Reconstruction of multidimensional bandlimited signals from multichannel samples in linear canonical transform domain
Reconstruction of multidimensional bandlimited signals from multichannel samples in linear canonical transform domain
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DOI：
10.1049/iet-spr.2013.0240
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发表时间：
2014-08
期刊：
影响因子：
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通讯作者：
Deyun Wei;Yuanmin Li
中科院分区：
文献类型：
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作者：
Deyun Wei;Yuanmin Li
线性正则变换（LCT）已被证明是光学和信号处理的有力工具。在本研究中，作者解决了LCT域中多维多通道样本的信号重构问题。首先，提出并解决了多维LCT核在初等函数中的表示问题。然后，他们提出了基于指数函数的基展开的LCT域带限信号的多维多通道采样（MMS）。由普通卷积结构构造的MMS展开可以减小频谱泄漏的影响，且易于实现。第三，在MMS展开的基础上，通过设计系统滤波器传递函数，得到了多维导数采样和周期非均匀采样的重构方法。最后，给出了仿真结果和MMS的应用前景。重点讨论了多维导数采样在图像超分辨率缩放中的应用。
The linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing. In this study, the authors address the problem of signal reconstruction from the multidimensional multichannel samples in the LCT domain. Firstly, they pose and solve the problem of expressing the kernel of the multidimensional LCT in the elementary functions. Then, they propose the multidimensional multichannel sampling (MMS) for the bandlimited signal in the LCT domain based on a basis expansion of an exponential function. The MMS expansion which is constructed by the ordinary convolution structure can reduce the effect of the spectral leakage and is easy to implement. Thirdly, based on the MMS expansion, they obtain the reconstruction method for the multidimensional derivative sampling and the periodic non-uniform sampling by designing the system filter transfer functions. Finally, the simulation results and the potential applications of the MMS are presented. Especially, the application of the multidimensional derivative sampling in the context of the image scaling about the image super-resolution is discussed.