IDENTIFICATION AND RESTORATION OF NOISY AND BLURRED IMAGES (ARMA MODEL, SPECTRAL FACTORIZATION, MAXIMUM LIKELIHOOD, KALMAN FILTERING, ADAPTIVE)

This thesis addresses the problem of identification and restoration of blurred images, given noisy observations. The blurred image is modeled as the output of a noncausal unknown linear system, which is characterized by a finite duration impulse response, called the point spread function (PSF). Two-dimensional Kalman filtering is used for the restoration process.; Unlike the previous deterministic blur identification techniques that search for the zero crossings of the blurred image spectrum, we formulate the PSF identification problem, as an optimal statistical parameter estimation problem. Since the Kalman filter requires the image model parameters as well as the PSF parameters, our method will provide estimates of the both image model and PSF parameters. We represent the degraded image with an autoregressive moving average (ARMA) model, where the image model parameters form the AR part and the PSF parameters form the MA part. The identification of these parameters from noise free and noisy observations are treated separately. The maximum likelihood estimates of the unknown parameters are then obtained as the solution of a set of recursive nonlinear equations. In order to ensure the stability of these recursive equations, the noncausal PSF's were decomposed into their causal and anti-causal parts.; The reduced update Kalman filter (RUKF) has been used as a suboptimal but efficient implementation of the two-dimensional linear shift-invariant Kalman filter. In this thesis, we combined our identification procedure with the RUKF for the restoration of unknown blurs. We investigated the sensitivity of the RUKF to the identified parameters. We also studied the effect of the boundary values in image restoration, and provided suboptimal alternatives for the two-dimensional boundary value set required by the RUKF.; We also extended RUKF to piecewise linear and space-variant restoration of noisy and blurred images. It is shown that a nonlinear and space-variant implementation of the RUKF is capable of preventing ringing, a commonly encountered artifact that is caused by linear shift-invariant image restoration. Furthermore, this extension allows us to restore space-variant blurs, commonly encountered in photographic imaging.; Identification and restoration results both on simulated blurs and real photographic blurs are included. These results are highly promising, and show that we can obtain significant visual and numerical improvements both in the case of simulated and photographically blurred images.