Reconstruction of two-dimensional signals from nonuniform samples or partial information

Abstract

The necessary and sufficient conditions for a set of nonuniform samples to determine a band-limited two-dimensional signal are discussed. The relationship between this set and the zero-crossing contours of any band-limited signal is elaborated. In general, the sampling set should not be a subset of the zero-crossing contours of functions of the same bandwidth. However, it is difficult to check whether nonuniform samples are a subset of zero-crossing contours, but some sufficient conditions and examples are discussed. Furthermore, these concepts are applied to the problem of reconstructing a two-dimensional signal from partial information.