Sufficient conditions for the uniqueness of solution of the weighted norm minimization problem

Najiya, K Z and Sonkar, Munnu and Sastry, Challa Subrahmanya (2019) Sufficient conditions for the uniqueness of solution of the weighted norm minimization problem. arXiv.org.

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Abstract

Prior support constrained compressed sensing, achieved via the weighted norm minimization, has of late become popular due to its potential for applications. For the weighted norm minimization problem, min∥x∥p,w subject to y=Ax,p=0,1, and w∈[0,1], uniqueness results are known when w=0,1. Here, ∥x∥p,w=w∥xT∥p+∥xTc∥p,p=0,1 with T representing the partial support information. The work reported in this paper presents the conditions that ensure the uniqueness of the solution of this problem for general w∈[0,1].

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