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.

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. This expanded and revised second edition contains updates to existing chapters and 16 additional entries on important mathematical methods such as graph cuts, morphology, discrete geometry, PDEs, conformal methods, to name a few. 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 200 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.

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. This expanded and revised second edition contains updates to existing chapters and 16 additional entries on important mathematical methods such as graph cuts, morphology, discrete geometry, PDEs, conformal methods, to name a few. 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 200 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.

Medical imaging is a major part of twenty-first century health care. This introduction explores the mathematical aspects of imaging in medicine to explain approximation methods in addition to computer implementation of inversion algorithms.

This handbook gathers together the state of the art on mathematical models and algorithms for imaging and vision. Its emphasis lies on rigorous mathematical methods, which represent the optimal solutions to a class of imaging and vision problems, and on effective algorithms, which are necessary for the methods to be translated to practical use in various applications. Viewing discrete images as data sampled from functional surfaces enables the use of advanced tools from calculus, functions and calculus of variations, and nonlinear optimization, and provides the basis of high-resolution imaging through geometry and variational models. Besides, optimization naturally connects traditional model-driven approaches to the emerging data-driven approaches of machine and deep learning. No other framework can provide comparable accuracy and precision to imaging and vision. Written by leading researchers in imaging and vision, the chapters in this handbook all start with gentle introductions, which make this work accessible to graduate students. For newcomers to the field, the book provides a comprehensive and fast-track introduction to the content, to save time and get on with tackling new and emerging challenges. For researchers, exposure to the state of the art of research works leads to an overall view of the entire field so as to guide new research directions and avoid pitfalls in moving the field forward and looking into the next decades of imaging and information services. This work can greatly benefit graduate students, researchers, and practitioners in imaging and vision; applied mathematicians; medical imagers; engineers; and computer scientists.

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. This book 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. A Taste of Inverse Problems: Basic Theory and Examples 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.

This is a companion textbook for an introductory course in physics. It aims to link the theories and models that students learn in class with practical problem-solving techniques. In other words, it should address the common complaint that 'I understand the concepts but I can't do the homework or tests'. The fundamentals of introductory physics courses are addressed in simple and concise terms, with emphasis on how the fundamental concepts and equations should be used to solve physics problems.