New sampling method associated with arbitrary lattices sampling in the Fourier domain

Abstract Fourier transform (FT) plays an important role in many fields of optics and signal processing. As its fundamental topics, various sampling theories have been established, of course, which include multidimensional (MD) sampling in the FT domain. However, given the deficiency of the existing sampling methods associated with arbitrary lattices sampling, we introduce a new simple method to get alias-free sampling matrix. Then under the premise of alias-free sampling, we drive an easy-to-compute reconstruction formula for MD bandlimited signal, which provides us with a simple way to reconstruct original signal from its sampled vision in terms of an arbitrary frequency support and has never been presented before. Consequently, the MD uniform sampling theorem about arbitrary lattices is proposed. Furthermore, in order to get optimal sampling matrix, we improve this sampling method by applying the idea of segmentation to the bandlimited area. Finally, simulations are presented to prove the rationality of the new sampling method.