title: Texas two-step: a framework for optimal multi-input single-output deconvolution.
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.
authors.affiliation: ExxonMobil Upstream Research Company, Houston, TX 77252-2189, USA. ramesh.neelamani@exxonmobil.com
authors.forename: Ramesh
authors.initials: R
authors.lastname: Neelamani
authors.forename: Max
authors.initials: M
authors.lastname: Deffenbaugh
authors.forename: Richard G
authors.initials: RG
authors.lastname: Baraniuk
mesh_terms: D000465:Algorithms; D016477:Artifacts; D001185:Artificial Intelligence; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D012044:Regression Analysis; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity