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At the intersection of mathematics, engineering, and computer
science sits the thriving field of compressive sensing. Based on
the premise that data acquisition and compression can be performed
simultaneously, compressive sensing finds applications in imaging,
signal processing, and many other domains. In the areas of applied
mathematics, electrical engineering, and theoretical computer
science, an explosion of research activity has already followed the
theoretical results that highlighted the efficiency of the basic
principles. The elegant ideas behind these principles are also of
independent interest to pure mathematicians. A Mathematical
Introduction to Compressive Sensing gives a detailed account of the
core theory upon which the field is build. With only moderate
prerequisites, it is an excellent textbook for graduate courses in
mathematics, engineering, and computer science. It also serves as a
reliable resource for practitioners and researchers in these
disciplines who want to acquire a careful understanding of the
subject. A Mathematical Introduction to Compressive Sensing uses a
mathematical perspective to present the core of the theory
underlying compressive sensing.
This contributed volume showcases the most significant results
obtained from the DFG Priority Program on Compressed Sensing in
Information Processing. Topics considered revolve around timely
aspects of compressed sensing with a special focus on applications,
including compressed sensing-like approaches to deep learning;
bilinear compressed sensing - efficiency, structure, and
robustness; structured compressive sensing via neural network
learning; compressed sensing for massive MIMO; and security of
future communication and compressive sensing.
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