Last January, I was honored to be invited in RWTH Aachen University by Holger Rauhut and Sjoerd Dirksen to give a talk on the general topic of quantized compressed sensing. In particular, I decided to focus my presentation on the quasi-isometric embeddings arising in 1-bit compressed sensing, as developed by a few researchers in this field (e.

\(\newcommand{\cl}{\mathcal}\newcommand{\bb}{\mathbb}%\)
Last January, I was honored to be invited in RWTH Aachen University by Holger Rauhut and Sjoerd Dirksen to give a talk on the general topic of quantized compressed sensing.

Abstract: The advent of Compressed Sensing (CS) ten years ago has precipitated a radical re-thinking of signal acquisition, sensing, processing and transmission system design. A significant aspect of such systems is quantization (or digitization) of the acquired data before further processing or for the purpose of transmission and compression.

Abstract: In 1733, Georges-Louis Leclerc, Comte de Buffon in France, set the ground of geometric probability theory by defining an enlightening problem: What is the probability that a needle thrown randomly on a ground made of equispaced parallel strips lies on two of them?

Abstract: Quantization is an essential step in digitizing signals, and, therefore, an indispensable component of any modern acquisition system. This chapter explores the interaction of quantization and compressive sensing and examines practical quantization strategies for compressive acquisition systems.

Abstract: In 1733, Georges-Louis Leclerc, Comte de Buffon in France, set the ground of geometric probability theory by defining an enlightening problem: What is the probability that a needle thrown randomly on a ground made of equispaced parallel strips lies on two of them?

Abstract: Schlieren deflectometry aims at measuring deflections of light rays from transparent objects, which is subsequently used to characterize the objects. With each location on a smooth object surface a sparse deflection map (or spectrum) is associated.

Abstract: In this work, we show that reconstructing a sparse signal from quantized compressive measurement can be achieved in an unified formalism whatever the (scalar) quantization resolution, i.e., from 1-bit to high resolution assumption.