Tight Performance Bounds for Compressed Sensing With Group Sparsit

Ranjan, S and Mathukumalli, V (2017) Tight Performance Bounds for Compressed Sensing With Group Sparsit. In: 3rd Indian Control Conference (ICC), JAN 04-06, 2017, Indian Inst Technol Guwahati Campus, Guwahati, INDIA.

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Abstract

Compressed sensing refers to the recovery of a high-dimensional but sparse vector using a small number of linear measurements. Minimizing the l(1)-norm is among the more popular approaches for compressed sensing. A recent paper has provided the "best possible" bounds for l(1)-norm minimization to achieve robust sparse recovery (a formal statement of compressed sensing). In some applications, "group sparsity" is more natural than conventional sparsity. In this paper we have presented sufficient conditions for l(1)-norm minimization to achieve robust group sparse recovery. When specialized to conventional sparsity, these conditions reduce to the known "best possible" bounds proved earlier. We have also derived bounds for the l(p)-norm of the residual error between the true vector and its approximation, for all p is an element of [1, 2]. These bounds are new even for conventional sparsity and of course also for group sparsity.

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