An adaptive nonlinear Kalman-type filter is presented in this dissertation for the restoration of two-dimensional images degraded by general image formation system degradations and additive white noise. A vector difference evaluation model is used to model the degradation process. The object plane distribution function is partitioned into disjoint regions based on the amount of spatial activity in the image, and difference evaluation models are used to characterize the object plane distribution function.

It is shown that each of the regions can be uniquely characterized by their second order statistics. The autocorrelation function for each region is then used to determine the coefficients of the difference evaluation model for each region. Recursive estimation techniques are applied to a composite difference evaluation model.

If the images are to be restored for human viewing it is desirable to account for the response of the human visual system as part of the receiver characteristics. This is done by weighting the variance of the additive noise by a visibility function. where the visibility function is a subjective measure of the visibility of additive noise in an image by the human visual system. As a consequence. the resulting effective variance depends nonlinearly on the state.

Two additional features are added to the new restoration filter to solve problems arising in the implementation phase. A nearest neighbor algorithm is proposed for the selection of a previously processed pixel for providing the previous state vector for the state OT pixel (i, j). Secondly, a two-dimensional interpolation scheme is proposed to improve the estimates of the initial states for each region.