线性正则变换域多通道采样理论及其在图像超分辨重建中的应用

Multichannel sampling is a key technique to improve the rate of the analog-to-digital conversion. However, with the deepening of information technology, the multichannel sampling with traditional Fourier transform domain can not meet the actual needs. In particular, it is unable to handle the sampling reconstruction problem of broadband and non-stationary signals associated with communication, radar information systems. The project will introduce a signal processing technique with linear canonical transform (LCT) domain, and then study multichannel sampling and its applications. According to the time-frequency analysis characteristic of the LCT, multichannel sampling associated with LCT provides a new theoretical tool for the broadband and non-stationary signal reconstruction. Key issues addressed by the project include the following three things. First, establish multichannel sampling theory in LCT domain for one-dimensional and multi-dimensional signals based on the LCT domain filtering ways. Second, develop interpolation and sampling identity structure of band-limited signals in the LCT domain through analyzing sampling rate conversion. Then, design effcient filter bank interpolation and reconstruction methods for one-dimensional and multi-dimensional multichannel sampling using the identity structure. Last, present new image scaling algorithms and image/video super-resolution analysis using multi-dimensional derivative sampling and periodic non-uniform sampling. The scientific significance of the research results will not only lay theoretical foundations for non-stationary signal processing in photovoltaic systems, multiplexer communication technology, as well as the parallel sampling analog-to-digital conversion system design; but also provide new ideas for the image/video resolution analysis.

多通道采样是提高模数转换速率的关键技术，然而随着信息化的不断深入，目前传统傅里叶变换域多通道采样已不能满足实际需要，尤其无法处理通信、雷达信息系统宽带和非平稳信号的采样重建问题。本项目将引入线性正则变换（LCT）域信号处理技术，研究多通道采样重构理论及应用。根据LCT在信号分析中的时频分析特性，其多通道采样理论为宽带非平稳信号重构提供了新的理论工具。项目解决的关键问题包括：借助LCT域滤波方式，建立LCT域一维和多维信号的多通道采样理论；并利用多维导数采样和周期非均匀采样分别给出图像缩放的新算法以及图像/视频的超分辨分析；建立LCT域带限信号插值和采样恒等结构，并据此给出LCT域一维和多维多通道采样的滤波器组高效插值和重建方法。本项目的研究成果将为光电系统非平稳信号处理奠定理论基础；为图像/视频的超分辨分析提供新的研究思路；为通信技术的多路复用以及并行采样模数转换系统设计提供理论依据。

多通道采样是提高模数转换速率的关键技术，然而随着信息化的不断深入，目前传统傅里叶变换域多通道采样已不能满足实际需要，尤其无法处理通信、雷达信息系统宽带和非平稳信号的采样重建问题。本项目引入了线性正则变换（LCT）域信号处理技术，建立了LCT域多通道采样相关理论和多通道采样重建的滤波器组高效实现方法，给出了变换域多通道采样理论在图像超分辨重建应用中的新算法。得出的重要结果包括：根据LCT域的滤波理论，在建立广义滤波和扫频滤波的多通道采样系统模型基础上，得到了LCT域一维带通信号的多通道采样理论。同时，给出一些特例分析。基于多维LCT的表达，得到了LCT域多维带限信号多通道采样重构理论。结合LCT的性质，通过设计特定的滤波器，给出了LCT域多维导数采样以及周期非均匀采样理论。通过研究，还得到了分数傅里叶域多采样率多通道采样相关理论。基于LCT域导数采样理论，分析插值滤波函数的优势，给出了数字图像缩放的多通道采样重构算法，该方法利用图像的导数特性加强图像的高频分量。另外，基于分数变换域导数采样，还给出导数插值数字彩色图像缩放算法。基于LCT域多抽样率转换理论，给出了LCT域一维带限信号插值和采样恒等结构，并据此得到了LCT域一维多通道采样、导数采样以及周期非均匀采样的滤波器组高效插值和重建方法。最后，建立了LCT域多通道采样和滤波器组之间的一一对应关系，并进一步指出可根据LCT域重建滤波器组，给出相应的采样和重建策略。本项目的研究成果将为光电系统非平稳信号处理奠定理论基础；为图像/视频的超分辨分析提供新的研究思路；为通信技术的多路复用以及并行采样模数转换系统设计提供理论依据。