Mathematical And Statistical Methods For Imaging
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| Author | : Habib Ammari |
| Publisher | : Springer |
| Total Pages | : 366 |
| Release | : 2013-11-29 |
| Genre | : Mathematics |
| ISBN | : 3319025856 |
This book covers recent mathematical, numerical, and statistical approaches for multistatic imaging of targets with waves at single or multiple frequencies. The waves can be acoustic, elastic or electromagnetic. They are generated by point sources on a transmitter array and measured on a receiver array. An important problem in multistatic imaging is to quantify and understand the trade-offs between data size, computational complexity, signal-to-noise ratio, and resolution. Another fundamental problem is to have a shape representation well suited to solving target imaging problems from multistatic data. In this book the trade-off between resolution and stability when the data are noisy is addressed. Efficient imaging algorithms are provided and their resolution and stability with respect to noise in the measurements analyzed. It also shows that high-order polarization tensors provide an accurate representation of the target. Moreover, a dictionary-matching technique based on new invariants for the generalized polarization tensors is introduced. Matlab codes for the main algorithms described in this book are provided. Numerical illustrations using these codes in order to highlight the performance and show the limitations of numerical approaches for multistatic imaging are presented.
| Author | : Habib Ammari |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 178 |
| Release | : 2011-07-20 |
| Genre | : Mathematics |
| ISBN | : 0821852892 |
This volume contains the proceedings of the NIMS Thematic Workshop on Mathematical and Statistical Methods for Imaging, which was held from August 10-13, 2010, at Inha University, Incheon, Korea. The goal of this volume is to give the reader a deep and unified understanding of the field of imaging and of the analytical and statistical tools used in imaging. It offers a good overview of the current status of the field and of directions for further research. Challenging problems are addressed from analytical, numerical, and statistical perspectives. The articles are devoted to four main areas: analytical investigation of robustness; hypothesis testing and resolution analysis, particularly for anomaly detection; new efficient imaging techniques; and the effects of anisotropy, dissipation, or attenuation in 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 | : Tianhu Lei |
| Publisher | : CRC Press |
| Total Pages | : 426 |
| Release | : 2011-12-19 |
| Genre | : Mathematics |
| ISBN | : 1420088432 |
More work is being done in the statistical aspects of medical imaging, and this book fills the gap to provide a unified framework of study by presenting a complete look at medical imaging and statistics - from the statistical aspects of imaging technology to the statistical analysis of images. It provides technicians and students with the statistical principles that underlay medical imaging, as required reference material for researchers involved in the design of new technology. Illustrations are included throughout as are many real examples, and algorithms. The text also includes exercises developed out of the author's many years experience with studying the statistics of medical imaging.
| Author | : Luc Florack |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 321 |
| Release | : 2012-01-13 |
| Genre | : Mathematics |
| ISBN | : 1447123522 |
Mathematical Methods for Signal and Image Analysis and Representation presents the mathematical methodology for generic image analysis tasks. In the context of this book an image may be any m-dimensional empirical signal living on an n-dimensional smooth manifold (typically, but not necessarily, a subset of spacetime). The existing literature on image methodology is rather scattered and often limited to either a deterministic or a statistical point of view. In contrast, this book brings together these seemingly different points of view in order to stress their conceptual relations and formal analogies. Furthermore, it does not focus on specific applications, although some are detailed for the sake of illustration, but on the methodological frameworks on which such applications are built, making it an ideal companion for those seeking a rigorous methodological basis for specific algorithms as well as for those interested in the fundamental methodology per se. Covering many topics at the forefront of current research, including anisotropic diffusion filtering of tensor fields, this book will be of particular interest to graduate and postgraduate students and researchers in the fields of computer vision, medical imaging and visual perception.
| Author | : Moo K. Chung |
| Publisher | : CRC Press |
| Total Pages | : 436 |
| Release | : 2013-07-23 |
| Genre | : Mathematics |
| ISBN | : 1439836353 |
The massive amount of nonstandard high-dimensional brain imaging data being generated is often difficult to analyze using current techniques. This challenge in brain image analysis requires new computational approaches and solutions. But none of the research papers or books in the field describe the quantitative techniques with detailed illustrations of actual imaging data and computer codes. Using MATLAB® and case study data sets, Statistical and Computational Methods in Brain Image Analysis is the first book to explicitly explain how to perform statistical analysis on brain imaging data. The book focuses on methodological issues in analyzing structural brain imaging modalities such as MRI and DTI. Real imaging applications and examples elucidate the concepts and methods. In addition, most of the brain imaging data sets and MATLAB codes are available on the author’s website. By supplying the data and codes, this book enables researchers to start their statistical analyses immediately. Also suitable for graduate students, it provides an understanding of the various statistical and computational methodologies used in the field as well as important and technically challenging topics.
| Author | : Xavier Pennec |
| Publisher | : Academic Press |
| Total Pages | : 636 |
| Release | : 2019-09-02 |
| Genre | : Computers |
| ISBN | : 0128147261 |
Over the past 15 years, there has been a growing need in the medical image computing community for principled methods to process nonlinear geometric data. Riemannian geometry has emerged as one of the most powerful mathematical and computational frameworks for analyzing such data. Riemannian Geometric Statistics in Medical Image Analysis is a complete reference on statistics on Riemannian manifolds and more general nonlinear spaces with applications in medical image analysis. It provides an introduction to the core methodology followed by a presentation of state-of-the-art methods. Beyond medical image computing, the methods described in this book may also apply to other domains such as signal processing, computer vision, geometric deep learning, and other domains where statistics on geometric features appear. As such, the presented core methodology takes its place in the field of geometric statistics, the statistical analysis of data being elements of nonlinear geometric spaces. The foundational material and the advanced techniques presented in the later parts of the book can be useful in domains outside medical imaging and present important applications of geometric statistics methodology Content includes: - The foundations of Riemannian geometric methods for statistics on manifolds with emphasis on concepts rather than on proofs - Applications of statistics on manifolds and shape spaces in medical image computing - Diffeomorphic deformations and their applications As the methods described apply to domains such as signal processing (radar signal processing and brain computer interaction), computer vision (object and face recognition), and other domains where statistics of geometric features appear, this book is suitable for researchers and graduate students in medical imaging, engineering and computer science. - A complete reference covering both the foundations and state-of-the-art methods - Edited and authored by leading researchers in the field - Contains theory, examples, applications, and algorithms - Gives an overview of current research challenges and future applications
| Author | : Paul Fieguth |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 465 |
| Release | : 2010-10-17 |
| Genre | : Mathematics |
| ISBN | : 1441972943 |
Images are all around us! The proliferation of low-cost, high-quality imaging devices has led to an explosion in acquired images. When these images are acquired from a microscope, telescope, satellite, or medical imaging device, there is a statistical image processing task: the inference of something—an artery, a road, a DNA marker, an oil spill—from imagery, possibly noisy, blurry, or incomplete. A great many textbooks have been written on image processing. However this book does not so much focus on images, per se, but rather on spatial data sets, with one or more measurements taken over a two or higher dimensional space, and to which standard image-processing algorithms may not apply. There are many important data analysis methods developed in this text for such statistical image problems. Examples abound throughout remote sensing (satellite data mapping, data assimilation, climate-change studies, land use), medical imaging (organ segmentation, anomaly detection), computer vision (image classification, segmentation), and other 2D/3D problems (biological imaging, porous media). The goal, then, of this text is to address methods for solving multidimensional statistical problems. The text strikes a balance between mathematics and theory on the one hand, versus applications and algorithms on the other, by deliberately developing the basic theory (Part I), the mathematical modeling (Part II), and the algorithmic and numerical methods (Part III) of solving a given problem. The particular emphases of the book include inverse problems, multidimensional modeling, random fields, and hierarchical methods.
| Author | : Habib Ammari |
| Publisher | : Princeton University Press |
| Total Pages | : 240 |
| Release | : 2015-04-06 |
| Genre | : Mathematics |
| ISBN | : 0691165319 |
This book is the first to comprehensively explore elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative–based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic structures, the book opens possibilities for a mathematical and numerical framework for elasticity imaging of nanoparticles and cellular structures.
| 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.
