English

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

Statistics Theory 2017-05-11 v3 Statistics Theory

Abstract

This paper concerns solving the sparse deconvolution and demixing problem using 1,2\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.

Keywords

Cite

@article{arxiv.1609.06357,
  title  = {Sparse Blind Deconvolution and Demixing Through $\ell_{1,2}$-Minimization},
  author = {Axel Flinth},
  journal= {arXiv preprint arXiv:1609.06357},
  year   = {2017}
}

Comments

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

R2 v1 2026-06-22T15:56:00.397Z