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 x i from convolutional measurements yi = 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.

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

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Deconvolution
Convolution
Recovery
Geometry
Experiments

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

Cite this

Global geometry of multichannel sparse blind deconvolution on the sphere. / Li, Yanjun; Bresler, Yoram.

In: Advances in Neural Information Processing Systems, Vol. 2018-December, 01.01.2018, p. 1132-1143.

Research output: Contribution to journalConference article

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