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

Neelamam, Ramesh Neelsh

doi:10.1109/TIP.2007.906251

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

2007-11-01

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Neelamam, Ramesh Neelsh *

Max Deffenbaugh

Richard G. Baraniuk

DOI：10.1109/TIP.2007.906251

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Abstract

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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.

Keywords:

curvelets

deblurring

deconvolution

minimax optimal

multichannel

restoration

sufficient statistics

wavelet-vaguelette

wavelets

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