Stability in blind deconvolution of sparse signals and reconstruction by alternating minimization

Kiryung Lee, Yanjun Li, Marius Junge, Yoram Bresler

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Blind deconvolution is the recovery of two unknown signals from their convolution. To overcome the ill-posedness of this problem, solutions based on priors tailored to specific application have been developed in practical applications. In particular, sparsity models have provided promising priors. In spite of empirical success in many applications, existing analyses are rather limited in two main ways: by disparity between theoretical assumptions on the signal and/or measurement model versus practical setups; or by failure to demonstrate success for parameter values within the optimal regime defined by the information theoretic limits. In particular, it has been shown that a naive sparsity model is not strong enough as a prior for identifiability in blind deconvolution problem. In addition to sparsity, we adopt a conic constraint by Ahmed et al., which enforces flat spectra in the Fourier domain. Under this prior, we provide an iterative algorithm that achieves guaranteed performance in blind deconvolution with number of measurements proportional (up to a logarithmic factor) to the sparsity level of the signal.

Original languageEnglish (US)
Title of host publication2015 International Conference on Sampling Theory and Applications, SampTA 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages158-162
Number of pages5
ISBN (Electronic)9781467373531
DOIs
StatePublished - Jul 2 2015
Event11th International Conference on Sampling Theory and Applications, SampTA 2015 - Washington, United States
Duration: May 25 2015May 29 2015

Publication series

Name2015 International Conference on Sampling Theory and Applications, SampTA 2015

Other

Other11th International Conference on Sampling Theory and Applications, SampTA 2015
CountryUnited States
CityWashington
Period5/25/155/29/15

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ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Signal Processing
  • Statistics and Probability

Cite this

Lee, K., Li, Y., Junge, M., & Bresler, Y. (2015). Stability in blind deconvolution of sparse signals and reconstruction by alternating minimization. In 2015 International Conference on Sampling Theory and Applications, SampTA 2015 (pp. 158-162). [7148871] (2015 International Conference on Sampling Theory and Applications, SampTA 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SAMPTA.2015.7148871