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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 text provides deep and comprehensive coverage of the
mathematical background for data science, including machine
learning, optimal recovery, compressed sensing, optimization, and
neural networks. In the past few decades, heuristic methods adopted
by big tech companies have complemented existing scientific
disciplines to form the new field of Data Science. This text
embarks the readers on an engaging itinerary through the theory
supporting the field. Altogether, twenty-seven lecture-length
chapters with exercises provide all the details necessary for a
solid understanding of key topics in data science. While the book
covers standard material on machine learning and optimization, it
also includes distinctive presentations of topics such as
reproducing kernel Hilbert spaces, spectral clustering, optimal
recovery, compressed sensing, group testing, and applications of
semidefinite programming. Students and data scientists with less
mathematical background will appreciate the appendices that provide
more background on some of the more abstract concepts.
This text provides deep and comprehensive coverage of the
mathematical background for data science, including machine
learning, optimal recovery, compressed sensing, optimization, and
neural networks. In the past few decades, heuristic methods adopted
by big tech companies have complemented existing scientific
disciplines to form the new field of Data Science. This text
embarks the readers on an engaging itinerary through the theory
supporting the field. Altogether, twenty-seven lecture-length
chapters with exercises provide all the details necessary for a
solid understanding of key topics in data science. While the book
covers standard material on machine learning and optimization, it
also includes distinctive presentations of topics such as
reproducing kernel Hilbert spaces, spectral clustering, optimal
recovery, compressed sensing, group testing, and applications of
semidefinite programming. Students and data scientists with less
mathematical background will appreciate the appendices that provide
more background on some of the more abstract concepts.
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