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Multichannel sampling expansion in the linear canonical transform domain and its application to superresolution
Authors:Deyun Wei  Qiwen Ran  Yuanmin Li
Affiliation:
  • a National Key Laboratory of Tunable Laser Technology, Harbin Institute of Technology, Harbin 150001, China
  • b Natural Science Research Center, Harbin Institute of Technology, Harbin 150001, China
  • c The Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
  • Abstract:The linear canonical transform (LCT) describes the effect of first-order quadratic phase optical system on a wave field. In this paper, we address the problem of signal reconstruction from multichannel samples in the LCT domain based on a new convolution theorem. Firstly, a new convolution structure is proposed for the LCT, which states that a modified ordinary convolution in the time domain is equivalent to a simple multiplication operation for LCT and Fourier transform (FT). Moreover, it is expressible by a one dimensional integral and easy to implement in the designing of filters. The convolution theorem in FT domain is shown to be a special case of our achieved results. Then, a practical multichannel sampling expansion for band limited signal with the LCT is introduced. This sampling expansion which is constructed by the new convolution structure can reduce the effect of spectral leakage and is easy to implement. Last, the potential application of the multichannel sampling is presented to show the advantage of the theory. Especially, the application of multichannel sampling in the context of the image superresolution is also discussed. The simulation results of superresolution are also presented.
    Keywords:Convolution and product theorems   Linear canonical transform   Filtering   Multichannel sampling   Superresolution
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