A Gaussian regularization for derivative sampling interpolation of signals in the linear canonical transform representations

• Published in: Signal, image and video processing Vol. 17; no. 5; pp. 2157 - 2165
• Main Authors: Annaby, M. H., Al-Abdi, I. A.
• Format: Journal Article
• Language: English
• Published: London Springer London 01-07-2023; Springer Nature B.V
• Subjects: Computer Imaging; Computer Science; Image processing; Image Processing and Computer Vision; Image reconstruction; Interpolation; Multimedia Information Systems; Original Paper; Pattern Recognition and Graphics; Regularization; Representations; Sampling; Signal,Image and Speech Processing; Vision; Sampling theory; Linear canonical transform; Truncation and amplitude errors
• ISSN: 1863-1703; 1863-1711
• DOI: 10.1007/s11760-022-02430-w

The linear canonical transform (LCT) plays an important role in signal and image processing from both theoretical and practical points of view. Various sampling representations for band-limited and non-band-limited signals in the LCT domain have been established. We focus in this paper on the derivative sampling reconstruction, where the reconstruction procedure utilizes samples of both the signal and its first derivative. Our major aim was to incorporate the reconstruction sampling operator with a Gaussian regularization kernel, which on the one hand is applicable for not necessarily band-limited signals and on the other hand hastens the convergence of the reconstruction procedure. The amplitude error is also considered with deriving rigorous estimates. The obtained theoretical results are tested through various simulated experiments.