Non-Convex Recovery from Phaseless Low-Resolution Blind Deconvolution Measurements using Noisy Masked Patterns

Samuel Pinilla, Kumar Vijay Mishra, Brian M. Sadler

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Abstract

This paper addresses recovery of a kernel h n and a signal x n from the low-resolution phaseless measurements of their noisy circular convolution y = |Flo(x h)|2 + η, where Flom×n stands for a partial discrete Fourier transform (m < n), η models the noise, and |•| is the element-wise absolute value function. This problem is severely ill-posed because both the kernel and signal are unknown and, in addition, the measurements are phaseless, leading to many x-h pairs that correspond to the measurements. Therefore, to guarantee a stable recovery of x and h from y, we assume that the kernel h and the signal x lie in known subspaces of dimensions k and s, respectively, such that m ≫ k + s. We solve this problem by proposing a blind deconvolution algorithm for phaseless super-resolution (BliPhaSu) to minimize a non-convex least-squares objective function. The method first estimates a low-resolution version of both signals through a spectral algorithm, which are then refined based upon a sequence of stochastic gradient iterations. We show that our BliPhaSu algorithm converges linearly to a pair of true signals on expectation under a proper initialization that is based on spectral method. Numerical results from experimental data demonstrate perfect recovery of both h and x using our method.

Original languageEnglish
Title of host publication55th Asilomar Conference on Signals, Systems and Computers, ACSSC 2021
EditorsMichael B. Matthews
PublisherIEEE
Pages876-880
Number of pages5
ISBN (Electronic)9781665458283
DOIs
Publication statusPublished - 2021
Publication typeA4 Article in a conference publication
EventAsilomar Conference on Signals, Systems, and Computers - Pacific Grove, United States
Duration: 31 Oct 20213 Nov 2021

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers
Volume2021-October
ISSN (Print)1058-6393

Conference

ConferenceAsilomar Conference on Signals, Systems, and Computers
Country/TerritoryUnited States
CityPacific Grove
Period31/10/213/11/21

Keywords

  • Blind deconvolution
  • masked diffraction patterns
  • non-convex optimization
  • phase retrieval
  • super-resolution

Publication forum classification

  • Publication forum level 1

ASJC Scopus subject areas

  • Signal Processing
  • Computer Networks and Communications

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