  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.
