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Direct Blind Deconvolution



Alfred S. Carasso


Blind deconvolution seeks to deblur an image without knowing the cause of the blur. Iterative methods are commonly applied to that problem, but the iterative process is slow, uncertain, and often ill-behaved. This paper considers a significant but limited class of blurs that can be expressed as convolutions of 2-D symmetric L vy stable probability density functions. This class includes and generalizes Gaussian and Lorentzian distributions. For such blurs, a method is developed that can detect the point spread function from 1-D Fourier analysis of the blurred image. A separate image deblurring technique uses this detected point spread function to deblur the image. Each of these two steps uses direct non-iterative methods, and requires interactive adjustment of parameters. Using this method, blind deblurring of 512 x 512 images can be accomplished in minutes of CPU time on current desktop workstations. Numerous blind experiments on synthetic data show that for a given blurred image, several distinct point spread functions may be detected that lead to useful yet visually distinct reconstructions.
Siam Journal on Applied Mathematics
Report Number
No. 6


APEX method, blind deconvolution, direct methods, image deblurring, Levy density functions, SECB methods


Carasso, A. (1999), Direct Blind Deconvolution, Siam Journal on Applied Mathematics, [online], (Accessed April 24, 2024)
Created November 1, 1999, Updated October 28, 2011