Sparse Blind Deconvolution and Demixing Through ${\ell }_{1,2}$-Minimization

Abstract

This paper concerns solving the sparse deconvolution and demixing problem using ${\ell }_{1,2}$-minimization. We show that under a certain structured random model, robust and stable recovery is possible. The results extend results of Ling and Strohmer [Self Calibration and Biconvex Compressive Sensing, Inverse Problems, 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.

Changes in v2: A few errors were fixed, resulting in slightly different results. Also, some efforts were made to increase readability. Changes in v3: Version accepted for publication

References in corpus (1)

• Self-Calibration and Biconvex Compressive Sensing

Cited by in corpus (4)

• Simultaneous Sparse Recovery and Blind Demodulation
• Timely and Painless Breakups: Off-the-grid Blind Message Recovery and Users' Demixing
• Support Recovery for Sparse Signals with Unknown Non-stationary Modulation
• Recovering Structured Data From Superimposed Non-Linear Measurements