New results in two-dimensional Kalman filtering with applications to image restoration

This paper describes the application of 2-D Kalman filtering to the restoration of images degraded by linear space invariant (LSI) blur and additive white Gaussian noise (WGN). The image restoration problem is formulated in the framework of the well-known Kalman strip filter. However, the Kalman filtering scheme assumes the availability of a statespace dynamic model for the image process as well as the blur. In the past, most researchers have sought to track the problem of image modeling by making the sometimes unrealistic assumption of separability of the image correlation. A new technique for image modeling which does not make this assumption is proposed. On-line, recursive methods for implementing the modeling algorithm are also presented. We then introduce a novel technique for the state-space realization of separable blurs, since separable 2-D blurs are often encountered in practice and constitute an important subset of 2-D blurs. This state-space model is rendered compatible with strip filtering by using a new recursive scheme which we call as pseudorecursion. An extension for estimating the blur when it is unknown, but can be parameterized, has also been indicated. Simulated experimental results using natural scenery are presented.