Theoretical Foundations And Numerical Methods For Sparse Recovery

Author : Massimo Fornasier
Publisher : Walter de Gruyter
Page : 351 pages
File Size : 45,5 Mb
Release : 2010-07-30
Category : Mathematics
ISBN : 9783110226157

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Theoretical Foundations and Numerical Methods for Sparse Recovery by Massimo Fornasier Pdf

The present collection is the very first contribution of this type in the field of sparse recovery. Compressed sensing is one of the important facets of the broader concept presented in the book, which by now has made connections with other branches such as mathematical imaging, inverse problems, numerical analysis and simulation. The book consists of four lecture notes of courses given at the Summer School on "Theoretical Foundations and Numerical Methods for Sparse Recovery" held at the Johann Radon Institute for Computational and Applied Mathematics in Linz, Austria, in September 2009. This unique collection will be of value for a broad community and may serve as a textbook for graduate courses. From the contents: "Compressive Sensing and Structured Random Matrices" by Holger Rauhut "Numerical Methods for Sparse Recovery" by Massimo Fornasier "Sparse Recovery in Inverse Problems" by Ronny Ramlau and Gerd Teschke "An Introduction to Total Variation for Image Analysis" by Antonin Chambolle, Vicent Caselles, Daniel Cremers, Matteo Novaga and Thomas Pock

Author : Otmar Scherzer
Publisher : Springer Science & Business Media
Page : 1626 pages
File Size : 48,7 Mb
Release : 2010-11-23
Category : Mathematics
ISBN : 9780387929194

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Handbook of Mathematical Methods in Imaging by Otmar Scherzer Pdf

The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Author : Eckhard Hitzer,Stephen J. Sangwine
Publisher : Springer Science & Business Media
Page : 338 pages
File Size : 49,7 Mb
Release : 2013-06-24
Category : Mathematics
ISBN : 9783034806039

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Quaternion and Clifford Fourier Transforms and Wavelets by Eckhard Hitzer,Stephen J. Sangwine Pdf

Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering. This edited volume presents the state of the art in these hypercomplex transformations. The Clifford algebras unify Hamilton’s quaternions with Grassmann algebra. A Clifford algebra is a complete algebra of a vector space and all its subspaces including the measurement of volumes and dihedral angles between any pair of subspaces. Quaternion and Clifford algebras permit the systematic generalization of many known concepts. This book provides comprehensive insights into current developments and applications including their performance and evaluation. Mathematically, it indicates where further investigation is required. For instance, attention is drawn to the matrix isomorphisms for hypercomplex algebras, which will help readers to see that software implementations are within our grasp. It also contributes to a growing unification of ideas and notation across the expanding field of hypercomplex transforms and wavelets. The first chapter provides a historical background and an overview of the relevant literature, and shows how the contributions that follow relate to each other and to prior work. The book will be a valuable resource for graduate students as well as for scientists and engineers.

Author : Yun-Bin Zhao
Publisher : CRC Press
Page : 284 pages
File Size : 49,6 Mb
Release : 2018-07-04
Category : Business & Economics
ISBN : 9781351624152

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Sparse Optimization Theory and Methods by Yun-Bin Zhao Pdf

Seeking sparse solutions of underdetermined linear systems is required in many areas of engineering and science such as signal and image processing. The efficient sparse representation becomes central in various big or high-dimensional data processing, yielding fruitful theoretical and realistic results in these fields. The mathematical optimization plays a fundamentally important role in the development of these results and acts as the mainstream numerical algorithms for the sparsity-seeking problems arising from big-data processing, compressed sensing, statistical learning, computer vision, and so on. This has attracted the interest of many researchers at the interface of engineering, mathematics and computer science. Sparse Optimization Theory and Methods presents the state of the art in theory and algorithms for signal recovery under the sparsity assumption. The up-to-date uniqueness conditions for the sparsest solution of underdertemined linear systems are described. The results for sparse signal recovery under the matrix property called range space property (RSP) are introduced, which is a deep and mild condition for the sparse signal to be recovered by convex optimization methods. This framework is generalized to 1-bit compressed sensing, leading to a novel sign recovery theory in this area. Two efficient sparsity-seeking algorithms, reweighted l1-minimization in primal space and the algorithm based on complementary slackness property, are presented. The theoretical efficiency of these algorithms is rigorously analysed in this book. Under the RSP assumption, the author also provides a novel and unified stability analysis for several popular optimization methods for sparse signal recovery, including l1-mininization, Dantzig selector and LASSO. This book incorporates recent development and the author’s latest research in the field that have not appeared in other books.

Author : Ran He,Baogang Hu,Xiaotong Yuan,Liang Wang
Publisher : Springer
Page : 110 pages
File Size : 52,7 Mb
Release : 2014-08-28
Category : Computers
ISBN : 9783319074160

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Robust Recognition via Information Theoretic Learning by Ran He,Baogang Hu,Xiaotong Yuan,Liang Wang Pdf

This Springer Brief represents a comprehensive review of information theoretic methods for robust recognition. A variety of information theoretic methods have been proffered in the past decade, in a large variety of computer vision applications; this work brings them together, attempts to impart the theory, optimization and usage of information entropy. The authors resort to a new information theoretic concept, correntropy, as a robust measure and apply it to solve robust face recognition and object recognition problems. For computational efficiency, the brief introduces the additive and multiplicative forms of half-quadratic optimization to efficiently minimize entropy problems and a two-stage sparse presentation framework for large scale recognition problems. It also describes the strengths and deficiencies of different robust measures in solving robust recognition problems.

Author : Zhu Han,Mingyi Hong,Dan Wang
Publisher : Cambridge University Press
Page : 375 pages
File Size : 43,8 Mb
Release : 2017-04-27
Category : Computers
ISBN : 9781107124387

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Signal Processing and Networking for Big Data Applications by Zhu Han,Mingyi Hong,Dan Wang Pdf

This unique text helps make sense of big data using signal processing techniques, in applications including machine learning, networking, and energy systems.

Author : Anonim
Publisher : Academic Press
Page : 650 pages
File Size : 47,7 Mb
Release : 2017-12-13
Category : Technology & Engineering
ISBN : 9780128118887

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Academic Press Library in Signal Processing, Volume 7 by Anonim Pdf

Academic Press Library in Signal Processing, Volume 7: Array, Radar and Communications Engineering is aimed at university researchers, post graduate students and R&D engineers in the industry, providing a tutorial-based, comprehensive review of key topics and technologies of research in Array and Radar Processing, Communications Engineering and Machine Learning. Users will find the book to be an invaluable starting point to their research and initiatives. With this reference, readers will quickly grasp an unfamiliar area of research, understand the underlying principles of a topic, learn how a topic relates to other areas, and learn of research issues yet to be resolved. Presents a quick tutorial of reviews of important and emerging topics of research Explores core principles, technologies, algorithms and applications Edited and contributed by international leading figures in the field Includes comprehensive references to journal articles and other literature upon which to build further, more detailed knowledge

Author : Alexandros Iosifidis,Anastasios Tefas
Publisher : Academic Press
Page : 638 pages
File Size : 51,5 Mb
Release : 2022-02-04
Category : Computers
ISBN : 9780323885720

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Deep Learning for Robot Perception and Cognition by Alexandros Iosifidis,Anastasios Tefas Pdf

Deep Learning for Robot Perception and Cognition introduces a broad range of topics and methods in deep learning for robot perception and cognition together with end-to-end methodologies. The book provides the conceptual and mathematical background needed for approaching a large number of robot perception and cognition tasks from an end-to-end learning point-of-view. The book is suitable for students, university and industry researchers and practitioners in Robotic Vision, Intelligent Control, Mechatronics, Deep Learning, Robotic Perception and Cognition tasks. Presents deep learning principles and methodologies Explains the principles of applying end-to-end learning in robotics applications Presents how to design and train deep learning models Shows how to apply deep learning in robot vision tasks such as object recognition, image classification, video analysis, and more Uses robotic simulation environments for training deep learning models Applies deep learning methods for different tasks ranging from planning and navigation to biosignal analysis

Author : Mahdi Khosravy,Nilanjan Dey,Carlos A. Duque
Publisher : Academic Press
Page : 308 pages
File Size : 46,9 Mb
Release : 2020-05-18
Category : Technology & Engineering
ISBN : 9780128212486

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Compressive Sensing in Healthcare by Mahdi Khosravy,Nilanjan Dey,Carlos A. Duque Pdf

Compressive Sensing in Healthcare, part of the Advances in Ubiquitous Sensing Applications for Healthcare series gives a review on compressive sensing techniques in a practical way, also presenting deterministic compressive sensing techniques that can be used in the field. The focus of the book is on healthcare applications for this technology. It is intended for both the creators of this technology and the end users of these products. The content includes the use of EEG and ECG, plus hardware and software requirements for building projects. Body area networks and body sensor networks are explored. Provides a toolbox for compressive sensing in health, presenting both mathematical and coding information Presents an intuitive introduction to compressive sensing, including MATLAB tutorials Covers applications of compressive sensing in health care

Author : Herb Kunze,Davide La Torre,Adam Riccoboni,Manuel Ruiz Galán
Publisher : CRC Press
Page : 530 pages
File Size : 52,8 Mb
Release : 2023-07-26
Category : Technology & Engineering
ISBN : 9781000907872

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Engineering Mathematics and Artificial Intelligence by Herb Kunze,Davide La Torre,Adam Riccoboni,Manuel Ruiz Galán Pdf

Explains the theory behind Machine Learning and highlights how Mathematics can be used in Artificial Intelligence Illustrates how to improve existing algorithms by using advanced mathematics and discusses how Machine Learning can support mathematical modeling Captures how to simulate data by means of artificial neural networks and offers cutting-edge Artificial Intelligence technologies Emphasizes the classification of algorithms, optimization methods, and statistical techniques Explores future integration between Machine Learning and complex mathematical techniques

Author : Simon Foucart,Holger Rauhut
Publisher : Springer Science & Business Media
Page : 625 pages
File Size : 54,8 Mb
Release : 2013-08-13
Category : Computers
ISBN : 9780817649487

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A Mathematical Introduction to Compressive Sensing by Simon Foucart,Holger Rauhut Pdf

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.

Author : Valerio Cambareri
Publisher : Lulu.com
Page : 283 pages
File Size : 47,5 Mb
Release : 2024-06-13
Category : Electronic
ISBN : 9781326226879

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Matrix Designs and Methods for Secure and Efficient Compressed Sensing by Valerio Cambareri Pdf

Author : Bo'az Klartag,Emanuel Milman
Publisher : Springer
Page : 366 pages
File Size : 47,9 Mb
Release : 2017-04-17
Category : Mathematics
ISBN : 9783319452821

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Geometric Aspects of Functional Analysis by Bo'az Klartag,Emanuel Milman Pdf

As in the previous Seminar Notes, the current volume reflects general trends in the study of Geometric Aspects of Functional Analysis, understood in a broad sense. A classical theme in the Local Theory of Banach Spaces which is well represented in this volume is the identification of lower-dimensional structures in high-dimensional objects. More recent applications of high-dimensionality are manifested by contributions in Random Matrix Theory, Concentration of Measure and Empirical Processes. Naturally, the Gaussian measure plays a central role in many of these topics, and is also studied in this volume; in particular, the recent breakthrough proof of the Gaussian Correlation Conjecture is revisited. The interplay of the theory with Harmonic and Spectral Analysis is also well apparent in several contributions. The classical relation to both the primal and dual Brunn-Minkowski theories is also well represented, and related algebraic structures pertaining to valuations and valent functions are discussed. All contributions are original research papers and were subject to the usual refereeing standards.

Author : Liao Heng,Bill McColl
Publisher : Cambridge University Press
Page : 399 pages
File Size : 40,6 Mb
Release : 2021-12-16
Category : Computers
ISBN : 9781316513583

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Mathematics for Future Computing and Communications by Liao Heng,Bill McColl Pdf

A panorama of new ideas in mathematics that are driving innovation in computing and communications.

Author : C.H. Chen
Publisher : CRC Press
Page : 379 pages
File Size : 46,9 Mb
Release : 2017-05-25
Category : Technology & Engineering
ISBN : 9781498774383

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Compressive Sensing of Earth Observations by C.H. Chen Pdf

Future remote sensing systems will make extensive use of Compressive Sensing (CS) as it becomes more integrated into the system design with increased high resolution sensor developments and the rising earth observation data generated each year. Written by leading experts in the field Compressive Sensing of Earth Observations provides a comprehensive and balanced coverage of the theory and applications of CS in all aspects of earth observations. This work covers a myriad of practical aspects such as the use of CS in detection of human vital signs in a cluttered environment and the corresponding modeling of rib-cage breathing. Readers are also presented with three different applications of CS to the ISAR imaging problem, which includes image reconstruction from compressed data, resolution enhancement, and image reconstruction from incomplete data.