Two-dimensional nonseparable discrete linear canonical transform based on CM-CC-CM-CC decomposition
Journal
Journal of the Optical Society of America A: Optics and Image Science, and Vision
Journal Volume
33
Journal Issue
2
Pages
214-227
Date Issued
2016-02
Author(s)
Shih-Gu Huang
Abstract
As a generalization of the 2D Fourier transform (2D FT) and 2D fractional Fourier transform, the 2D nonseparable linear canonical transform (2D NsLCT) is useful in optics and 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. 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 a perfect reversibility property, meaning that one can reconstruct the input signal/image losslessly from the output. © 2016 Optical Society of America.
Other Subjects
As a generalization of the 2D Fourier transform (2D FT) and 2D fractional Fourier transform, the 2D nonseparable linear canonical transform (2D NsLCT) is useful in optics and 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. No 2D affine transforms are involved. Simulation results show that the proposed methods have higher accuracy, lower computational complexity, and Image processing; Mathematical transformations; Optical data processing; 2d fourier transforms; Affine transformations; Digital implementation; Fractional Fourier transforms; Interpolation error; Linear canonical transform; Reversibility properties; Signal and image processing; Affine transforms
Type
journal article