Lattice-based multi-channel sampling theorem for linear canonical transform

The multi-channel sampling theorem has flourished as one of the nicest alternatives to the classical Shanon's sampling theorem which relies on non-uniform or multi-channel data acquisition. Although, a primary attempt to study the multi-channel sampling theorem for the multi-dimensional linear canonical transform (LCT) was made by D. Wei and Y. Li (2014) [16], however, it lacks the inherent multidimensional nature in the sense that the associated kernel is a product of N-copies of the usual one dimensional kernel, restricting the degrees of freedom only to three. The goal of this paper is to fill this gap by studying the lattice-based multi-channel sampling theorem for the multi-dimensional LCT with N(2N + 1) degrees of freedom. The idea is accomplished in two steps: firstly, an elegant convolution structure is presented for constructing the multiplicative filters; secondly, the sampling lattices are constructed via general separable and non-separable matrices which often provide more flexibility and better performance in the context of multi-dimensional signal analysis. In the sequel, the Shanon's sampling theorem for the multi-dimensional LCT is deduced as a particular case of the proposed multichannel sampling theorem. Finally, some potential applications including signal reconstruction and image super-resolution are presented to validate the obtained results. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

This paper studies the lattice-based multi-channel sampling theorem for the multi-dimensional linear canonical transform with N(2N+1) degrees of freedom, aiming to fill the gap in existing research. By constructing an elegant convolution structure and utilizing separable and non-separable matrices for sampling lattices, it enhances flexibility and performance in multi-dimensional signal analysis. Finally, Shannon's sampling theorem is derived as a specific case of the proposed multichannel sampling theorem, with potential applications in signal reconstruction and image super-resolution.