{arxiv.1403.6541,
title = {A note on compressed sensing of structured sparse wavelet coefficients from subsampled Fourier measurements},
author = {Ben Adcock and Anders C. Hansen and Bogdan Roman},
journal= {arXiv preprint arXiv:1403.6541},
year = {2014}
}
Comments
8 pages, companion paper