Multichannel Sparse Blind Deconvolution on the Sphere
arXiv:1805.10437
Abstract
Multichannel blind deconvolution is the problem of recovering an unknown signal and multiple unknown channels from their circular convolution (). We consider the case where the 's are sparse, and convolution with is invertible. Our nonconvex optimization formulation solves for a filter on the unit sphere that produces sparse output . Under some technical assumptions, we show that all local minima of the objective function correspond to the inverse filter of up to an inherent sign and shift ambiguity, and all saddle points have strictly negative curvatures. This geometric structure allows successful recovery of and using a simple manifold gradient descent (MGD) algorithm. Our theoretical findings are complemented by numerical experiments, which demonstrate superior performance of the proposed approach over the previous methods.
arXiv comment50 pages, 10 figures. Some of the results in this paper were presented at NeurIPS 2018
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