Global geometry of multichannel sparse blind deconvolution on the sphere

Yanjun Li, Yoram Bresler

Research output: Contribution to journalConference article

Abstract

Multichannel blind deconvolution is the problem of recovering an unknown signal f and multiple unknown channels xi from convolutional measurements yi = xi~f (i = 1, 2, . . ., N). We consider the case where the xi'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 yi ~ 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 xi 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.

Original languageEnglish (US)
Pages (from-to)1132-1143
Number of pages12
JournalAdvances in Neural Information Processing Systems
Volume2018-December
StatePublished - Jan 1 2018
Event32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada
Duration: Dec 2 2018Dec 8 2018

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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