Parameter estimation for image restoration

Image restoration has been investigated for the past two decades and numerous optimal filters have been proposed. In each case a criterion is chosen and an optimal solution is derived. However these filters can only be described as optimal in ideal settings; in practice they are implemented with incomplete prior knowledge based on real images resulting in sub-optimal performance. Often overlooked, yet critical to practical performance, is the accuracy of the underlying models and their parameters used in the implementation. In practice the method used to estimate the required model parameters plays a critical role in the filter performance. Issues concerning the estimation of these parameters and the consequence of using inaccurately-estimated parameters in optimally-derived restoration are investigated.; This thesis first investigates the Wiener restoration of images in a practical setting where the unknown filter parameters, specifically the image autocorrelation, are estimated from the only available to-be-restored degraded image.; An iterative procedure, the so-called iterative Wiener filter which successively uses the Wiener-filtered signal as an improved prototype to update the covariance estimates, is examined next. The convergence of this iterative procedure is analyzed. It has been shown that the procedure does not terminate at the true covariance. Based on the analysis, two new iterative filters are proposed.; Another iterative approach to estimate the autocovariance, the expectation-maximization (EM) algorithm, is investigated and shown to be identical to one of the proposed new filters. The EM-estimated parameters converge to the maximum likelihood estimates, which are subsequently applied to an optimal restoration filter. However, the maximum likelihood parameters yield unacceptable restoration results due to error in the covariance estimates.; A direct method of using the observed degraded image to obtain the maximum likelihood (ML) estimate of the image autocovariance is investigated. Improvements to this ML point estimate are further proposed including, a weighted estimate, and methods of regularization to address the ill-conditioned nature of restoration.; A number of experiments and comparative studies were conducted in a practical setting to demonstrate the effectiveness of the proposed methods.