Blind restoration of noisy blurred image using a constrained maximum likelihood method

This paper focuses on blur estimation for image restoration. In real-life applications, blur characteristics are usually unknown, and the point spread function (PSF) must be determined from the degraded image. The identification and restoration procedure uses the fast Kalman filter structure. Processing on columns is decorrelated by first applying fast Fourier transform on the rows. To overcome the boundary problems, a mirror image is used. The 2-D identification and restoration problem is then transformed into a set of N 1-D identification and restoration problems on the columns. If the blur is assumed to be linear and spatially invariant, the problem is to estimate the coefficients of the PSF. This function extends over a large but limited number of pixels, thus leading to a large number of parameters that must be evaluated. The usual procedures for ARMA parameter estimation have failed in image parameter estimation, primarily due to the size of the MA part. The parameters are then constrained to be smooth by assuming that they are on a continuous function such as a Gaussian, polynomial, or wavelet function. The estimation then consists in evaluating hyperparameters computed by optimization of a likelihood function. The global procedure involves recursively estimating the unknown parameters using the maximum likelihood method, and restoring the image using the Kalman filter. Results are presented for an artificially blurred gray-level image.