Texas two-step: A framework for optimal multi-input single-output deconvolution

Ramesh Neelsh Neelamani, Max Deffenbaugh, Richard G. Baraniuk

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

Multi-input single-output deconvolution (MISO-D) aims to extract a deblurred estimate of a target signal from several blurred and noisy observations. This paper develops a new two step framework - Texas Two-Step-to solve MISO-D problems with known blurs. Texas Two-Step first reduces the MISO-D problem to a related single-input single-output deconvolution (SISO-D) problem by invoking the concept of sufficient statistics (SSs) and then solves the simpler SISO-D problem using an appropriate technique. The two-step framework enables new MISO-D techniques (both optimal and suboptimal) based on the rich suite of existing SISO-D techniques. In fact, the properties of SSs imply that a MISO-D algorithm is mean-squared-error optimal if and only if it can be rearranged to conform to the Texas Two-Step framework. Using this insight, we construct new wavelet- and curvelet-based MISO-D algorithms with asymptotically optimal performance. Simulated and real data experiments verify that the framework is indeed effective.

Original languageEnglish (US)
Pages (from-to)2752-2765
Number of pages14
JournalIEEE Transactions on Image Processing
Volume16
Issue number11
DOIs
StatePublished - Nov 1 2007

Keywords

  • Curvelets
  • Deblurring
  • Deconvolution
  • Minimax optimal
  • Multichannel
  • Restoration
  • Sufficient statistics
  • Wavelet-vaguelette
  • Wavelets

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Graphics and Computer-Aided Design
  • Software
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Computer Vision and Pattern Recognition

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