Bisparse Blind Deconvolution through Hierarchical Sparse Recovery
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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 ∈𝕂^μ and σ-sparse b ∈𝕂^n with high probability can be recovered when μ≽ s^2log(μ) + s^2σlog(n).
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