压缩感知及其图像处理应用研究进展与展望

摘要

Compressed sensing (CS) can perceive the original structure of signals through a few measured values, and reconstruct the signal by solving an optimal problem accurately. The theory of CS not only reduces the cost of the storage and transmission during the acquisition of images and videos, but also provides new opportunities for the follow-up image processing and recognition, promoting the combination of theory and engineering application. This paper presents the principles of CS, and surveys the latest theory achievements and development of sparse representation, design of measurement matrix and reconstruction algorithm. Then this paper analyzes and discusses the research and development of CS theory in its application of image processing field. In the end, the paper points out the existing problems and the future application.%压缩感知理论(Compressed sensing, CS)通过少量的线性测量值感知信号的原始结构,并通过求解最优化问题精确地重构原信号。该理论减少了数字图像及视频获取时的存储及传输代价,也为后续的图像处理及识别的研究提供了新的契机,促进了理论和工程应用的结合。阐述了CS 的基本原理,综述了其关键技术稀疏变换、观测矩阵设计、重构算法的一系列最新理论成果和发展,深入分析和比较了CS 理论应用到图像处理领域的研究和发展状况,总结了其中存在的问题,并对未来的应用前景进行了展望。