Sparse blind deconvolution and demixing through ℓ1,2-minimization

This paper concerns solving the sparse deconvolution and demixing problem using ℓ1,2-minimization. We show that under a certain structured random model, robust and stable recovery is possible. The results extend results of Ling and Strohmer (Inverse Probl. 31, 115002 2015), and in particular theoretically explain certain experimental findings from that paper. Our results do not only apply to the deconvolution and demixing problem, but to recovery of column-sparse matrices in general.

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