Two-dimensional nonseparable discrete linear canonical transform based on CM-CC-CM-CC decomposition

TL;DR

This paper introduces a new decomposition method for the 2D nonseparable linear canonical transform that reduces complexity and errors by avoiding affine transformations, enabling more accurate and reversible digital implementations.

Contribution

The paper proposes the CM-CC-CM-CC decomposition for 2D NsLCT, eliminating affine transforms and improving accuracy, complexity, and reversibility over previous methods.

Findings

Higher accuracy in 2D NsLCT implementation

Lower computational complexity

Perfect reversibility of the transform

Abstract

As a generalization of the two-dimensional Fourier transform (2D FT) and 2D fractional Fourier transform, the 2D nonseparable linear canonical transform (2D NsLCT) is useful in optics, signal and image processing. To reduce the digital implementation complexity of the 2D NsLCT, some previous works decomposed the 2D NsLCT into several low-complexity operations, including 2D FT, 2D chirp multiplication (2D CM) and 2D affine transformations. However, 2D affine transformations will introduce interpolation error. In this paper, we propose a new decomposition called CM-CC-CM-CC decomposition, which decomposes the 2D NsLCT into two 2D CMs and two 2D chirp convolutions (2D CCs). No 2D affine transforms are involved. Simulation results show that the proposed methods have higher accuracy, lower computational complexity and smaller error in the additivity property compared with the previous works. Plus, the proposed methods have perfect reversibility property that one can reconstruct the input signal/image losslessly from the output.