Posedness of a band-limited image-extension problem in tomography.

The posedness of extending a band-limited image known only within a cone is considered. The problem is globally ill posed in the sense that the output-error energy cannot be bound over the entire unknown image region corresponding to a given input-data error energy. We demonstrate, however, that the problem is locally well posed in the sense that, within a finite area of the unknown image region, the error can be bound.