Multichannel Sparse Blind Deconvolution on the Sphere

Yanjun Li; Yoram Bresler

ICASSP 2019accepted0 citations

Multichannel Sparse Blind Deconvolution on the Sphere

Abstract

Multichannel blind deconvolution is the problem of recovering an unknown signal f and multiple unknown channels x i from convolutional measurements y i = x i ⊕ f (i = 1, 2, ..., N). We consider the case where the x i 's are sparse, and convolution with f is invertible. Our nonconvex optimization formulation solves for a filter h on the unit sphere that produces sparse output y i ⊕ h. Under some technical assumptions, we show that all local minima of the objective function correspond to the inverse filter of f up to an inherent sign and shift ambiguity, and all saddle points have strictly negative curvatures. This geometric structure allows successful recovery of f and x i using a simple manifold gradient descent algorithm with random initialization. Our theoretical findings are complemented by numerical experiments, which demonstrate superior performance of the proposed approach over the previous methods.

BibTeX

@inproceedings{icassp2019_multichannelspar,
  title = {Multichannel Sparse Blind Deconvolution on the Sphere},
  author = {Yanjun Li and Yoram Bresler},
  booktitle = {ICASSP 2019},
  year = {2019}
}