Quantization, frames, and compressed sensing

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Digital computers and their efficiency at processing data is one of the main driving forces behind much of our modern technology. My research program includes mathematical problems related to acquiring inherently analogue data (e.g., audio and images), converting them to digital bit-streams, and processing the data digitally for several purposes such as denoising and compression. This research proposal is on three main research lines in the areas of applied and computational harmonic analysis, signal processing, and information theory: (i) approximation theory of quantization of redundant expansions, (ii) quantization for compressed sensing, and (iii) various open mathematical problems in the area of sparse approximations and compressed sensing. The interactions between (i) and (ii), i.e., quantization of compressively sampled measurements of sparse signals, are in the focus of this research program.