压缩传感综述

在传统采样过程中, 为了避免信号失真, 采样频率不得低于信号最高频率的2倍. 然而对于数字图像、视频的获取, 依照香农(Shannon)定理会导致海量采样数据, 大大增加了存储和传输的代价. 近年来, 一种新兴的压缩传感理论为数据采集技术带来了革命性的突破, 得到了研究人员的广泛关注. 压缩传感采用非自适应线性投影来保持信号的原始结构, 能通过数值最优化问题准确重构原始信号. 压缩传感以远低于奈奎斯特频率进行采样, 在压缩成像系统、模拟/信息转换、生物传感等领域有着广阔的应用前景. 本文主要介绍了压缩传感的基本理论及相关应用, 并对其研究前景进行了展望.

A Survey on Compressive Sensing

In the traditional signal sampling process, Shannon theorem must be satisfied for preventing signal distortion. But in some practical applications (such as image and video processing systems), an increased sampling frequency will substantially increase the data storage and transmission costs. Different from the traditional signal acquisition process, compressive sensing, which is a new theory that captures and represents compressible signals at a sampling rate significantly below the Nyquist rate. It first employs nonadaptive linear projections that preserve the structure of the signal, and then the signal reconstruction is conducted using an optimization process from these projections. Compressive sensing has broad applications such as compressive imaging, analog-to-information conversion, biosensing, etc. This paper surveys the principles of compressive sensing and its related applications. Some further work on this theory is also presented.