Multidimensional state-space model Kalman filtering with application to image restoration

In this paper a set of three-dimensional (3-D) state-space models based on Roesser's model is employed to restore the degraded image by Kalman filtering. The 3-D models extend the regions of the correlation of image pixels and of the point spread function (PSF) of blur to a nonsymmetric half-plane (NSHP). In addition, the correlations of both models may be inseparable in vertical and horizontal directions, so that these models are more compatible with the innate characters of image and blur processes. Furthermore, these two models (image process and PSF of blur) may be reduced to one by merging their signal flow graphs, thus lowering the order of states and simplifying the computational algorithm. A state-space model for strip filtering can then be derived from this merged 3-D model. A numerical example is presented below to illustrate this idea, and a strip filtering model with two scan lines is derived from it for the image restoration. As can be seen from the restored images resulting from the simulation experiment, this 3-D model has been very effective.