0000001288 00000 n 0000047741 00000 n 0000048845 00000 n A Mathematical Introduction to Compressive Sensing 1§? Birkhäuser . x�mRKN�0=��0˲���^! 0000049930 00000 n 1 1.2 Applications, Motivations, and Extensions 8 1.3 Overview of the Book 23 Notes 33 2 Sparse Solutions of Underdetermined Systems 41 2.1 Sparsity and Compressibility 41 2.2 Minimal Number of Measurements 48 2.3 NP-Hardness of ^ … 209.126.8.79, https://doi.org/10.1007/978-0-8176-4948-7, Springer Science+Business Media New York 2013, Sparse Solutions of Underdetermined Systems, Instance Optimality and Quotient Property, Random Sampling in Bounded Orthonormal Systems, Lossless Expanders in Compressive Sensing, Recovery of Random Signals using Deterministic Matrices. Compressed sensing and images Two differences with the CS framework introduced above: 1 images are almost sparse 2 images are (almost) sparse not in the canonical basis but in some other (wavelet) basis. 0000001145 00000 n Chapter 2 Page 45, Remark 2.8 is incorrect, hence Exercise 2.2 should be discarded. At the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing. � endstream endobj 40 0 obj 80 endobj 29 0 obj << /Type /Page /Parent 28 0 R /MediaBox [ 0 0 409.920 643.200 ] /Resources 30 0 R /Contents 31 0 R /Tabs /S >> endobj 30 0 obj << /ProcSet [ /PDF /Text /ImageB ] /Font << /F0 35 0 R /F2 36 0 R /F1 37 0 R /F3 38 0 R >> /XObject << /im1 33 0 R >> >> endobj 31 0 obj << /Length 32 0 R /Filter /FlateDecode >> stream Not affiliated © 2020 Springer Nature Switzerland AG. With only moderate prerequisites, it is an excellent textbook for graduate courses in mathematics, engineering, and computer science. %PDF-1.2 %���� 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. 0000000824 00000 n A Mathematical Introduction to Compressive Sensing gives a detailed account of the core theory upon which the field is build. Request PDF | A mathematical introduction to compressive sensing | At the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing. With only moderate prerequisites, A Mathematical Introduction to Compressive Sensing is an excellent textbook for graduate courses in mathematics, engineering, and computer science. This first chapter formulates the objectives of compressive sensing. CS theory asserts that one can recover certain signals and images from far fewer samples or measurements than tradition- al methods use. This article surveys the theory of compressive sampling, also known as compressed sensing or CS, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisi- ... various subdisciplines within the applied mathematical sci-ences, most notably probability theory. With only moderate prerequisites, A Mathematical Introduction to Compressive Sensing is an excellent textbook for graduate courses in mathematics, engineering, and computer science. It presents all the necessary background material without assuming any special prior knowledge—just basic analysis, linear algebra, and probability theory. Based on the premise that data acquisition and compression … It concludes with an overview of the book that summarizes the content of each of the following chapters. Two consequences: 1 our procedures will be asked to "adapt" to this almost sparse situation: stability property 2 we need to introduce astuctured sparsity: being sparse in some general
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