Compressed sensing and related areas: bridging theory with practice

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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).