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Bisparse Blind Deconvolution through Hierarchical Sparse Recovery
- Publication Year :
- 2022
-
Abstract
- The bi-sparse blind deconvolution problem is studied -- that is, from the knowledge of $h*(Qb)$, where $Q$ is some linear operator, recovering $h$ and $b$, which are both assumed to be sparse. The approach rests upon lifting the problem to a linear one, and then applying the hierarchical sparsity framework. In particular, the efficient HiHTP algorithm is proposed for performing the recovery. Then, under a random model on the matrix $Q$, it is theoretically shown that an $s$-sparse $h \in \mathbb{K}^\mu$ and $\sigma$-sparse $b \in \mathbb{K}^n$ with high probability can be recovered when $\mu \succcurlyeq s\log(s)^2\log(\mu)\log(\mu n) + s\sigma \log(n)$.<br />Comment: V2: Completely revised version, entirely different proof, resulting in the recovery guarantee improved by a factor s
- Subjects :
- Computer Science - Information Theory
Mathematics - Numerical Analysis
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2210.11993
- Document Type :
- Working Paper