On sparsity averaging

2013/07/04 by Carrillo, Rafael E., McEwen, Jason D., Wiaux, Yves
#FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Instrumentation and Methods for Astrophysics (astro-ph.IM)

paper · doi:10.48550/arxiv.1307.1360

Abstract

Recent developments in Carrillo et al. (2012) and Carrillo et al. (2013) introduced a novel regularization method for compressive imaging in the context of compressed sensing with coherent redundant dictionaries. The approach relies on the observation that natural images exhibit strong average sparsity over multiple coherent frames. The associated reconstruction algorithm, based on an analysis prior and a reweighted ℓ₁ scheme, is dubbed Sparsity Averaging Reweighted Analysis (SARA). We review these advances and extend associated simulations establishing the superiority of SARA to regularization methods based on sparsity in a single frame, for a generic spread spectrum acquisition and for a Fourier acquisition of particular interest in radio astronomy.

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