Search results for: handbook-of-mathematical-methods-in-imaging

Handbook of Mathematical Methods in Imaging

Author : Otmar Scherzer
File Size : 33.99 MB
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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.

Handbook of Mathematical Methods in Imaging

Author : Otmar Scherzer
File Size : 78.3 MB
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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.

Handbook of Mathematical Methods in Imaging

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File Size : 73.78 MB
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Handbook of Convex Optimization Methods in Imaging Science

Author : Vishal Monga
File Size : 55.22 MB
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This book covers recent advances in image processing and imaging sciences from an optimization viewpoint, especially convex optimization with the goal of designing tractable algorithms. Throughout the handbook, the authors introduce topics on the most key aspects of image acquisition and processing that are based on the formulation and solution of novel optimization problems. The first part includes a review of the mathematical methods and foundations required, and covers topics in image quality optimization and assessment. The second part of the book discusses concepts in image formation and capture from color imaging to radar and multispectral imaging. The third part focuses on sparsity constrained optimization in image processing and vision and includes inverse problems such as image restoration and de-noising, image classification and recognition and learning-based problems pertinent to image understanding. Throughout, convex optimization techniques are shown to be a critically important mathematical tool for imaging science problems and applied extensively. Convex Optimization Methods in Imaging Science is the first book of its kind and will appeal to undergraduate and graduate students, industrial researchers and engineers and those generally interested in computational aspects of modern, real-world imaging and image processing problems.

Handbook of Mathematical Geodesy

Author : Willi Freeden
File Size : 80.76 MB
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Written by leading experts, this book provides a clear and comprehensive survey of the “status quo” of the interrelating process and cross-fertilization of structures and methods in mathematical geodesy. Starting with a foundation of functional analysis, potential theory, constructive approximation, special function theory, and inverse problems, readers are subsequently introduced to today’s least squares approximation, spherical harmonics reflected spline and wavelet concepts, boundary value problems, Runge-Walsh framework, geodetic observables, geoidal modeling, ill-posed problems and regularizations, inverse gravimetry, and satellite gravity gradiometry. All chapters are self-contained and can be studied individually, making the book an ideal resource for both graduate students and active researchers who want to acquaint themselves with the mathematical aspects of modern geodesy.

Handbook of Convex Optimization Methods in Imaging Science

Author : Vishal Monga
File Size : 22.78 MB
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This book covers recent advances in image processing and imaging sciences from an optimization viewpoint, especially convex optimization with the goal of designing tractable algorithms. Throughout the handbook, the authors introduce topics on the most key aspects of image acquisition and processing that are based on the formulation and solution of novel optimization problems. The first part includes a review of the mathematical methods and foundations required, and covers topics in image quality optimization and assessment. The second part of the book discusses concepts in image formation and capture from color imaging to radar and multispectral imaging. The third part focuses on sparsity constrained optimization in image processing and vision and includes inverse problems such as image restoration and de-noising, image classification and recognition and learning-based problems pertinent to image understanding. Throughout, convex optimization techniques are shown to be a critically important mathematical tool for imaging science problems and applied extensively. Convex Optimization Methods in Imaging Science is the first book of its kind and will appeal to undergraduate and graduate students, industrial researchers and engineers and those generally interested in computational aspects of modern, real-world imaging and image processing problems.

Mathematical Modeling in Biomedical Imaging II

Author : Habib Ammari
File Size : 70.35 MB
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This volume reports on recent mathematical and computational advances in optical, ultrasound, and opto-acoustic tomographies. It outlines the state-of-the-art and future directions in these fields and provides readers with the most recently developed mathematical and computational tools. It is particularly suitable for researchers and graduate students in applied mathematics and biomedical engineering.

Time dependent Problems in Imaging and Parameter Identification

Author : Barbara Kaltenbacher
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Inverse problems such as imaging or parameter identification deal with the recovery of unknown quantities from indirect observations, connected via a model describing the underlying context. While traditionally inverse problems are formulated and investigated in a static setting, we observe a significant increase of interest in time-dependence in a growing number of important applications over the last few years. Here, time-dependence affects a) the unknown function to be recovered and / or b) the observed data and / or c) the underlying process. Challenging applications in the field of imaging and parameter identification are techniques such as photoacoustic tomography, elastography, dynamic computerized or emission tomography, dynamic magnetic resonance imaging, super-resolution in image sequences and videos, health monitoring of elastic structures, optical flow problems or magnetic particle imaging to name only a few. Such problems demand for innovation concerning their mathematical description and analysis as well as computational approaches for their solution.

Biomedical Photonics Handbook Second Edition

Author : Tuan Vo-Dinh
File Size : 89.47 MB
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Shaped by Quantum Theory, Technology, and the Genomics Revolution The integration of photonics, electronics, biomaterials, and nanotechnology holds great promise for the future of medicine. This topic has recently experienced an explosive growth due to the noninvasive or minimally invasive nature and the cost-effectiveness of photonic modalities in medical diagnostics and therapy. The second edition of the Biomedical Photonics Handbook presents fundamental developments as well as important applications of biomedical photonics of interest to scientists, engineers, manufacturers, teachers, students, and clinical providers. The second volume, Biomedical Diagnostics, focuses on biomedical diagnostic technologies and their applications from the bench to the bedside. Represents the Collective Work of over 150 Scientists, Engineers, and Clinicians Designed to display the most recent advances in instrumentation and methods, as well as clinical applications in important areas of biomedical photonics to a broad audience, this three-volume handbook provides an inclusive forum that serves as an authoritative reference source for a broad audience involved in the research, teaching, learning, and practice of medical technologies. What’s New in This Edition: A wide variety of photonic biochemical sensing technologies have already been developed for clinical monitoring of physiological parameters, such as blood pressure, blood chemistry, pH, temperature, and the presence of pathological organisms or biochemical species of clinical importance. Advanced photonic detection technologies integrating the latest knowledge of genomics, proteomics and metabolomics allow sensing of early disease state biomarkers, thus revolutionizing the medicine of the future. Nanobiotechnology has opened new possibilities for detection of biomarkers of disease, imaging single molecules and in situ diagnostics at the single cell level. In addition to these state-of-the art advancements, the second edition contains new topics and chapters including: • Fiber Optic Probe Design • Laser and Optical Radiation Safety • Photothermal Detection • Multidimensional Fluorescence Imaging • Surface Plasmon Resonance Imaging • Molecular Contrast Optical Coherence Tomography • Multiscale Photoacoustics • Polarized Light for Medical Diagnostics • Quantitative Diffuse Reflectance Imaging • Interferometric Light Scattering • Nonlinear Interferometric Vibrational Imaging • Multimodality Theranostics Nanoplatforms • Nanoscintillator-Based Therapy • SERS Molecular Sentinel Nanoprobes • Plasmonic Coupling Interference Nanoprobes Comprised of three books: Volume I: Fundamentals, Devices, and Techniques; Volume II: Biomedical Diagnostics; and Volume III: Therapeutics and Advanced Biophotonics, this second edition contains eight sections, and provides introductory material in each chapter. It also includes an overview of the topic, an extensive collection of spectroscopic data, and lists of references for further reading.

Biomedical Photonics Handbook 3 Volume Set

Author : Tuan Vo-Dinh
File Size : 78.26 MB
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Shaped by Quantum Theory, Technology, and the Genomics RevolutionThe integration of photonics, electronics, biomaterials, and nanotechnology holds great promise for the future of medicine. This topic has recently experienced an explosive growth due to the noninvasive or minimally invasive nature and the cost-effectiveness of photonic modalities in

The Mathematical Legacy of Leon Ehrenpreis

Author : Irene Sabadini
File Size : 89.28 MB
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Leon Ehrenpreis has been one of the leading mathematicians in the twentieth century. His contributions to the theory of partial differential equations were part of the golden era of PDEs, and led him to what is maybe his most important contribution, the Fundamental Principle, which he announced in 1960, and fully demonstrated in 1970. His most recent work, on the other hand, focused on a novel and far reaching understanding of the Radon transform, and offered new insights in integral geometry. Leon Ehrenpreis died in 2010, and this volume collects writings in his honor by a cadre of distinguished mathematicians, many of which were his collaborators.

The Radon Transform and Medical Imaging

Author : Peter Kuchment
File Size : 85.88 MB
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This book surveys the main mathematical ideas and techniques behind some well-established imaging modalities such as X-ray CT and emission tomography, as well as a variety of newly developing coupled-physics or hybrid techniques, including thermoacoustic tomography. The Radon Transform and Medical Imaging emphasizes mathematical techniques and ideas arising across the spectrum of medical imaging modalities and explains important concepts concerning inversion, stability, incomplete data effects, the role of interior information, and other issues critical to all medical imaging methods. For nonexperts, the author provides appendices that cover background information on notation, Fourier analysis, geometric rays, and linear operators. The vast bibliography, with over 825 entries, directs readers to a wide array of additional information sources on medical imaging for further study.

Partial Differential Equation Methods for Image Inpainting

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A Taste of Inverse Problems

Author : Martin Hanke
File Size : 40.95 MB
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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.

Mathematical Models in Biology

Author : Valeria Zazzu
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This book presents an exciting collection of contributions based on the workshop “Bringing Maths to Life” held October 27-29, 2014 in Naples, Italy. The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content useful as it addresses existing challenges in identifying the gaps between mathematical modeling and biological research. The shared solutions will aid and promote further collaboration between life sciences and mathematics.

Hybrid Imaging in Cardiovascular Medicine

Author : Yi-Hwa Liu
File Size : 29.84 MB
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This comprehensive book focuses on multimodality imaging technology, including overviews of the instruments and methods followed by practical case studies that highlight use in the detection and treatment of cardiovascular diseases. Chapters cover PET-CT, SPECT-CT, SPECT-MRI, PET-MRI, PET-optical imaging, SPECT-optical imaging, photoacoustic Imaging, and hybrid intravascular imaging. It also addresses the important issues of multimodality imaging probes and image quantification. Readers from radiology and cardiology as well as medical imaging and biomedical engineering will learn essentials of the field. They will be shown how the field has advanced quantitative analysis of molecularly targeted imaging through improvements in the reliability and reproducibility of imaging data. Moreover, they will be presented with quantification algorithms and case illustrations, including coverage of such topics such as multimodality image fusion and kinetic modeling. Yi-Hwa Liu, PhD is Senior Research Scientist in Cardiovascular Medicine at Yale University School of Medicine and Technical Director of Nuclear Cardiology at Yale New Haven Hospital. He is also an Associate Professor (Adjunct) of Biomedical Imaging and Radiological Sciences at National Yang-Ming University, Taipei, Taiwan, and Professor (Adjunct) of Biomedical Engineering at Chung Yuan Christian University, Taoyuan, Taiwan. He is an elected senior member of Institute of Electrical and Electronic Engineers (IEEE) and a full member of Sigma Xi of The Scientific Research Society of North America. Albert J. Sinusas, M.D., FACC, FAHA is Professor of Medicine (Section of Cardiovascular Medicine) and Radiology and Biomedical Imaging, at Yale University School of Medicine, and Director of the Yale Translational Research Imaging Center (Y-TRIC), and Director of Advanced Cardiovascular Imaging at Yale New Haven Hospital. He is a recipient of the Society of Nuclear Medicine’s Hermann Blumgart Award.

Geometric Partial Differential Equations Part 2

Author : Andrea Bonito
File Size : 46.69 MB
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Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. It includes basic ideas, analysis and applications of state-of-the-art fundamental algorithms for the approximation of geometric PDEs together with their impacts in a variety of fields within mathematics, science, and engineering. About every aspect of computational geometric PDEs is discussed in this and a companion volume. Topics in this volume include stationary and time-dependent surface PDEs for geometric flows, large deformations of nonlinearly geometric plates and rods, level set and phase field methods and applications, free boundary problems, discrete Riemannian calculus and morphing, fully nonlinear PDEs including Monge-Ampere equations, and PDE constrained optimization Each chapter is a complete essay at the research level but accessible to junior researchers and students. The intent is to provide a comprehensive description of algorithms and their analysis for a specific geometric PDE class, starting from basic concepts and concluding with interesting applications. Each chapter is thus useful as an introduction to a research area as well as a teaching resource, and provides numerous pointers to the literature for further reading The authors of each chapter are world leaders in their field of expertise and skillful writers. This book is thus meant to provide an invaluable, readable and enjoyable account of computational geometric PDEs

Scale Space and Variational Methods in Computer Vision

Author : Alfred M. Bruckstein
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This book constitutes the thoroughly refereed post-conference proceedings of the Third International Conference on Scale Space Methods and Variational Methods in Computer Vision, SSVM 2011, held in Ein-Gedi, Israel in May/June 2011. The 24 revised full papers presented together with 44 poster papers were carefully reviewed and selected from 78 submissions. The papers are organized in topical sections on denoising and enhancement, segmentation, image representation and invariants, shape analysis, and optical flow.

Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Author : Ke Chen
File Size : 37.20 MB
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Pattern Recognition

Author : Volker Roth
File Size : 80.88 MB
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This book constitutes the refereed proceedings of the 39th German Conference on Pattern Recognition, GCPR 2017, held in Basel, Switzerland, in September 2017.The 33 revised full papers presented were carefully reviewed and selected from 60 submissions. The papers are organized in topical sections on biomedical image processing and analysis; classification and detection; computational photography; image and video processing; machine learning and pattern recognition; mathematical foundations, statistical data analysis and models; motion and segmentation; pose, face and gesture; reconstruction and depth; and tracking.