Tight performance bounds for compressed sensing with group sparsity

Ranjan, Shashank and Vidyasagar, Mathukumalli (2017) Tight performance bounds for compressed sensing with group sparsity. In: Control Conference (ICC), 2017 Indian, 4-6 Jan. 2017, 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 ℓ1-norm is among the more popular approaches for compressed sensing. A recent paper has provided the "best possible" bounds for ℓ1-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 ℓ1-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 ℓp-norm of the residual error between the true vector and its approximation, for all p ϵ [1, 2]. These bounds are new even for conventional sparsity and of course also for group sparsity.

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