压缩感知理论及其在成像技术中的应用

在传统的Shannon/Nyquist采样定理指导下,信号处理往往面临两大难题:A/D转换器技术的限制和海量采样数据的处理压力.压缩感知(CS)理论表明当信号具有稀疏性或可压缩性时,可以通过全局非自适应线性投影的方式,用远低于Shannon/Nyquist采样定理要求的频率获取信号的全部信息.以CS理论为基础的压缩成像(CI)技术在近年来得到了快速的发展.在概述CS理论的基础上,着重介绍了CI技术的原理及其发展状况,并从稀疏分解、观测矩阵的构造和重建算法3个方面对其关键问题进行了分析.CI系统可以显著节省感光器件的数量,避免了传统成像技术"先采样再压缩"方式带来的资源浪费.

Compressive sensing theory and its application in imaging technology

Under the guidance of the traditional Shannon/Nyquist sampling theorem,signal processing often faces two problems: technology limitation of the A/D converter and processing pressure caused by a mass of sampled data.Compressive sensing(CS) theory suggests that when the signal is sparse or compressible,by means of global non-adaptive linear projection,all the signal information can be obtained with the samples much less than the sampling theorem required.CS theory based compressive imaging(CI) technology has been developed significantly in recent years.This paper first reviewed the principles of CS,and on this basis,discussed the theory and development of CI technology.The key issues of CI were also analyzed from three aspects of sparse decomposition,construction of measurement matrix,and the reconstruction algorithm.The CI system can significantly cut down on the number of photosensitive devices to avoid resource waste caused by a traditional "sample-then-compress" framework.