The chapters in this volume highlight the state-of-the-art of compressed sensing and are based on talks given at the third international MATHEON conference on the same topic, held from December 4-8, 2017 at the Techni...
详细信息
ISBN:
(数字)9783319730745
ISBN:
(纸本)9783319730738
The chapters in this volume highlight the state-of-the-art of compressed sensing and are based on talks given at the third international MATHEON conference on the same topic, held from December 4-8, 2017 at the Technical University in Berlin. In addition to methods in compressed sensing, chapters provide insights into cutting edge applications of deep learning in data science, highlighting the overlapping ideas and methods that connect the fields of compressed sensing and deep learning. Specific topics covered include:;This volume will be a valuable resource for graduate students and researchers in the areas of mathematics, computer science, and engineering, as well as other applied scientists exploring potential applications of compressed sensing.
The classical subject of bases in Banach spaces has taken on a new life in the modern development of appliedharmonicanalysis. This textbook is a self-contained introduction to the abstract theory of bases and redund...
详细信息
ISBN:
(数字)9780817646875
ISBN:
(纸本)9780817646868
The classical subject of bases in Banach spaces has taken on a new life in the modern development of appliedharmonicanalysis. This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and their use in both applied and classical harmonicanalysis. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory. Extensive exercises complement the text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses. The self-contained presentation with clear proofs is accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications. No other text develops the ties between classical basis theory and its modern uses in appliedharmonicanalysis.
New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier meth...
详细信息
ISBN:
(数字)9783031350054
ISBN:
(纸本)9783031350047;9783031350078
New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods. To address this growing need, this monograph combines mathematical theory and numerical algorithms to offer a unified and self-contained presentation of Fourier analysis.;The first four chapters of the text serve as an introduction to classical Fourier analysis in the univariate and multivariate cases, including the discrete Fourier transforms, providing the necessary background for all further chapters. Next, chapters explore the construction and analysis of corresponding fast algorithms in the one- and multidimensional cases. The well-known fast Fourier transforms (FFTs) are discussed, as well as recent results on the construction of the nonequispaced FFTs, high-dimensional FFTs on special lattices, and sparse FFTs. An additional chapter is devoted to discrete trigonometric transforms and Chebyshev expansions. The final two chapters consider various applications of numerical Fourier methods for improved function approximation, including Prony methods for the recovery of structured functions.;This new edition has been revised and updated throughout, featuring new material on a new Fourier approach to the ANOVA decomposition of high-dimensional trigonometric polynomials; new research results on the approximation errors of the nonequispaced fast Fourier transform based on special window functions; and the recently developed ESPIRA algorithm for recovery of exponential sums, among others.;will be of interest to graduate students and researchers in applied mathematics, physics, computer science, engineering, and other areas where Fourier methods play an important role in applications.
Recently there has been intense research activity on the subject of wavelet and subband theory. Experts in diverse fields such as mathematics, physics, electrical engineering, and image processing have provided origin...
详细信息
ISBN:
(数字)9781461201137
ISBN:
(纸本)9780817641368;9781461266181
Recently there has been intense research activity on the subject
of wavelet and subband theory. Experts in diverse fields such as
mathematics, physics, electrical engineering, and image processing
have provided original and pioneering works and results. But this
diversity, while rich and productive, has led to a sense of
fragmentation, especially to those new to the field and to
nonspecialists who are trying to understand the connections between
the different aspects of wavelet and subband theory.
`Wavelets and Subbands' is designed to present an understanding
of wavelets and their development from a continuous-domain
transformation to a frame representation and finally to
multiresolution analysis tools such as subband decomposition. The book
presents a theoretical understanding of the subject that is
intertwined with practical examples and applications of wavelets in
ultrasonic and biomedical domains. There is special emphasis on
applications in communications, compression, and image processing.
Topics and Features: * Provides an understanding of the link
between the continuous wavelet transform, the fast wavelet transform,
and subband decomposition * Algorithms and numerical examples are
implemented in MATLAB * Discusses the design of wavelet bases and
details how to implement the transform both in hardware and software *
Covers the fundamentals and the developments of the links between
areas such as time-frequency analysis, digital signal processing,
image processing, and Fourier and wavelet transform, both continuous
and discrete * Offers extended mathematical treatment and numerous
examples, with particular emphasis on the transition from the
continuous domain to multiresolution and subband decomposition.
The book is an essential text and reference for graduates,
researchers, and professionals in electrical engineering,
is a comprehensive exposition on analytic methods for solving science and engineering problems which is written from the unifying viewpoint of distribution theory and enriched with many modern topics which are importa...
详细信息
ISBN:
(数字)9783319979588
ISBN:
(纸本)9783319979571;9783030074272
is a comprehensive exposition on analytic methods for solving science and engineering problems which is written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important to practitioners and researchers. The goal of the book is to give the reader, specialist and non-specialist usable and modern mathematical tools in their research and analysis. This new text is intended for graduate students and researchers in applied mathematics, physical sciences and engineering. The careful explanations, accessible writing style, and many illustrations/examples also make it suitable for use as a self-study reference by anyone seeking greater understanding and proficiency in the problem solving methods presented. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. The present, softcover reprint is designed to make this classic textbookavailable to a wider audience.
暂无评论