A Gaussian regularization for derivative sampling interpolation of signals in the linear canonical transform representations
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 deriva...
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| Published in: | Signal, image and video processing Vol. 17; no. 5; pp. 2157 - 2165 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Annaby, M. H. Al-Abdi, I. A. |
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| Cites_doi | 10.1080/01630563.2015.1013550 10.1109/LSP.2010.2048642 10.1093/imanum/dru020 10.1007/s00034-010-9155-y 10.1016/j.sigpro.2005.07.031 10.1016/S0165-1684(03)00196-8 10.1109/97.481159 10.1016/j.sigpro.2009.09.030 10.1109/TSP.2008.929333 10.1109/78.972478 10.1364/JOSAA.27.001885 10.1016/j.sigpro.2010.09.020 10.1109/LSP.2009.2014290 10.1016/j.sigpro.2006.09.008 10.1016/S0165-1684(99)00064-X 10.1109/78.806089 10.1364/OL.33.000228 10.1109/LSP.2011.2172606 10.1109/LSP.2009.2030098 10.1007/BF03549472 10.1063/1.1665805 10.1007/978-1-4939-3028-9 10.1007/s11760-007-0029-0 10.1016/j.sigpro.2014.11.021 10.1016/j.sigpro.2022.108569 10.1109/TSP.2006.880224 10.1007/BF03549439 |
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| SubjectTerms | 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 |
| Title | A Gaussian regularization for derivative sampling interpolation of signals in the linear canonical transform representations |
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