Multiresolution Signal Decomposition
Multiresolution Signal Decomposition

Author: Paul A. Haddad

Publisher: Academic Press

Published: 2012-12-02

Total Pages: 389

ISBN-13: 0323138365

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This book provides an in-depth, integrated, and up-to-date exposition of the topic of signal decomposition techniques. Application areas of these techniques include speech and image processing, machine vision, information engineering, High-Definition Television, and telecommunications. The book will serve as the major reference for those entering the field, instructors teaching some or all of the topics in an advanced graduate course and researchers needing to consult an authoritative source.n The first book to give a unified and coherent exposition of multiresolutional signal decomposition techniquesn Classroom tested textbook clearly describes the commonalities among three key methods-transform coding, and wavelet transformsn Gives comparative performance evaluations of many proposed techniques

Multiresolution Signal and Geometry Processing: Filter Banks, Wavelets, and Subdivision (Version: 2013-09-26)
Multiresolution Signal and Geometry Processing: Filter Banks, Wavelets, and Subdivision (Version: 2013-09-26)

Author: Michael D. Adams

Publisher: Michael Adams

Published: 2013-09-26

Total Pages: 580

ISBN-13: 1550585088

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This book is intended for use in the teaching of graduate and senior undergraduate courses on multiresolution signal and geometry processing in the engineering and related disciplines. It has been used for several years for teaching purposes in the Department of Electrical and Computer Engineering at the University of Victoria and has been well received by students. This book provides a comprehensive introduction to multiresolution signal and geometry processing, with a focus on both theory and applications. The book has two main components, corresponding to multiresolution processing in the contexts of: 1) signal processing and 2) geometry processing. The signal-processing component of the book studies one-dimensional and multi-dimensional multirate systems, considering multirate structures such as sampling-rate converters, filter banks, and transmultiplexers. A particularly strong emphasis is placed on filter banks. Univariate and multivariate wavelet systems are examined, with the biorthogonal and orthonormal cases both being considered. The relationship between filter banks and wavelet systems is established. Several applications of filter banks and wavelets in signal processing are covered, including signal coding, image compression, and noise reduction. For readers interested in image compression, a detailed overview of the JPEG-2000 standard is also provided. Some other applications of multirate systems are considered, such as transmultiplexers for communication systems (e.g., multicarrier modulation). The geometry-processing component of the book studies subdivision surfaces and subdivision wavelets. Some mathematical background relating to geometry processing is provided, including topics such as homogeneous coordinate transformations, manifolds, surface representations, and polygon meshes. Several subdivision schemes are examined in detail, including the Loop, Kobbelt sqrt(3), and Catmull-Clark methods. The application of subdivision surfaces in computer graphics is considered. A detailed introduction to functional analysis is provided, for those who would like a deeper understanding of the mathematics underlying wavelets and filter banks. For those who are interested in software applications of the material covered in the book, appendices are included that introduce the CGAL and OpenGL libraries. Also, an appendix on the SPL library (which was developed for use with this book) is included. Throughout the book, many worked-through examples are provided. Problem sets are also provided for each major topic covered.

Multiscale and Multiresolution Methods
Multiscale and Multiresolution Methods

Author: Timothy J. Barth

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 396

ISBN-13: 3642562051

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Many computionally challenging problems omnipresent in science and engineering exhibit multiscale phenomena so that the task of computing or even representing all scales of action is computationally very expensive unless the multiscale nature of these problems is exploited in a fundamental way. Some diverse examples of practical interest include the computation of fluid turbulence, structural analysis of composite materials, terabyte data mining, image processing, and a multitude of others. This book consists of both invited and contributed articles which address many facets of efficient multiscale representation and scientific computation from varied viewpoints such as hierarchical data representations, multilevel algorithms, algebraic homogeni- zation, and others. This book should be of particular interest to readers interested in recent and emerging trends in multiscale and multiresolution computation with application to a wide range of practical problems.

Geometry, Morphology, and Computational Imaging
Geometry, Morphology, and Computational Imaging

Author: Tetsuo Asano

Publisher: Springer Science & Business Media

Published: 2003-04-08

Total Pages: 449

ISBN-13: 3540009167

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This book constitutes the thoroughly refereed post-proceedings of the 11th International Workshop on Theoretical Foundations of Computer Vision, held in Dagstuhl Castle, Germany in April 2002. The 27 revised full papers presented went through two rounds of reviewing and improvement and assess the state of the art in geometry, morphology, and computational imaging. The papers are organized in sections on geometry - models and algorithms; property measurement in the grid and on finite samples; features, shape, and morphology; and computer vision and scene analysis.

Mathematical Morphology and Its Applications to Signal and Image Processing
Mathematical Morphology and Its Applications to Signal and Image Processing

Author: Jón Atli Benediktsson

Publisher: Springer

Published: 2015-05-15

Total Pages: 761

ISBN-13: 3319187201

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This book contains the thoroughly refereed proceedings of the 12th International Symposium on Mathematical Morphology, ISMM 2015 held in Reykjavik, Iceland, in May 2015. The 62 revised full papers were carefully reviewed and selected from 72 submissions. The papers are organized in topical sections on evaluations and applications; hierarchies; color, multivalued and orientation fields; optimization, differential calculus and probabilities; topology and discrete geometry; and algorithms and implementation.

Space, Structure and Randomness
Space, Structure and Randomness

Author: Michel Bilodeau

Publisher: Springer Science & Business Media

Published: 2007-12-23

Total Pages: 402

ISBN-13: 0387291156

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Space, structure, and randomness: these are the three key concepts underlying Georges Matheron’s scientific work. He first encountered them at the beginning of his career when working as a mining engineer, and then they resurfaced in fields ranging from meteorology to microscopy. What could these radically different types of applications possibly have in common? First, in each one only a single realisation of the phenomenon is available for study, but its features repeat themselves in space; second, the sampling pattern is rarely regular, and finally there are problems of change of scale. This volume is divided in three sections on random sets, geostatistics and mathematical morphology. They reflect his professional interests and his search for underlying unity. Some readers may be surprised to find theoretical chapters mixed with applied ones. We have done this deliberately. GM always considered that the distinction between the theory and practice was purely academic. When GM tackled practical problems, he used his skill as a physicist to extract the salient features and to select variables which could be measured meaningfully and whose values could be estimated from the available data. Then he used his outstanding ability as a mathematician to solve the problems neatly and efficiently. It was his capacity to combine a physicist’s intuition with a mathematician’s analytical skills that allowed him to produce new and innovative solutions to difficult problems. The book should appeal to graduate students and researchers working in mathematics, probability, statistics, physics, spatial data analysis, and image analysis. In addition it will be of interest to those who enjoy discovering links between scientific disciplines that seem unrelated at first glance. In writing the book the contributors have tried to put GM’s ideas into perspective. During his working life, GM was a genuinely creative scientist. He developed innovative concepts whose usefulness goes far beyond the confines of the discipline for which they were originally designed. This is why his work remains as pertinent today as it was when it was first written.

Sparse Image and Signal Processing
Sparse Image and Signal Processing

Author: Jean-Luc Starck

Publisher: Cambridge University Press

Published: 2015-10-14

Total Pages: 449

ISBN-13: 1316483304

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This thoroughly updated new edition presents state-of-the-art sparse and multiscale image and signal processing. It covers linear multiscale geometric transforms, such as wavelet, ridgelet, or curvelet transforms, and non-linear multiscale transforms based on the median and mathematical morphology operators. Along with an up-to-the-minute description of required computation, it covers the latest results in inverse problem solving and regularization, sparse signal decomposition, blind source separation, in-painting, and compressed sensing. New chapters and sections cover multiscale geometric transforms for three-dimensional data (data cubes), data on the sphere (geo-located data), dictionary learning, and nonnegative matrix factorization. The authors wed theory and practice in examining applications in areas such as astronomy, including recent results from the European Space Agency's Herschel mission, biology, fusion physics, cold dark matter simulation, medical MRI, digital media, and forensics. MATLAB® and IDL code, available online at www.SparseSignalRecipes.info, accompany these methods and all applications.

Wavelets from a Statistical Perspective
Wavelets from a Statistical Perspective

Author: Maarten Jansen

Publisher: CRC Press

Published: 2022-04-18

Total Pages: 474

ISBN-13: 1000564177

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Wavelets from a Statistical Perspective offers a modern, 2nd generation look on wavelets, far beyond the rigid setting of the equispaced, dyadic wavelets in the early days. With the methods of this book, based on the lifting scheme, researchers can set up a wavelet or another multiresolution analysis adapted to their data, ranging from images to scattered data or other irregularly spaced observations. Whereas classical wavelets stand a bit apart from other nonparametric methods, this book adds a multiscale touch to your spline, kernel or local polynomial smoothing procedure, thereby extending its applicability to nonlinear, nonparametric processing for piecewise smooth data. One of the chapters of the book constructs B-spline wavelets on nonequispaced knots and multiscale local polynomial transforms. In another chapter, the link between wavelets and Fourier analysis, ubiquitous in the classical approach, is explained, but without being inevitable. In further chapters the discrete wavelet transform is contrasted with the continuous version, the nondecimated (or maximal overlap) transform taking an intermediate position. An important principle in designing a wavelet analysis through the lifting scheme is finding the right balance between bias and variance. Bias and variance also play a crucial role in the nonparametric smoothing in a wavelet framework, in finding well working thresholds or other smoothing parameters. The numerous illustrations can be reproduced with the online available, accompanying software. The software and the exercises can also be used as a starting point in the further exploration of the material.

Proceedings of the Third International Conference on Wavelet Analysis and Its Applications (WAA)
Proceedings of the Third International Conference on Wavelet Analysis and Its Applications (WAA)

Author: Jian Ping Li

Publisher: World Scientific

Published: 2003

Total Pages: 533

ISBN-13: 9812796762

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This book captures the essence of the current state of research in wavelet analysis and its applications, and identifies the changes and opportunities OCo both current and future OCo in the field. Distinguished researchers such as Prof John Daugman from Cambridge University and Prof Victor Wickerhauser from Washington University present their research papers. Contents: Volume 1: Accelerating Convergence of Monte Carlo Simulations and Measuring Weak Biosignals Using Wavelet Threshold Denoising (M V Wickerhauser); One of Image Compression Methods Based on Biorthogonal Wavelet Transform and LBG Algorithm (J Lin et al.); A Video Watermarking Algorithm Using Fast Wavelet (J Zhang et al.); Structural and Geometric Characteristics of Sets of Convergence and Divergence of Multiple Fourier Series of Functions which Equal Zero on Some Set (I L Bloshanskii); Sequence Images Data Fusion Based on Wavelet Transform Approach (H Tao et al.); Radar Detection of Minimum Altitude Flying Targets Based on Wavelet Transforms (H Li et al.); Precursors of Engine Failures Revealed by Wavelet Analysis (I M Dremin); Volume 2: Demodulation by Complex-Valued Wavelets for Stochastic Pattern Recognition: How Iris Recognition Works (J Daugman); Wavelets and Image Compression (V A Nechitailo); Fast Wavelet-Based Video Codec and its Application in an IP Version 6-Ready Serverless Videoconferencing (H L Cycon et al.); On a Class of Optimal Wavelets (N A Strelkov & V L Dol''nikov); A Wavelet-Based Digital Watermarking Algorithm (H Q Sun et al.); Research of the Gyro Signal De-Noising Method Based on Stationary Wavelets Transform (J Guo et al.); Adaptive De-Noising of Low SNR Signals (D Isar & A Isar); Analysis of the DLA-Process with Gravitational Interaction of Particles and Growing Cluster (A Loskutov et al.); and other papers. Readership: Graduate students, academics and researchers in computer science and engineering."