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arXiv · 1911.08840

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

K. Z. Najiya·Munnu Sonkar·C. S. Sastry
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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, $$ min \|x\|_{p,w} \text{ subject to } y=Ax, \; p=0,1, \text{ and } w \in [0,1], $$ uniqueness results are known when $w=0,1$. Here, $\|x\|_{p,w}=w\|x_T\|_p+\|x_{T^c}\|_p, \; p=0,1$ 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 $w \in [0,1]$.

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K. Z. Najiya, Munnu Sonkar, C. S. Sastry. 2019-11-20. Sufficient conditions for the uniqueness of solution of the weighted norm minimization problem. https://arxiv.org/abs/1911.08840

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