2014/02/21 by Alex D. Jones, Ben Adcock, Jones, Alex D. +3
Computer Science · Engineering · #FOS: Computer and information sciences #FOS: Mathematics #Image and Signal Denoising Methods #Information Theory (cs.IT) #Numerical Analysis (math.NA) #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1402.5324
openalex publication_date 2014/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, it has been shown that incoherence is an unrealistic assumption for\ncompressed sensing when applied to many inverse problems. Instead, the key\nproperty that permits efficient recovery in such problems is so-called local\nincoherence. Similarly, the standard notion of sparsity is also inadequate for\nmany real world problems. In particular, in many applications, the optimal\nsampling strategy depends on asymptotic incoherence and the signal sparsity\nstructure. The purpose of this paper is to study asymptotic incoherence and its\nimplications towards the design of optimal sampling strategies and efficient\nsparsity bases. It is determined how fast asymptotic incoherence can decay in\ngeneral for isometries. Furthermore it is shown that Fourier sampling and\nwavelet sparsity, whilst globally coherent, yield optimal asymptotic\nincoherence as a power law up to a constant factor. Sharp bounds on the\nasymptotic incoherence for Fourier sampling with polynomial bases are also\nprovided. A numerical experiment is also presented to demonstrate the role of\nasymptotic incoherence in finding good subsampling strategies.\n