ABSTRACT
The reconstruction of multidimensional signals, in particular the band-limited ones, from their values at a discrete set of sample points is of great importance in many applications, such as image processing, acoustics and geophysics. There are several results on the uniqueness of such reconstructions. For example, as we have seen in Theorem 3.9, any band-limited function f( x ) defined on ℜ N https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136905/8d9d10fc-52c4-499e-9d59-3190680e8bbd/content/eq1351.tif"/> is uniquely determined by its values at an appropriate set of points { x k }. However, when it comes down to the problem of how to reconstruct f( x ) from its values {( x k }, especially when the sample points { x k } are irregularly spaced, only a few answers seem to exist and most of them do not go beyond the obvious generalizations of the one-dimensional case.
