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| Author | : Alexander G. Ramm |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 262 |
| Release | : 2013-11-11 |
| Genre | : Technology & Engineering |
| ISBN | : 1402079753 |
Proceedings of Sessions from the First Congress of the International Society for Analysis, Applications, and Computind held in Newark, Delaware, June 2-6, 1997
| Author | : Xue-Cheng Tai |
| Publisher | : Springer Nature |
| Total Pages | : 226 |
| Release | : 2021-09-25 |
| Genre | : Mathematics |
| ISBN | : 9811627010 |
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.
| Author | : Otmar Scherzer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1626 |
| Release | : 2010-11-23 |
| Genre | : Mathematics |
| ISBN | : 0387929193 |
The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.
| Author | : Jin Keun Seo |
| Publisher | : John Wiley & Sons |
| Total Pages | : 379 |
| Release | : 2012-11-16 |
| Genre | : Technology & Engineering |
| ISBN | : 1118478150 |
This book provides researchers and engineers in the imaging field with the skills they need to effectively deal with nonlinear inverse problems associated with different imaging modalities, including impedance imaging, optical tomography, elastography, and electrical source imaging. Focusing on numerically implementable methods, the book bridges the gap between theory and applications, helping readers tackle problems in applied mathematics and engineering. Complete, self-contained coverage includes basic concepts, models, computational methods, numerical simulations, examples, and case studies. Provides a step-by-step progressive treatment of topics for ease of understanding. Discusses the underlying physical phenomena as well as implementation details of image reconstruction algorithms as prerequisites for finding solutions to non linear inverse problems with practical significance and value. Includes end of chapter problems, case studies and examples with solutions throughout the book. Companion website will provide further examples and solutions, experimental data sets, open problems, teaching material such as PowerPoint slides and software including MATLAB m files. Essential reading for Graduate students and researchers in imaging science working across the areas of applied mathematics, biomedical engineering, and electrical engineering and specifically those involved in nonlinear imaging techniques, impedance imaging, optical tomography, elastography, and electrical source imaging
| Author | : Curtis R. Vogel |
| Publisher | : SIAM |
| Total Pages | : 195 |
| Release | : 2002-01-01 |
| Genre | : Mathematics |
| ISBN | : 0898717574 |
Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
| Author | : Gary Francis Roach |
| Publisher | : Chapman & Hall/CRC |
| Total Pages | : 290 |
| Release | : 1991 |
| Genre | : Mathematics |
| ISBN | : |
This volume contains the invited papers presented at an international workship on inverse problems and imaging held at Ross Priory, University of Strathclyde, 1988.
| Author | : Martin Hanke |
| Publisher | : SIAM |
| Total Pages | : 171 |
| Release | : 2017-01-01 |
| Genre | : Mathematics |
| ISBN | : 1611974933 |
Inverse problems need to be solved in order to properly interpret indirect measurements. Often, inverse problems are ill-posed and sensitive to data errors. Therefore one has to incorporate some sort of regularization to reconstruct significant information from the given data. A Taste of Inverse Problems: Basic Theory and Examples?presents the main achievements that have emerged in regularization theory over the past 50 years, focusing on linear ill-posed problems and the development of methods that can be applied to them. Some of this material has previously appeared only in journal articles. This book rigorously discusses state-of-the-art inverse problems theory, focusing on numerically relevant aspects and omitting subordinate generalizations; presents diverse real-world applications, important test cases, and possible pitfalls; and treats these applications with the same rigor and depth as the theory.
| Author | : Seppo Pohjolainen |
| Publisher | : Springer |
| Total Pages | : 247 |
| Release | : 2016-07-14 |
| Genre | : Mathematics |
| ISBN | : 3319278363 |
This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.
| Author | : Per Christian Hansen |
| Publisher | : SIAM |
| Total Pages | : 220 |
| Release | : 2010-01-01 |
| Genre | : Mathematics |
| ISBN | : 089871883X |
This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, we demonstrate that insight about them goes hand in hand with algorithms.
| Author | : Ali Mohamad-Djafari |
| Publisher | : John Wiley & Sons |
| Total Pages | : 369 |
| Release | : 2013-01-29 |
| Genre | : Technology & Engineering |
| ISBN | : 1118600460 |
The concept of an inverse problem is a familiar one to most scientists and engineers, particularly in the field of signal and image processing, imaging systems (medical, geophysical, industrial non-destructive testing, etc.), and computer vision. In imaging systems, the aim is not just to estimate unobserved images but also their geometric characteristics from observed quantities that are linked to these unobserved quantities by a known physical or mathematical relationship. In this manner techniques such as image enhancement or addition of hidden detail can be delivered. This book focuses on imaging and vision problems that can be clearly described in terms of an inverse problem where an estimate for the image and its geometrical attributes (contours and regions) is sought. The book uses a consistent methodology to examine inverse problems such as: noise removal; restoration by deconvolution; 2D or 3D reconstruction in X-ray, tomography or microwave imaging; reconstruction of the surface of a 3D object using X-ray tomography or making use of its shading; reconstruction of the surface of a 3D landscape based on several satellite photos; super-resolution; motion estimation in a sequence of images; separation of several images mixed using instruments with different sensitivities or transfer functions; and much more.
