Adaptive nonlinear image restoration by a modified Kalman filtering approach

An adaptive nonlinear Kalman-type filter is presented for the restoration of two-dimensional images degraded by general image formation system degradations and additive white noise. A vector difference equation model is used to represent the degradation process. Due to the nonstationarity of an image the object plane distribution function, i.e. the original image, is partitioned into disjoint regions based on the amount of spatial activity in the image. Difference equation models are used to characterize each of the regions of this nonstationary object plane distribution function. Features of the restoration filter include the ability to account for the response of the human visual system to additive noise in the image; a two-dimensional interpolation scheme to improve the estimates of the initial states in each region; and a nearest neighbor algorithm to choose the previous state vector for the state of pixel (i,j).