Recursive blind image deconvolution via dispersion minimization

• Published in: International journal of adaptive control and signal processing 2005-10, Vol.19 (8), p.601-622
• Main Authors: Vural, C., Sethares, W. A.
• Format: Article
• Language: English
• Subjects: blind image deconvolution; Blinds; blur identification; Computer simulation; constant modulus algorithm; Deconvolution; Dispersions; FIR filters; image restoration; local stability analysis; Mathematical analysis; Recursion; recursive adaptive filtering
• ISSN: 0890-6327; 1099-1115
• DOI: 10.1002/acs.867

This paper presents an adaptive autoregressive (AR) approach to the blind image deconvolution problem which has several advantages over standard adaptive FIR filters. There is no need to figure out the optimum filter support when using an AR deconvolution filter because it is the same as the support of the blur. Thus there is no distortion introduced by the finite support of the FIR filter. While an FIR filter provides an approximate inverse to the blur at convergence, the AR filter converges to an approximation of the blur itself. Hence, the method can be used for blur identification. Simulations suggest that convergence of the adaptive AR filter coefficients occur rapidly and the improvement in signal‐to‐noise ratios are higher than in the FIR case for a given blur (and with the same step‐size for the adaptive algorithms). When the adaptive AR method is derived naively to minimize the dispersion, it requires a recursion within a recursion which is computationally complex. We propose a simplification that removes the inner recursion, and prove conditions under which this simplification is valid when dealing with binary images. Simulations are used to show that the method may also be applied to certain multi‐valued images as well. Copyright © 2005 John Wiley & Sons, Ltd.