Multiscale Signal Analysis and Modeling

Multiscale Signal Analysis and Modeling PDF

Author: Xiaoping Shen

Publisher: Springer Science & Business Media

Published: 2012-09-18

Total Pages: 388

ISBN-13: 1461441455

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Multiscale Signal Analysis and Modeling presents recent advances in multiscale analysis and modeling using wavelets and other systems. This book also presents applications in digital signal processing using sampling theory and techniques from various function spaces, filter design, feature extraction and classification, signal and image representation/transmission, coding, nonparametric statistical signal processing, and statistical learning theory.

Multiscale Statistical Models for Signal and Image Processing

Multiscale Statistical Models for Signal and Image Processing PDF

Author:

Publisher:

Published: 2004

Total Pages: 10

ISBN-13:

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We are developing a general theory for multi scale signal and image modeling, processing, and analysis that matched to singularity-rich data, such as transients and images with edges. Using a linguistic analogy, our model can be interpreted as grammars that constrain the wavelet vocabulary. Our investigation focuses on probabilistic graph models (tree-based hidden Markov models) that can accurately, realistically, and efficiently represent singularity structure in the wavelet domain. Grammar design is being guided by a detailed study of the final structure of singularities using Besov spaces and multifractal analysis.

Multiscale Analysis of Complex Time Series

Multiscale Analysis of Complex Time Series PDF

Author: Jianbo Gao

Publisher: John Wiley & Sons

Published: 2007-12-04

Total Pages: 368

ISBN-13: 0470191643

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The only integrative approach to chaos and random fractal theory Chaos and random fractal theory are two of the most important theories developed for data analysis. Until now, there has been no single book that encompasses all of the basic concepts necessary for researchers to fully understand the ever-expanding literature and apply novel methods to effectively solve their signal processing problems. Multiscale Analysis of Complex Time Series fills this pressing need by presenting chaos and random fractal theory in a unified manner. Adopting a data-driven approach, the book covers: DNA sequence analysis EEG analysis Heart rate variability analysis Neural information processing Network traffic modeling Economic time series analysis And more Additionally, the book illustrates almost every concept presented through applications and a dedicated Web site is available with source codes written in various languages, including Java, Fortran, C, and MATLAB, together with some simulated and experimental data. The only modern treatment of signal processing with chaos and random fractals unified, this is an essential book for researchers and graduate students in electrical engineering, computer science, bioengineering, and many other fields.

Higher-Dimensional Signal Processing Via Multiscale Geometric Analysis

Higher-Dimensional Signal Processing Via Multiscale Geometric Analysis PDF

Author:

Publisher:

Published: 2010

Total Pages: 28

ISBN-13:

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This project pursued a general theory for complex-valued multiscale signal and image modeling, processing, and analysis that is matched to singularity-rich data. Higher-dimensional signals that feature geometric manifold structures were of particular interest in developing theory and a practical toolset for analysis and processing. We pursued a three-pronged approach in creating new multiscale transforms, new geometric statistical models, and new manifold-based signal representations. The results of our research include (1) the Dual Tree Quaternion Wavelet, an efficient transform and analysis tool that features near shift invariance and linear computational complexity; (2) a geometric hidden Markov tree wavelet model, which accounts for geometric regularity by capturing the dependencies between complex wavelet coefficients along a contour; and (3) surflet representations of signal discontinuities with near optimal rate-distortion performance. These new tools have led to significant performance gains immediately applicable to a number of important Navy-relevant applications, including target detection and classification, image segmentation and fusion, and computer network traffic modeling.

Multiscale Analysis, Modeling, and Processing of Higher-Dimensional Geometric Data

Multiscale Analysis, Modeling, and Processing of Higher-Dimensional Geometric Data PDF

Author:

Publisher:

Published: 2007

Total Pages: 15

ISBN-13:

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The wavelet transform has emerged over the last decade as a powerful new tool for statistical signal processing. The wavelet domain provides a natural setting for many applications involving real-world signals and images, especially those rich in singularities (edges, ridges, and other transients). In this project, we extended wavelet transform modeling and processing algorithms to handle multidimensional signals that are smooth save for singularities along lower-dimensional manifolds. The key building block is a new quaternion wavelet transform (QWT) that generalizes the complex wavelet transform to higher dimensions using a multidimensional Hilbert transform. The QWT has a quaternion magnitude-phase representation that encodes image shifts in an absolute (x, y)-coordinate system and thus provides a theoretical framework for analyzing the phase behavior of 2-D image shifts. We conducted a thorough analysis of the QWT phase around edge regions and thereby developed efficient multiscale edge localization and flow/motion estimation algorithms for image registration based on the QWT phase.

Multiscale Modeling of Cancer

Multiscale Modeling of Cancer PDF

Author: Vittorio Cristini

Publisher: Cambridge University Press

Published: 2010-09-09

Total Pages: 299

ISBN-13: 1139491504

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Mathematical modeling, analysis and simulation are set to play crucial roles in explaining tumor behavior, and the uncontrolled growth of cancer cells over multiple time and spatial scales. This book, the first to integrate state-of-the-art numerical techniques with experimental data, provides an in-depth assessment of tumor cell modeling at multiple scales. The first part of the text presents a detailed biological background with an examination of single-phase and multi-phase continuum tumor modeling, discrete cell modeling, and hybrid continuum-discrete modeling. In the final two chapters, the authors guide the reader through problem-based illustrations and case studies of brain and breast cancer, to demonstrate the future potential of modeling in cancer research. This book has wide interdisciplinary appeal and is a valuable resource for mathematical biologists, biomedical engineers and clinical cancer research communities wishing to understand this emerging field.

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