Compressed sensing and related areas: bridging theory with practice

从20世纪80年代中期开始，应用和计算谐波分析社区构建了构建块（例如，小波和曲线），允许对许多感兴趣的信号（例如，自然图像和音频）进行有效分解。这一领域的活动导致了工业的根本变化，为数字革命做出了贡献。小波技术已经渗透到许多相关领域，包括图像压缩、模式识别、雷达、医学成像和地球物理学。构建这些构建块的主要动机之一是获得实际感兴趣的信号的稀疏近似。这项研究为一项新技术打开了大门：压缩传感（CS）。

Starting in the mid 1980s, the applied and computational harmonic analysis community constructed building blocks (e.g., wavelets and curvelets) that allow for efficient decomposition of many signals of interest (e.g., natural images and audio). The activity in this area led to fundamental changes in industry that have contributed to the digital revolution. Wavelet techniques have penetrated many related areas, including image compression, pattern recognition, radar, medical imaging, and geophysics. One of the main motivations when constructing these building blocks was to obtain sparse approximations for signals of practical interest. This research opened the door to a new technology: compressed sensing (CS).