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We consider the problem of reconstructing a set of sparse vectors sharing a common sparsity pattern from incomplete measurements. To take account of the joint sparsity and promote the coupling… Click to show full abstract
We consider the problem of reconstructing a set of sparse vectors sharing a common sparsity pattern from incomplete measurements. To take account of the joint sparsity and promote the coupling of nonvanishing components, we employ a convex relaxation approach with mixed norm penalty $\ell_{2,1}$. This paper discusses the computation of the solutions of linear inverse problems with such relaxation by forward-backward splitting algorithm. We establish new strong convergence results for the algorithm, in particular when the set of jointly sparse vectors is infinite.
Journal Title: Set-Valued and Variational Analysis
Year Published: 2021
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