An Introduction to Sparse Stochastic Processes

An Introduction to Sparse Stochastic Processes

Author: Michael Unser

Publisher: Cambridge University Press

Published: 2014-08-21

Total Pages: 387

ISBN-13: 1107058546

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A detailed guide to sparsity, providing a description of their transform-domain statistics and applying the models to practical algorithms.


An Introduction to Sparse Stochastic Processes

An Introduction to Sparse Stochastic Processes

Author: Michael A. Unser

Publisher:

Published: 2014

Total Pages: 367

ISBN-13: 9781316054505

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Providing a novel approach to sparsity, this comprehensive book presents the theory of stochastic processes that are ruled by linear stochastic differential equations, and that admit a parsimonious representation in a matched wavelet-like basis. Two key themes are the statistical property of infinite divisibility, which leads to two distinct types of behaviour - Gaussian and sparse - and the structural link between linear stochastic processes and spline functions, which is exploited to simplify the mathematical analysis. The core of the book is devoted to investigating sparse processes, including a complete description of their transform-domain statistics. The final part develops practical signal-processing algorithms that are based on these models, with special emphasis on biomedical image reconstruction. This is an ideal reference for graduate students and researchers with an interest in signal/image processing, compressed sensing, approximation theory, machine learning, or statistics.


An Introduction to Stochastic Modeling

An Introduction to Stochastic Modeling

Author: Howard M. Taylor

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 410

ISBN-13: 1483269272

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An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.


An Introduction to Stochastic Processes with Applications to Biology

An Introduction to Stochastic Processes with Applications to Biology

Author: Linda J. S. Allen

Publisher: CRC Press

Published: 2010-12-02

Total Pages: 486

ISBN-13: 143989468X

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An Introduction to Stochastic Processes with Applications to Biology, Second Edition presents the basic theory of stochastic processes necessary in understanding and applying stochastic methods to biological problems in areas such as population growth and extinction, drug kinetics, two-species competition and predation, the spread of epidemics, and


Probability and Stochastics

Probability and Stochastics

Author: Erhan Çınlar

Publisher: Springer Science & Business Media

Published: 2011-02-21

Total Pages: 567

ISBN-13: 0387878599

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This text is an introduction to the modern theory and applications of probability and stochastics. The style and coverage is geared towards the theory of stochastic processes, but with some attention to the applications. In many instances the gist of the problem is introduced in practical, everyday language and then is made precise in mathematical form. The first four chapters are on probability theory: measure and integration, probability spaces, conditional expectations, and the classical limit theorems. There follows chapters on martingales, Poisson random measures, Levy Processes, Brownian motion, and Markov Processes. Special attention is paid to Poisson random measures and their roles in regulating the excursions of Brownian motion and the jumps of Levy and Markov processes. Each chapter has a large number of varied examples and exercises. The book is based on the author’s lecture notes in courses offered over the years at Princeton University. These courses attracted graduate students from engineering, economics, physics, computer sciences, and mathematics. Erhan Cinlar has received many awards for excellence in teaching, including the President’s Award for Distinguished Teaching at Princeton University. His research interests include theories of Markov processes, point processes, stochastic calculus, and stochastic flows. The book is full of insights and observations that only a lifetime researcher in probability can have, all told in a lucid yet precise style.


Stochastic Processes: Modeling and Simulation

Stochastic Processes: Modeling and Simulation

Author: D N Shanbhag

Publisher: Gulf Professional Publishing

Published: 2003-02-24

Total Pages: 1028

ISBN-13: 9780444500137

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This sequel to volume 19 of Handbook on Statistics on Stochastic Processes: Modelling and Simulation is concerned mainly with the theme of reviewing and, in some cases, unifying with new ideas the different lines of research and developments in stochastic processes of applied flavour. This volume consists of 23 chapters addressing various topics in stochastic processes. These include, among others, those on manufacturing systems, random graphs, reliability, epidemic modelling, self-similar processes, empirical processes, time series models, extreme value therapy, applications of Markov chains, modelling with Monte Carlo techniques, and stochastic processes in subjects such as engineering, telecommunications, biology, astronomy and chemistry. particular with modelling, simulation techniques and numerical methods concerned with stochastic processes. The scope of the project involving this volume as well as volume 19 is already clarified in the preface of volume 19. The present volume completes the aim of the project and should serve as an aid to students, teachers, researchers and practitioners interested in applied stochastic processes.


Deep Learning for Biomedical Image Reconstruction

Deep Learning for Biomedical Image Reconstruction

Author: Jong Chul Ye

Publisher: Cambridge University Press

Published: 2023-09-30

Total Pages: 365

ISBN-13: 1316517519

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Discover the power of deep neural networks for image reconstruction with this state-of-the-art review of modern theories and applications. The background theory of deep learning is introduced step-by-step, and by incorporating modeling fundamentals this book explains how to implement deep learning in a variety of modalities, including X-ray, CT, MRI and others. Real-world examples demonstrate an interdisciplinary approach to medical image reconstruction processes, featuring numerous imaging applications. Recent clinical studies and innovative research activity in generative models and mathematical theory will inspire the reader towards new frontiers. This book is ideal for graduate students in Electrical or Biomedical Engineering or Medical Physics.


Explorations in Time-Frequency Analysis

Explorations in Time-Frequency Analysis

Author: Patrick Flandrin

Publisher: Cambridge University Press

Published: 2018-09-06

Total Pages: 231

ISBN-13: 1108421024

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Understand the methods of modern non-stationary signal processing with authoritative insights from a leader in the field.