On Asymptotic Incoherence and Its Implications for Compressed Sensing of Inverse Problems

Recently, it has been shown that incoherence is an unrealistic assumption for compressed sensing when applied to infinite-dimensional inverse problems. Instead, the key property that permits efficient recovery in such problems is so-called asymptotic incoherence. The purpose of this paper is to study this new concept, and its implications towards the design of optimal sampling strategies. We determine how fast the asymptotic incoherence can decay in general for isometries. Furthermore it is shown that Fourier sampling and wavelet sparsity, whilst globally coherent, yield optimal asymptotic incoherence as a power law up to a constant factor. Sharp bounds on the asymptotic incoherence for Fourier sampling with polynomial bases are also provided. A numerical experiment is also presented to demonstrate the role of asymptotic incoherence in finding good subsampling strategies.

• Type: Journal
• Year: 2016
• Where: TIT
• Authors: Alexander Daniel Jones, Ben Adcock, Anders C. Hansen
• Keywords: Education, TIT 2016