Texas two-step: a framework for optimal multi-input single-output deconvolution.
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.
Neelamani
Ramesh
R
ExxonMobil Upstream Research Company, Houston, TX 77252-2189, USA. ramesh.neelamani@exxonmobil.com
Deffenbaugh
Max
M
Baraniuk
Richard G
RG
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