Publisher Summary This chapter offers information on space-variant image restoration. The inhomogeneity assumption introduced in this chapter allows the edges to be directly taken into account by the image model. A stochastic image-generating process is so obtained describing the gray level discontinuities by a space-varying model, where only the information on edge location is needed. Consequently, the optimal restoration procedure is guaranteed by the corresponding nonstationary Kalman filter. Blurring is intrinsically avoided because at any pixel the estimate is obtained by using the information carried by the neighboring pixels belonging to a convex set contained in the same subregion. The information on edge location can be obtained by an edge-detector operator, whose main feature should be robustness with respect to noise. In discussing Kalman filtering, a brief account on the Kalman approach to the filtering of noisy signals is presented. The discussion is on sampled signals as all the data processing is currently performed by means of computers; moreover, the mathematics involved is greatly simplified. The chapter presents the constitutive equation, discusses space-variant realization of the image, explains deblurring, and so on.