22 September 1998 Regularization of the image division approach to blind deconvolution
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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.
© (1998) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Sergio Barraza-Felix, Sergio Barraza-Felix, B. Roy Frieden, B. Roy Frieden, } "Regularization of the image division approach to blind deconvolution", Proc. SPIE 3459, Bayesian Inference for Inverse Problems, (22 September 1998); doi: 10.1117/12.323820; https://doi.org/10.1117/12.323820
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