Reduced order strip Kalman filtering using singular perturbation method

Abstract

Strip Kalman filtering for restoration of images degraded by linear shift invariant (LSI) blur and additive white Gaussian (WG) noise is considered. The image process is modeled by a 1-D vector autoregressive (AR) model in each strip. It is shown that the composite dynamic model that is obtained by combining the image model and the blur model takes the form of a singularly perturbed system owing to the strong-weak correlation effects within a window. The time scale property of the singularly perturbed system is then utilized to decompose the original system into reduced order subsystems which closely capture the behavior of the full order system. For these subsystems the relevant Kalman filtering equations are given which provide the suboptimal filtered estimates of the image and the one-step prediction estimates of the blur needed for the next stage. Simulation results are also provided.