Bayesian filters for image estimation

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 squared error (MMSE) estimate of each scene pixel using a fixed lookahead of D rows and D columns of the observations. Our method is based on a simple approximation which facilitates the development of a useful suboptimal nonlinear estimator. In the process, we draw on the well-known reduced update Kalman filter to circumvent computational load problems. A simulation example demonstrates the non-Gaussian nature of the residual for an AR image model and that our algorithm compares favourably with Kalman filtering techniques in such cases