When a multidimensional signal is uniformly sampled, its spectrum is replicated. If the signal is band limited and the replications (1) contain regions that are identically zero and (2) are not aliased, then the samples are dependent. Indeed, lost samples can be regained from those remaining. In dimensions greater than one, there are spectral regions of support for which this is the case even when sampling is performed at the Nyquist (minimum) density (e.g., a circular spectral region of support in two dimensions). When the known samples are perturbed by additive noise, lost-sample restoration noise levels in certain cases can be obtained by simple geometrical observations in the frequency domain. The results are specifically applied to coherent and incoherent optical images of objects of finite extent obtained from imaging systems with circular pupils.
© 1986 Optical Society of America
Original Manuscript: July 2, 1984
Manuscript Accepted: September 23, 1985
Published: February 1, 1986
Robert J. Marks, "Multidimensional-signal sample dependency at Nyquist densities," J. Opt. Soc. Am. A 3, 268-273 (1986)