Topological Signal Processing

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Topological Signal Processing

Author : Michael Robinson
Publisher : Springer Science & Business Media
ISBN 13 : 3642361048
Total Pages : 245 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Topological Signal Processing by : Michael Robinson

Download or read book Topological Signal Processing written by Michael Robinson and published by Springer Science & Business Media. This book was released on 2014-01-07 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Signal processing is the discipline of extracting information from collections of measurements. To be effective, the measurements must be organized and then filtered, detected, or transformed to expose the desired information. Distortions caused by uncertainty, noise, and clutter degrade the performance of practical signal processing systems. In aggressively uncertain situations, the full truth about an underlying signal cannot be known. This book develops the theory and practice of signal processing systems for these situations that extract useful, qualitative information using the mathematics of topology -- the study of spaces under continuous transformations. Since the collection of continuous transformations is large and varied, tools which are topologically-motivated are automatically insensitive to substantial distortion. The target audience comprises practitioners as well as researchers, but the book may also be beneficial for graduate students.

Dynamical Systems Analysis Using Topological Signal Processing

Author : Audun Myers
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.4/5 (387 download)

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Book Synopsis Dynamical Systems Analysis Using Topological Signal Processing by : Audun Myers

Download or read book Dynamical Systems Analysis Using Topological Signal Processing written by Audun Myers and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological Signal Processing (TSP) is the study of time series data through the lens of Topological Data Analysis (TDA)-a process of analyzing data through its shape. This work focuses on developing novel TSP tools for the analysis of dynamical systems. A dynamical system is a term used to broadly refer to a system whose state changes in time. These systems are formally assumed to be a continuum of states whose values are real numbers. However, real-life measurements of these systems only provide finite information from which the underlying dynamics must be gleaned. This necessitates making conclusions on the continuous structure of a dynamical system using noisy finite samples or time series. The interest often lies in capturing qualitative changes in the system's behavior known as a bifurcation through changes in the shape of the state space as one or more of the system parameters vary. Current literature on time series analysis aims to study this structure by searching for a lower-dimensional representation; however, the need for user-defined inputs, the sensitivity of these inputs to noise, and the expensive computational effort limit the usability of available knowledge especially for in-situ signal processing.This research aims to use and develop TSP tools to extract useful information about the underlying dynamical system's structure. The first research direction investigates the use of sublevel set persistence-a form of persistent homology from TDA-for signal processing with applications including parameter estimation of a damped oscillator and signal complexity measures to detect bifurcations. The second research direction applies TDA to complex networks to investigate how the topology of such complex networks corresponds to the state space structure. We show how TSP applied to complex networks can be used to detect changes in signal complexity including chaotic compared to periodic dynamics in a noise-contaminated signal. The last research direction focuses on the topological analysis of dynamical networks. A dynamical network is a graph whose vertices and edges have state values driven by a highly interconnected dynamical system. We show how zigzag persistence-a modification of persistent homology-can be used to understand the changing structure of such dynamical networks.

Embedded Signal Processing with the Micro Signal Architecture

Author : Woon-Seng Gan
Publisher : John Wiley & Sons
ISBN 13 : 0470112263
Total Pages : 508 pages
Book Rating : 4.4/5 (71 download)

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Book Synopsis Embedded Signal Processing with the Micro Signal Architecture by : Woon-Seng Gan

Download or read book Embedded Signal Processing with the Micro Signal Architecture written by Woon-Seng Gan and published by John Wiley & Sons. This book was released on 2007-02-26 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a real-time digital signal processing textbook using the latest embedded Blackfin processor Analog Devices, Inc (ADI). 20% of the text is dedicated to general real-time signal processing principles. The remaining text provides an overview of the Blackfin processor, its programming, applications, and hands-on exercises for users. With all the practical examples given to expedite the learning development of Blackfin processors, the textbook doubles as a ready-to-use user's guide. The book is based on a step-by-step approach in which readers are first introduced to the DSP systems and concepts. Although, basic DSP concepts are introduced to allow easy referencing, readers are recommended to complete a basic course on "Signals and Systems" before attempting to use this book. This is also the first textbook that illustrates graphical programming for embedded processor using the latest LabVIEW Embedded Module for the ADI Blackfin Processors. A solutions manual is available for adopters of the book from the Wiley editorial department.

Computational Topology for Biomedical Image and Data Analysis

Author : Rodrigo Rojas Moraleda
Publisher : CRC Press
ISBN 13 : 0429810997
Total Pages : 116 pages
Book Rating : 4.4/5 (298 download)

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Book Synopsis Computational Topology for Biomedical Image and Data Analysis by : Rodrigo Rojas Moraleda

Download or read book Computational Topology for Biomedical Image and Data Analysis written by Rodrigo Rojas Moraleda and published by CRC Press. This book was released on 2019-07-12 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible yet rigorous introduction to topology and homology focused on the simplicial space. It presents a compact pipeline from the foundations of topology to biomedical applications. It will be of interest to medical physicists, computer scientists, and engineers, as well as undergraduate and graduate students interested in this topic. Features: Presents a practical guide to algebraic topology as well as persistence homology Contains application examples in the field of biomedicine, including the analysis of histological images and point cloud data

Statistical Signal Processing for Neuroscience and Neurotechnology

Author : Karim G. Oweiss
Publisher : Academic Press
ISBN 13 : 0080962963
Total Pages : 441 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Statistical Signal Processing for Neuroscience and Neurotechnology by : Karim G. Oweiss

Download or read book Statistical Signal Processing for Neuroscience and Neurotechnology written by Karim G. Oweiss and published by Academic Press. This book was released on 2010-09-22 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a uniquely comprehensive reference that summarizes the state of the art of signal processing theory and techniques for solving emerging problems in neuroscience, and which clearly presents new theory, algorithms, software and hardware tools that are specifically tailored to the nature of the neurobiological environment. It gives a broad overview of the basic principles, theories and methods in statistical signal processing for basic and applied neuroscience problems.Written by experts in the field, the book is an ideal reference for researchers working in the field of neural engineering, neural interface, computational neuroscience, neuroinformatics, neuropsychology and neural physiology. By giving a broad overview of the basic principles, theories and methods, it is also an ideal introduction to statistical signal processing in neuroscience. A comprehensive overview of the specific problems in neuroscience that require application of existing and development of new theory, techniques, and technology by the signal processing community Contains state-of-the-art signal processing, information theory, and machine learning algorithms and techniques for neuroscience research Presents quantitative and information-driven science that has been, or can be, applied to basic and translational neuroscience problems

Foundations of Signal Processing

Author : Martin Vetterli
Publisher : Cambridge University Press
ISBN 13 : 1139916572
Total Pages : 745 pages
Book Rating : 4.1/5 (399 download)

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Book Synopsis Foundations of Signal Processing by : Martin Vetterli

Download or read book Foundations of Signal Processing written by Martin Vetterli and published by Cambridge University Press. This book was released on 2014-09-04 with total page 745 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive and engaging textbook introduces the basic principles and techniques of signal processing, from the fundamental ideas of signals and systems theory to real-world applications. Students are introduced to the powerful foundations of modern signal processing, including the basic geometry of Hilbert space, the mathematics of Fourier transforms, and essentials of sampling, interpolation, approximation and compression The authors discuss real-world issues and hurdles to using these tools, and ways of adapting them to overcome problems of finiteness and localization, the limitations of uncertainty, and computational costs. It includes over 160 homework problems and over 220 worked examples, specifically designed to test and expand students' understanding of the fundamentals of signal processing, and is accompanied by extensive online materials designed to aid learning, including Mathematica® resources and interactive demonstrations.

Biomedical Signal Processing

Author : Metin Akay
Publisher : Academic Press
ISBN 13 : 0323140149
Total Pages : 393 pages
Book Rating : 4.3/5 (231 download)

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Book Synopsis Biomedical Signal Processing by : Metin Akay

Download or read book Biomedical Signal Processing written by Metin Akay and published by Academic Press. This book was released on 2012-12-02 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sophisticated techniques for signal processing are now available to the biomedical specialist! Written in an easy-to-read, straightforward style, Biomedical Signal Processing presents techniques to eliminate background noise, enhance signal detection, and analyze computer data, making results easy to comprehend and apply. In addition to examining techniques for electrical signal analysis, filtering, and transforms, the author supplies an extensive appendix with several computer programs that demonstrate techniques presented in the text.

Numerical Bayesian Methods Applied to Signal Processing

Author : Joseph J.K. O Ruanaidh
Publisher : Springer Science & Business Media
ISBN 13 : 1461207177
Total Pages : 256 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Numerical Bayesian Methods Applied to Signal Processing by : Joseph J.K. O Ruanaidh

Download or read book Numerical Bayesian Methods Applied to Signal Processing written by Joseph J.K. O Ruanaidh and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the processing of signals that have been sam pled and digitized. The fundamental theory behind Digital Signal Process ing has been in existence for decades and has extensive applications to the fields of speech and data communications, biomedical engineering, acous tics, sonar, radar, seismology, oil exploration, instrumentation and audio signal processing to name but a few [87]. The term "Digital Signal Processing", in its broadest sense, could apply to any operation carried out on a finite set of measurements for whatever purpose. A book on signal processing would usually contain detailed de scriptions of the standard mathematical machinery often used to describe signals. It would also motivate an approach to real world problems based on concepts and results developed in linear systems theory, that make use of some rather interesting properties of the time and frequency domain representations of signals. While this book assumes some familiarity with traditional methods the emphasis is altogether quite different. The aim is to describe general methods for carrying out optimal signal processing.

Signal Processing for Neuroscientists

Author : Wim van Drongelen
Publisher : Elsevier
ISBN 13 : 008046775X
Total Pages : 319 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Signal Processing for Neuroscientists by : Wim van Drongelen

Download or read book Signal Processing for Neuroscientists written by Wim van Drongelen and published by Elsevier. This book was released on 2006-12-18 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Signal Processing for Neuroscientists introduces analysis techniques primarily aimed at neuroscientists and biomedical engineering students with a reasonable but modest background in mathematics, physics, and computer programming. The focus of this text is on what can be considered the ‘golden trio’ in the signal processing field: averaging, Fourier analysis, and filtering. Techniques such as convolution, correlation, coherence, and wavelet analysis are considered in the context of time and frequency domain analysis. The whole spectrum of signal analysis is covered, ranging from data acquisition to data processing; and from the mathematical background of the analysis to the practical application of processing algorithms. Overall, the approach to the mathematics is informal with a focus on basic understanding of the methods and their interrelationships rather than detailed proofs or derivations. One of the principle goals is to provide the reader with the background required to understand the principles of commercially available analyses software, and to allow him/her to construct his/her own analysis tools in an environment such as MATLAB®. Multiple color illustrations are integrated in the text Includes an introduction to biomedical signals, noise characteristics, and recording techniques Basics and background for more advanced topics can be found in extensive notes and appendices A Companion Website hosts the MATLAB scripts and several data files: http://www.elsevierdirect.com/companion.jsp?ISBN=9780123708670

Topological Data Analysis for Scientific Visualization

Author : Julien Tierny
Publisher : Springer
ISBN 13 : 3319715070
Total Pages : 158 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Topological Data Analysis for Scientific Visualization by : Julien Tierny

Download or read book Topological Data Analysis for Scientific Visualization written by Julien Tierny and published by Springer. This book was released on 2018-01-16 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining theoretical and practical aspects of topology, this book provides a comprehensive and self-contained introduction to topological methods for the analysis and visualization of scientific data. Theoretical concepts are presented in a painstaking but intuitive manner, with numerous high-quality color illustrations. Key algorithms for the computation and simplification of topological data representations are described in detail, and their application is carefully demonstrated in a chapter dedicated to concrete use cases. With its fine balance between theory and practice, "Topological Data Analysis for Scientific Visualization" constitutes an appealing introduction to the increasingly important topic of topological data analysis for lecturers, students and researchers.

Computational Topology

Author : Herbert Edelsbrunner
Publisher : American Mathematical Society
ISBN 13 : 1470467690
Total Pages : 241 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Computational Topology by : Herbert Edelsbrunner

Download or read book Computational Topology written by Herbert Edelsbrunner and published by American Mathematical Society. This book was released on 2022-01-31 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.

A Wavelet Tour of Signal Processing

Author : Stephane Mallat
Publisher : Elsevier
ISBN 13 : 0080520839
Total Pages : 663 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis A Wavelet Tour of Signal Processing by : Stephane Mallat

Download or read book A Wavelet Tour of Signal Processing written by Stephane Mallat and published by Elsevier. This book was released on 1999-09-14 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and École Polytechnique in Paris. Provides a broad perspective on the principles and applications of transient signal processing with wavelets Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurements Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet Content is accessible on several level of complexity, depending on the individual reader's needs New to the Second Edition Optical flow calculation and video compression algorithms Image models with bounded variation functions Bayes and Minimax theories for signal estimation 200 pages rewritten and most illustrations redrawn More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics

Currents in Biomedical Signals Processing - Methods and Applications

Author : Aleksandra Dagmara Kawala-Sterniuk
Publisher : Frontiers Media SA
ISBN 13 : 2889769011
Total Pages : 148 pages
Book Rating : 4.8/5 (897 download)

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Book Synopsis Currents in Biomedical Signals Processing - Methods and Applications by : Aleksandra Dagmara Kawala-Sterniuk

Download or read book Currents in Biomedical Signals Processing - Methods and Applications written by Aleksandra Dagmara Kawala-Sterniuk and published by Frontiers Media SA. This book was released on 2022-09-05 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Topics in Signal Processing

Author : Suhash Chandra Dutta Roy
Publisher : Springer Nature
ISBN 13 : 9811395322
Total Pages : 330 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Topics in Signal Processing by : Suhash Chandra Dutta Roy

Download or read book Topics in Signal Processing written by Suhash Chandra Dutta Roy and published by Springer Nature. This book was released on 2019-10-11 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of specific research problems in signal processing and their solutions. It touches upon most core topics, including active and passive processing, discrete-time and continuous signals, and design of filters and networks for specific applications. This unique collection of design problems and conceptual insights will be useful to graduate students, researchers, and professionals working on signal processing problems. In addition, the book can also be used as a supplementary text for graduate courses in advanced signal processing, and for professional development courses for practicing engineers.

Persistence Theory: From Quiver Representations to Data Analysis

Author : Steve Y. Oudot
Publisher : American Mathematical Soc.
ISBN 13 : 1470434431
Total Pages : 229 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Persistence Theory: From Quiver Representations to Data Analysis by : Steve Y. Oudot

Download or read book Persistence Theory: From Quiver Representations to Data Analysis written by Steve Y. Oudot and published by American Mathematical Soc.. This book was released on 2017-05-17 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organized into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis.

Geometric and Topological Inference

Author : Jean-Daniel Boissonnat
Publisher : Cambridge University Press
ISBN 13 : 1108419399
Total Pages : 247 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Geometric and Topological Inference by : Jean-Daniel Boissonnat

Download or read book Geometric and Topological Inference written by Jean-Daniel Boissonnat and published by Cambridge University Press. This book was released on 2018-09-27 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.

Signal Processing and Machine Learning for Biomedical Big Data

Author : Ervin Sejdic
Publisher : CRC Press
ISBN 13 : 149877346X
Total Pages : 624 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Signal Processing and Machine Learning for Biomedical Big Data by : Ervin Sejdic

Download or read book Signal Processing and Machine Learning for Biomedical Big Data written by Ervin Sejdic and published by CRC Press. This book was released on 2018-07-04 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within the healthcare domain, big data is defined as any ``high volume, high diversity biological, clinical, environmental, and lifestyle information collected from single individuals to large cohorts, in relation to their health and wellness status, at one or several time points.'' Such data is crucial because within it lies vast amounts of invaluable information that could potentially change a patient's life, opening doors to alternate therapies, drugs, and diagnostic tools. Signal Processing and Machine Learning for Biomedical Big Data thus discusses modalities; the numerous ways in which this data is captured via sensors; and various sample rates and dimensionalities. Capturing, analyzing, storing, and visualizing such massive data has required new shifts in signal processing paradigms and new ways of combining signal processing with machine learning tools. This book covers several of these aspects in two ways: firstly, through theoretical signal processing chapters where tools aimed at big data (be it biomedical or otherwise) are described; and, secondly, through application-driven chapters focusing on existing applications of signal processing and machine learning for big biomedical data. This text aimed at the curious researcher working in the field, as well as undergraduate and graduate students eager to learn how signal processing can help with big data analysis. It is the hope of Drs. Sejdic and Falk that this book will bring together signal processing and machine learning researchers to unlock existing bottlenecks within the healthcare field, thereby improving patient quality-of-life. Provides an overview of recent state-of-the-art signal processing and machine learning algorithms for biomedical big data, including applications in the neuroimaging, cardiac, retinal, genomic, sleep, patient outcome prediction, critical care, and rehabilitation domains. Provides contributed chapters from world leaders in the fields of big data and signal processing, covering topics such as data quality, data compression, statistical and graph signal processing techniques, and deep learning and their applications within the biomedical sphere. This book’s material covers how expert domain knowledge can be used to advance signal processing and machine learning for biomedical big data applications.