This book is a detailed and self-contained introduction to the rich and elegant mathematical theory of compressive sensing. It also serves as a reliable resource for practitioners and researchers in these disciplines who want to acquire a careful understanding of the subject. With only moderate prerequisites, it is an excellent textbook for graduate courses in mathematics, engineering, and computer science. A Mathematical Introduction to Compressive Sensing 1§? An extensive bibliography with over 500 references that guide researchers through the literature. 0000048845 00000 n Part of Springer Nature. 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. With only moderate prerequisites, it 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. x�mRKN�0=��0˲���^! 26 0 obj << /Linearized 1 /L 685745 /H [ 824 186 ] /O 29 /E 52229 /N 5 /T 685181 >> endobj xref 26 15 0000000016 00000 n 0000001145 00000 n With only moderate prerequisites, A Mathematical Introduction to Compressive Sensing is an excellent textbook for graduate courses in mathematics, engineering, and computer science. 0000047741 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 ^ … With only moderate prerequisites, A Mathematical Introduction to Compressive Sensing is an excellent textbook for graduate courses in mathematics, engineering, and computer science. Chapter 2 Page 45, Remark 2.8 is incorrect, hence Exercise 2.2 should be discarded. Over 10 million scientific documents at your fingertips. 0000000673 00000 n Introduction to Compressed Sensing 5 p= 1 p= 2 p= 1 p= 1 2 Figure 1.1 Unit spheres in R2 for the ‘ p norms with p = 1 ;2 1, and for the ‘ p quasinorm with p = 1 2. the linear structure that we often desire, namely that if we add two signals 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. T�`���@�@> q���8��Uټ��ͼy�7"���3p���rpVY%�UM,A� 5�A��&�Ж���d�n�'"�6d�(j6#�MQ�g`� �U�T1 ���Q��u��M��. 0000001717 00000 n With only moderate prerequisites, it is an excellent textbook for graduate courses in mathematics, engineering, and computer science. 0000001010 00000 n Request PDF | A mathematical introduction to compressive sensing | At the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing. 0000049930 00000 n 0000000728 00000 n A Mathematical Introduction to Compressive Sensing gives a detailed account of the core theory upon which the field is build. It introduces the standard compressive problem studied throughout the book and reveals its ubiquity in many concrete situations by providing a selection of motivations, applications, and extensions of the theory. A Mathematical Introduction to Compressive Sensing Simon Foucart and Holger Rauhut This list was last updated on July 29, 2020. CS theory asserts that one can recover certain signals and images from far fewer samples or measurements than tradition- al methods use. %PDF-1.2 %���� Contents 1 An Invitation to Compressive Sensing 1 1.1 What is Compressive Sensing? Not logged in 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- tion. 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 This first chapter formulates the objectives of compressive sensing. An Introduction To Compressive Sampling ... MARCH 2008. Request PDF | On Jan 1, 2013, S. Foucart and others published A mathematical introduction to compressive sensing | Find, read and cite all the research you need on ResearchGate

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