Recursive estimation of images using non-Gaussian autoregressive models

We consider recursive estimation of images modeled by non-Gaussian autoregressive (AR) models and corrupted by spatially white Gaussian noise. The goal is to find a recursive algorithm to compute a near minimum mean square error (MMSE) estimate of each pixel of the scene using a fixed lookahead of D rows and D columns of the observations. Our method is based on a simple approximation that makes possible the development of a useful suboptimal nonlinear estimator. The algorithm is first developed for a non-Gaussian AR time-series and then generalized to two dimensions. In the process, we draw on the well-known reduced update Kalman filter (KF) technique of Woods and Radewan (1977) to circumvent computational load problems. Several examples demonstrate the non-Gaussian nature of residuals for AR image models and that our algorithm compares favorably with the Kalman filtering techniques in such cases