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Proceedings Paper

Regularization of the image division approach to blind deconvolution
Author(s): Sergio Barraza-Felix; B. Roy Frieden
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Paper Abstract

A problem of blind deconvolution arises when attempting to restore a short-exposure a short-exposure image that has been degraded by random atmospheric turbulence. We attack the problem by using two short-exposure images as data inputs. The Fourier transform of each is taken, an the two are divided. The unknown object spectrum cancels. What remains is the quotient of the two unknown transfer functions that formed the images. These are expressed, via the sampling theorem, as Fourier series in the corresponding PSFs, the unknowns of the problem. Cross-multiplying the division equation gives an equation that is linear in the unknowns. However, the problem is rank deficient in the absence of prior knowledge. We use the prior knowledge that the object and the PSFs have finite support extensions, and also are positive. The linear problem is least-squares solved many times over, assuming different support values and enforcing positivity. The two support values that minimize the rms image data inconsistency define the final solution. This regularizes the solution to the presence of 4-15 percent additive noise of detection.

Paper Details

Date Published: 22 September 1998
PDF: 11 pages
Proc. SPIE 3459, Bayesian Inference for Inverse Problems, (22 September 1998); doi: 10.1117/12.323820
Show Author Affiliations
Sergio Barraza-Felix, Optical Sciences Ctr./Univ. of Arizona (United States)
B. Roy Frieden, Optical Sciences Ctr./Univ. of Arizona (United States)

Published in SPIE Proceedings Vol. 3459:
Bayesian Inference for Inverse Problems
Ali Mohammad-Djafari, Editor(s)

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