Reduced order strip Kalman filtering using singular perturbation method

Strip Kalman filtering for restoration of images degraded by linear-shift-invariant blur and additive white Gaussian noise is considered. The image process is modeled by a large-order perturbed vector AR (autoregressive) model which takes into account the strong-weak correlation effects within a window. It has been 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. The time-scale property of this singularly perturbed system is then utilized to decompose the large-order system into a reduced-order subsystem which closely captures the behavior of the original system. For this subsystem the relevant Kalman filtering equations are obtained which at each stage provide the suboptimal filtered estimates of the image and the one-step prediction estimates of the blur that are needed for the next stage.<>