Inverse Problems Image Analysis and Medical Imaging

Inverse Problems  Image Analysis  and Medical Imaging
Author: M. Zuhair Nashed,Otmar Scherzer,AMS Special Session on Interaction of Inverse Problems
Publsiher: American Mathematical Soc.
Total Pages: 322
Release: 2002
Genre: Diagnostic imaging
ISBN: 9780821829790

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This book contains the proceedings of the Special Session, Interaction of Inverse Problems and Image Analysis, held at the January 2001 meeting of the AMS in New Orleans, LA. The common thread among inverse problems, signal analysis, and image analysis is a canonical problem: recovering an object (function, signal, picture) from partial or indirect information about the object. Both inverse problems and imaging science have emerged in recent years as interdisciplinary research fields with profound applications in many areas of science, engineering, technology, and medicine. Research in inverse problems and image processing shows rich interaction with several areas of mathematics and strong links to signal processing, variational problems, applied harmonic analysis, and computational mathematics. This volume contains carefully referred and edited original research papers and high-level survey papers that provide overview and perspective on the interaction of inverse problems, image analysis, and medical imaging. The book is suitable for graduate students and researchers interested in signal and image processing and medical imaging.

Computational Methods for Inverse Problems in Imaging

Computational Methods for Inverse Problems in Imaging
Author: Marco Donatelli,Stefano Serra-Capizzano
Publsiher: Springer Nature
Total Pages: 171
Release: 2019-11-26
Genre: Mathematics
ISBN: 9783030328825

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This book presents recent mathematical methods in the area of inverse problems in imaging with a particular focus on the computational aspects and applications. The formulation of inverse problems in imaging requires accurate mathematical modeling in order to preserve the significant features of the image. The book describes computational methods to efficiently address these problems based on new optimization algorithms for smooth and nonsmooth convex minimization, on the use of structured (numerical) linear algebra, and on multilevel techniques. It also discusses various current and challenging applications in fields such as astronomy, microscopy, and biomedical imaging. The book is intended for researchers and advanced graduate students interested in inverse problems and imaging.

Introduction to Inverse Problems in Imaging

Introduction to Inverse Problems in Imaging
Author: M. Bertero,P. Boccacci
Publsiher: CRC Press
Total Pages: 366
Release: 2020-08-30
Genre: Technology & Engineering
ISBN: 1439822069

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This is a graduate textbook on the principles of linear inverse problems, methods of their approximate solution, and practical application in imaging. The level of mathematical treatment is kept as low as possible to make the book suitable for a wide range of readers from different backgrounds in science and engineering. Mathematical prerequisites are first courses in analysis, geometry, linear algebra, probability theory, and Fourier analysis. The authors concentrate on presenting easily implementable and fast solution algorithms. With examples and exercises throughout, the book will provide the reader with the appropriate background for a clear understanding of the essence of inverse problems (ill-posedness and its cure) and, consequently, for an intelligent assessment of the rapidly growing literature on these problems.

Introduction to Inverse Problems in Imaging

Introduction to Inverse Problems in Imaging
Author: M. Bertero,P. Boccacci,Christine De Mol
Publsiher: CRC Press
Total Pages: 358
Release: 2021-12-20
Genre: Science
ISBN: 9781000516357

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Fully updated throughout and with several new chapters, this second edition of Introduction to Inverse Problems in Imaging guides advanced undergraduate and graduate students in physics, computer science, mathematics and engineering through the principles of linear inverse problems, in addition to methods of their approximate solution and their practical applications in imaging. This second edition contains new chapters on edge-preserving and sparsity-enforcing regularization in addition to maximum likelihood methods and Bayesian regularization for Poisson data. The level of mathematical treatment is kept as low as possible to make the book suitable for a wide range of students from different backgrounds, with readers needing just a rudimentary understanding of analysis, geometry, linear algebra, probability theory, and Fourier analysis. The authors concentrate on presenting easily implementable and fast solution algorithms, and this second edition is accompanied by numerical examples throughout. It will provide readers with the appropriate background needed for a clear understanding of the essence of inverse problems (ill-posedness and its cure) and, consequently, for an intelligent assessment of the rapidly growing literature on these problems. Key features: Provides an accessible introduction to the topic while keeping mathematics to a minimum Interdisciplinary topic with growing relevance and wide-ranging applications Accompanied by numerical examples throughout

Medical Images Formation Handling and Evaluation

Medical Images  Formation  Handling and Evaluation
Author: Andrew E. Todd-Pokropek,Max A. Viergever
Publsiher: Springer Science & Business Media
Total Pages: 700
Release: 2013-06-29
Genre: Medical
ISBN: 9783642778889

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Medical imaging is a very important area in diagnostic (and increasingly therapeutic) medicine. Many new techniques are being developed or extended which depend on digital methods. Although conventional x-radiographs still comprise the bulk of the medical images acquired in a hospital, digital methods such as computerized tomography and magnetic resonance imaging are now often claimed to have a more significant clinical impact. This book is concerned with three aspects of such digital images: their formation, or how they can be acquired; their handling, or how they may be manipulated to increase their clinical value; and their evaluation, or how their impact and value may be assessed. The book is divided into three parts. Part 1 comprises a series of reviews in the general subject area written by authorities in the field. Part 2 includes papers on theoretical aspects: 3D images, reconstruction, perception, and image processing. Part 3includes papers on applications in nuclear medicine, magnetic resonance, andradiology.

Variational Methods in Imaging

Variational Methods in Imaging
Author: Otmar Scherzer,Markus Grasmair,Harald Grossauer,Markus Haltmeier,Frank Lenzen
Publsiher: Springer Science & Business Media
Total Pages: 323
Release: 2008-09-26
Genre: Mathematics
ISBN: 9780387692777

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This book is devoted to the study of variational methods in imaging. The presentation is mathematically rigorous and covers a detailed treatment of the approach from an inverse problems point of view. Many numerical examples accompany the theory throughout the text. It is geared towards graduate students and researchers in applied mathematics. Researchers in the area of imaging science will also find this book appealing. It can serve as a main text in courses in image processing or as a supplemental text for courses on regularization and inverse problems at the graduate level.

Mathematical Methods in Image Processing and Inverse Problems

Mathematical Methods in Image Processing and Inverse Problems
Author: Xue-Cheng Tai,Suhua Wei,Haiguang Liu
Publsiher: Springer Nature
Total Pages: 226
Release: 2021-09-25
Genre: Mathematics
ISBN: 9789811627019

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This book contains eleven original and survey scientific research articles arose from presentations given by invited speakers at International Workshop on Image Processing and Inverse Problems, held in Beijing Computational Science Research Center, Beijing, China, April 21–24, 2018. The book was dedicated to Professor Raymond Chan on the occasion of his 60th birthday. The contents of the book cover topics including image reconstruction, image segmentation, image registration, inverse problems and so on. Deep learning, PDE, statistical theory based research methods and techniques were discussed. The state-of-the-art developments on mathematical analysis, advanced modeling, efficient algorithm and applications were presented. The collected papers in this book also give new research trends in deep learning and optimization for imaging science. It should be a good reference for researchers working on related problems, as well as for researchers working on computer vision and visualization, inverse problems, image processing and medical imaging.

Regularization and Bayesian Methods for Inverse Problems in Signal and Image Processing

Regularization and Bayesian Methods for Inverse Problems in Signal and Image Processing
Author: Jean-Francois Giovannelli,Jérôme Idier
Publsiher: John Wiley & Sons
Total Pages: 322
Release: 2015-02-02
Genre: Technology & Engineering
ISBN: 9781118827079

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The focus of this book is on "ill-posed inverse problems". These problems cannot be solved only on the basis of observed data. The building of solutions involves the recognition of other pieces of a priori information. These solutions are then specific to the pieces of information taken into account. Clarifying and taking these pieces of information into account is necessary for grasping the domain of validity and the field of application for the solutions built. For too long, the interest in these problems has remained very limited in the signal-image community. However, the community has since recognized that these matters are more interesting and they have become the subject of much greater enthusiasm. From the application field’s point of view, a significant part of the book is devoted to conventional subjects in the field of inversion: biological and medical imaging, astronomy, non-destructive evaluation, processing of video sequences, target tracking, sensor networks and digital communications. The variety of chapters is also clear, when we examine the acquisition modalities at stake: conventional modalities, such as tomography and NMR, visible or infrared optical imaging, or more recent modalities such as atomic force imaging and polarized light imaging.