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Author: Vladimir Temlyakov Publisher: Birkhäuser ISBN: 3034808909 Category : Mathematics Languages : en Pages : 261
Book Description
This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and does not require a broad background in the field.
Author: Vladimir Temlyakov Publisher: Birkhäuser ISBN: 3034808909 Category : Mathematics Languages : en Pages : 261
Book Description
This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and does not require a broad background in the field.
Author: Ben Adcock Publisher: SIAM ISBN: 161197688X Category : Mathematics Languages : en Pages : 310
Book Description
Over seventy years ago, Richard Bellman coined the term “the curse of dimensionality” to describe phenomena and computational challenges that arise in high dimensions. These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data. This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods. These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering. It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations. It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques. Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing. It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code. The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book’s companion website (www.sparse-hd-book.com). This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.
Author: V. Temlyakov Publisher: Cambridge University Press ISBN: 1108608639 Category : Mathematics Languages : en Pages :
Book Description
This self-contained, systematic treatment of multivariate approximation begins with classical linear approximation, and moves on to contemporary nonlinear approximation. It covers substantial new developments in the linear approximation theory of classes with mixed smoothness, and shows how it is directly related to deep problems in other areas of mathematics. For example, numerical integration of these classes is closely related to discrepancy theory and to nonlinear approximation with respect to special redundant dictionaries, and estimates of the entropy numbers of classes with mixed smoothness are closely related to (in some cases equivalent to) the Small Ball Problem from probability theory. The useful background material included in the book makes it accessible to graduate students. Researchers will find that the many open problems in the theory outlined in the book provide helpful directions and guidance for their own research in this exciting and active area.
Author: Avishy Y. Carmi Publisher: Springer Science & Business Media ISBN: 364238398X Category : Technology & Engineering Languages : en Pages : 505
Book Description
This book is aimed at presenting concepts, methods and algorithms ableto cope with undersampled and limited data. One such trend that recently gained popularity and to some extent revolutionised signal processing is compressed sensing. Compressed sensing builds upon the observation that many signals in nature are nearly sparse (or compressible, as they are normally referred to) in some domain, and consequently they can be reconstructed to within high accuracy from far fewer observations than traditionally held to be necessary. Apart from compressed sensing this book contains other related approaches. Each methodology has its own formalities for dealing with such problems. As an example, in the Bayesian approach, sparseness promoting priors such as Laplace and Cauchy are normally used for penalising improbable model variables, thus promoting low complexity solutions. Compressed sensing techniques and homotopy-type solutions, such as the LASSO, utilise l1-norm penalties for obtaining sparse solutions using fewer observations than conventionally needed. The book emphasizes on the role of sparsity as a machinery for promoting low complexity representations and likewise its connections to variable selection and dimensionality reduction in various engineering problems. This book is intended for researchers, academics and practitioners with interest in various aspects and applications of sparse signal processing.
Author: Yo-Sung Ho Publisher: Springer ISBN: 3319240781 Category : Computers Languages : en Pages : 683
Book Description
The two-volume proceedings LNCS 9314 and 9315, constitute the proceedings of the 16th Pacific-Rim Conference on Multimedia, PCM 2015, held in Gwangju, South Korea, in September 2015. The total of 138 full and 32 short papers presented in these proceedings was carefully reviewed and selected from 224 submissions. The papers were organized in topical sections named: image and audio processing; multimedia content analysis; multimedia applications and services; video coding and processing; multimedia representation learning; visual understanding and recognition on big data; coding and reconstruction of multimedia data with spatial-temporal information; 3D image/video processing and applications; video/image quality assessment and processing; social media computing; human action recognition in social robotics and video surveillance; recent advances in image/video processing; new media representation and transmission technologies for emerging UHD services.
Author: Stephane Mallat Publisher: Academic Press ISBN: 9780080922027 Category : Technology & Engineering Languages : en Pages : 832
Book Description
Mallat's book is the undisputed reference in this field - it is the only one that covers the essential material in such breadth and depth. - Laurent Demanet, Stanford University The new edition of this classic book gives all the major concepts, techniques and applications of sparse representation, reflecting the key role the subject plays in today's signal processing. The book clearly presents the standard representations with Fourier, wavelet and time-frequency transforms, and the construction of orthogonal bases with fast algorithms. The central concept of sparsity is explained and applied to signal compression, noise reduction, and inverse problems, while coverage is given to sparse representations in redundant dictionaries, super-resolution and compressive sensing applications. Features: * Balances presentation of the mathematics with applications to signal processing * Algorithms and numerical examples are implemented in WaveLab, a MATLAB toolbox New in this edition * Sparse signal representations in dictionaries * Compressive sensing, super-resolution and source separation * Geometric image processing with curvelets and bandlets * Wavelets for computer graphics with lifting on surfaces * Time-frequency audio processing and denoising * Image compression with JPEG-2000 * New and updated exercises A Wavelet Tour of Signal Processing: The Sparse Way, Third Edition, is an invaluable resource for researchers and R&D engineers wishing to apply the theory in fields such as image processing, video processing and compression, bio-sensing, medical imaging, machine vision and communications engineering. Stephane Mallat is Professor in Applied Mathematics at École Polytechnique, Paris, France. From 1986 to 1996 he was a Professor at the Courant Institute of Mathematical Sciences at New York University, and between 2001 and 2007, he co-founded and became CEO of an image processing semiconductor company. Includes all the latest developments since the book was published in 1999, including its application to JPEG 2000 and MPEG-4 Algorithms and numerical examples are implemented in Wavelab, a MATLAB toolbox Balances presentation of the mathematics with applications to signal processing
Author: Yusheng Xue Publisher: Springer ISBN: 981139783X Category : Technology & Engineering Languages : en Pages : 1028
Book Description
This book presents original, peer-reviewed research papers from the 4th Purple Mountain Forum –International Forum on Smart Grid Protection and Control (PMF2019-SGPC), held in Nanjing, China on August 17–18, 2019. Addressing the latest research hotspots in the power industry, such as renewable energy integration, flexible interconnection of large scale power grids, integrated energy system, and cyber physical power systems, the papers share the latest research findings and practical application examples of the new theories, methodologies and algorithms in these areas. As such book a valuable reference for researchers, engineers, and university students.
Author: Mitsuko Aramaki Publisher: Springer ISBN: 3642412483 Category : Computers Languages : en Pages : 502
Book Description
This book constitutes the thoroughly refereed post-conference proceedings of the 9th International Symposium on Computer Music Modeling and Retrieval, CMMR 2012, held in London, UK, in June 2012. The 28 revised full papers presented were carefully reviewed and selected for inclusion in this volume. The papers have been organized in the following topical sections: music emotion analysis; 3D audio and sound synthesis; computer models of music perception and cognition; music emotion recognition; music information retrieval; film soundtrack and music recommendation; and computational musicology and music education. The volume also includes selected papers from the Cross-Disciplinary Perspectives on Expressive Performance Workshop held within the framework of CMMR 2012.
Author: De-Shuang Huang Publisher: Springer Science & Business Media ISBN: 3642148301 Category : Computers Languages : en Pages : 593
Book Description
The International Conference on Intelligent Computing (ICIC) was formed to provide an annual forum dedicated to the emerging and challenging topics in artificial intel- gence, machine learning, pattern recognition, image processing, bioinformatics, and computational biology. It aims to bring together researchers and practitioners from both academia and industry to share ideas, problems, and solutions related to the m- tifaceted aspects of intelligent computing. ICIC 2010, held in Changsha, China, August 18-21, 2010, constituted the 6th - ternational Conference on Intelligent Computing. It built upon the success of ICIC 2009, ICIC 2008, ICIC 2007, ICIC 2006, and ICIC 2005, that were held in Ulsan, Korea, Shanghai, Qingdao, Kunming and Hefei, China, respectively. This year, the conference concentrated mainly on the theories and methodologies as well as the emerging applications of intelligent computing. Its aim was to unify the picture of contemporary intelligent computing techniques as an integral concept that highlights the trends in advanced computational intelligence and bridges theoretical research with applications. Therefore, the theme for this conference was “Advanced Intelligent Computing Technology and Applications.” Papers focusing on this theme were solicited, addressing theories, methodologies, and applications in science and technology.
Author: Vladimir Temlyakov
Author: Vladimir Temlyakov
Author: Ben Adcock 
Author: V. Temlyakov
Author: Avishy Y. Carmi
Author: Joel Aaron Tropp
Author: Yo-Sung Ho
Author: Stephane Mallat
Author: Yusheng Xue
Author: Mitsuko Aramaki
Author: De-Shuang Huang