压缩感知：信号处理的范式转变
Compressive sensing: a paradigm shift in signal processing
摘要：
我们调查一个新的范例，在信号处理称为“压缩传感”。与基于Shannon-Nyquist采样原理的数据采集和重建的旧实践相反，新理论表明，可以从远小于图像/信号的期望分辨率的样本个数准确地甚至精确地重建科学感兴趣的图像或信号，例如，图像中的像素数。这种新技术借鉴了几个数学领域的成果，包括代数、优化、概率论和调和分析。我们将讨论压缩感知背后的一些关键数学思想，以及它对其他领域的影响：数值分析，信息论，理论计算机科学和工程。
英文摘要：
We survey a new paradigm in signal processing known as "compressive sensing". Contrary to old practices of data acquisition and reconstruction based on the Shannon-Nyquist sampling principle, the new theory shows that it is possible to reconstruct images or signals of scientific interest accurately and even exactly from a number of samples which is far smaller than the desired resolution of the image/signal, e.g., the number of pixels in the image. This new technique draws from results in several fields of mathematics, including algebra, optimization, probability theory, and harmonic analysis. We will discuss some of the key mathematical ideas behind compressive sensing, as well as its implications to other fields: numerical analysis, information theory, theoretical computer science, and engineering.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
