The University of Montana
Department of Mathematical Sciences

Technical report #2/2006

A Computational Method for the Restoration of Images with an Unknown, Spatially-Varying Blur

John Bardsley
University of Montana

Stuart Jefferies
Maui Scientific Research Center

James Nagy
Emory University

and

Robert Plemmons
Wake Forest University

Abstract

In this paper, we present an algorithm for the restoration of images with an unknown, spatially-varying blur. Existing computational methods for image restoration require the assumption that the blur is known and/or spatially-invariant. Our algorithm uses a combination of techniques. First, we section the image, and then treat the sections as a sequence of frames whose unknown PSFs are correlated and approximately spatially-invariant. To estimate the PSFs in each section, phase diversity is used. With the PSF estimates in hand, we then use a technique by Nagy and O'Leary for the restoration of images with a known, spatially-varying blur to restore the image globally. Test results on star cluster data are presented.

Keywords: Image reconstruction-restoration, Atmospheric turbulence, Inverse problems, Phase retrieval

AMS Subject Classification: 65F20, 65F30

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