The stochastic modeling aspects of image restoration are considered for 2-D nonstationary processes. We develop a space variaflt Roesser madel for such processes, a d deyive prnY&xres for stocha5tic identification ard estimation in the context of a v i s u a l q u a l i t y c r i t e r i a n .

After introducing a two-dimensional (2-D) model for the class of quarter-plane-causal, recursive and separable in denominator (CRSD) filters, a technique for approximating a given 2-D filter by a CRSD one is presented which also yields a model reduction procedure. Both the stability and minimality properties of the approximate model are explored. An example is also given to illustrate the proposed technique.

The restoration of images degraded by an additive white noise is performed by nonlinearly filtering a noisy image. The standard Wiener approach to this problem is modified to take into account the edge information of the image. Various filters of increasing complexity are derived. Experimental results are shown and compared to the standard Wiener filter results and other earlier attempts involving nonstationary filters.

We consider plane-wave motion at normal incidence in a horizontally layered system. The system is assumed lossless, and only the compressional waves are treated. A procedure is introduced for determining the reflection coefficients of the layered system when the observed seismic data may contain random noise. No deconvolution of the measured seismic data is required by the procedure when the input is a narrow wavelet.

A necessary and sufficient condition for a linear sequential circuit to possess a feedforward inverse is given for the class of linear sequential circuits that possess delay-free inverses. Unlike previous work, this condition is given in terms of the difference (state) equation matrices rather than minors of the system transfer-function matrix. The constructive proof yields the following corollary: if a linear sequential circuit requiringnmemory elements has a feedforward delay-free inverse, then there exists at least one such inverse that requires no more thannmemory elements.