Download or read book Stability of Diffuse Optical Tomography in the Bayesian Framework written by Kit Newton and published by . This book was released on 2020 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems arising in the sciences and engineering require solving an inverse problem, measuring data and inferring the model parameters using the collected information. However, often the available data does not have enough information to uniquely or stably reconstruct the parameters, making the problem ill-posed. We study ill-posedness in the context of optical tomography, a medical imaging technique that uses light to probe tissue structure. Experimentally, light is sent into biological tissue, and the outgoing light intensity on the surface of the material is measured in order to reconstruct the optical properties of the tissue. In the regime of high-energy light, the light scatters infrequently, and the radiative transfer equation ("RTE'') is used as the underlying model. Optical tomography in this regime is mathematically represented as inverting the so-called albedo operator, which maps the incoming light to the outgoing light intensity. This process is proved to be well-posed, in the sense that the information collected uniquely and stably reconstructs the optical parameter in the RTE. In the regime of low-energy light, the light scatters frequently, and the diffusion equation ("DE'') is a good approximation. Mathematically, the Dirichlet-to-Neumann ("DtN'') operator maps the light incoming to the tissue to the light current on the surface of the tissue. Inverting this map to learn the tissue's properties is known as the Calderon problem, which is ill-posed, in the sense that the reconstruction of the optical parameter is unstable. As the energy of the photons decreases and the scattering increases, it is shown that the RTE and DE are asymptotically equivalent in the low-energy regime. The procedue that asymptotically connects the two equations is called the diffusion limit. Since inverting the albedo operator is a well-posed problem, whereas inverting the DtN map is ill-posed, the well-posedness must deteriorate in the diffusion limit. In the Bayesian framework, the solution to an inverse problem is seen as the distribution of possible parameters. In the diffusion limit, the distribution based on the RTE converges to the distribution based on the DE. We rigorously prove this convergence in both Kullback-Leibler divergence and the Hellinger distance. Numerically, using this convergence, we develop a two-stage Markov chain Monte Carlo ("MCMC'') method that leverages the diffusion limit to improve the efficiency of sampling from the distribution based on the RTE. Upon linearization and discretization, inverse problems are represented as a matrix equation Ax ≈ b, where A [epsilon] R^(n x p) arises from the PDE and b [epsilon] R^n is the data. The matrix A is semi-infinite, with n representing the infinite number of measurements required on the boundary, and p finite. A common way to find x is to formulate a least-squares ("LS'') problem min_x, ||Ax-b||_2. In practice, only finitely many experimental data can be obtained to infer a finite dimensional parameter, meaning the number of constraints in A and the number of data points in b is finite. The question in reality is how to choose finitely many data points that are as informative as possible. We use random sketching to study this problem: we find a "sketching matrix'' S, so that SAx - Sb approximates Ax-b. However, when the LS problem arises from an inverse problem with a PDE as the underlying model (called "PDE-based inverse problems''), such as optical tomography and the Calderon problem, then the matrix A has a special tensor structure, which must be accounted for in the design of S. In this thesis, we display two structures of S suitable for use in PDE-based inverse problems, and give a lower bound on the number of necessary rows in S that is independent of the number of measurements n.

Download or read book Towards a Bayesian Framework for Optical Tomography written by Ivo Widjaja Kwee and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Journal of the Optical Society of America written by and published by . This book was released on 2003 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Hyperbolic Problems Theory Numerics Applications Volume II written by Carlos Parés and published by Springer Nature. This book was released on with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Probabilistic Finite Element Model Updating Using Bayesian Statistics written by Tshilidzi Marwala and published by John Wiley & Sons. This book was released on 2016-09-23 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic Finite Element Model Updating Using Bayesian Statistics: Applications to Aeronautical and Mechanical Engineering Tshilidzi Marwala and Ilyes Boulkaibet, University of Johannesburg, South Africa Sondipon Adhikari, Swansea University, UK Covers the probabilistic finite element model based on Bayesian statistics with applications to aeronautical and mechanical engineering Finite element models are used widely to model the dynamic behaviour of many systems including in electrical, aerospace and mechanical engineering. The book covers probabilistic finite element model updating, achieved using Bayesian statistics. The Bayesian framework is employed to estimate the probabilistic finite element models which take into account of the uncertainties in the measurements and the modelling procedure. The Bayesian formulation achieves this by formulating the finite element model as the posterior distribution of the model given the measured data within the context of computational statistics and applies these in aeronautical and mechanical engineering. Probabilistic Finite Element Model Updating Using Bayesian Statistics contains simple explanations of computational statistical techniques such as Metropolis-Hastings Algorithm, Slice sampling, Markov Chain Monte Carlo method, hybrid Monte Carlo as well as Shadow Hybrid Monte Carlo and their relevance in engineering. Key features: Contains several contributions in the area of model updating using Bayesian techniques which are useful for graduate students. Explains in detail the use of Bayesian techniques to quantify uncertainties in mechanical structures as well as the use of Markov Chain Monte Carlo techniques to evaluate the Bayesian formulations. The book is essential reading for researchers, practitioners and students in mechanical and aerospace engineering.

Download or read book Bayesian Filtering and Smoothing written by Simo Särkkä and published by Cambridge University Press. This book was released on 2013-09-05 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.

Download or read book Statistical Parametric Mapping The Analysis of Functional Brain Images written by William D. Penny and published by Elsevier. This book was released on 2011-04-28 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an age where the amount of data collected from brain imaging is increasing constantly, it is of critical importance to analyse those data within an accepted framework to ensure proper integration and comparison of the information collected. This book describes the ideas and procedures that underlie the analysis of signals produced by the brain. The aim is to understand how the brain works, in terms of its functional architecture and dynamics. This book provides the background and methodology for the analysis of all types of brain imaging data, from functional magnetic resonance imaging to magnetoencephalography. Critically, Statistical Parametric Mapping provides a widely accepted conceptual framework which allows treatment of all these different modalities. This rests on an understanding of the brain's functional anatomy and the way that measured signals are caused experimentally. The book takes the reader from the basic concepts underlying the analysis of neuroimaging data to cutting edge approaches that would be difficult to find in any other source. Critically, the material is presented in an incremental way so that the reader can understand the precedents for each new development. This book will be particularly useful to neuroscientists engaged in any form of brain mapping; who have to contend with the real-world problems of data analysis and understanding the techniques they are using. It is primarily a scientific treatment and a didactic introduction to the analysis of brain imaging data. It can be used as both a textbook for students and scientists starting to use the techniques, as well as a reference for practicing neuroscientists. The book also serves as a companion to the software packages that have been developed for brain imaging data analysis. - An essential reference and companion for users of the SPM software - Provides a complete description of the concepts and procedures entailed by the analysis of brain images - Offers full didactic treatment of the basic mathematics behind the analysis of brain imaging data - Stands as a compendium of all the advances in neuroimaging data analysis over the past decade - Adopts an easy to understand and incremental approach that takes the reader from basic statistics to state of the art approaches such as Variational Bayes - Structured treatment of data analysis issues that links different modalities and models - Includes a series of appendices and tutorial-style chapters that makes even the most sophisticated approaches accessible

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Modelling written by Seppo Pohjolainen and published by Springer. This book was released on 2016-07-14 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Wiley Encyclopedia of Clinical Trials written by Lisa Marie Sullivan and published by Wiley-Blackwell. This book was released on 2008 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here you'll find more than 500 entries from the world's leading experts in the field on the basic concepts, methodologies, and applications in clinical trials. The range of topics includes: basic statistical concepts, design and analysis of clinical trials, ethics, regulatory issues, and methodologies for clinical data management and analysis

Download or read book Bayesian Approach to Inverse Problems written by Jérôme Idier and published by John Wiley & Sons. This book was released on 2013-03-01 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many scientific, medical or engineering problems raise the issue of recovering some physical quantities from indirect measurements; for instance, detecting or quantifying flaws or cracks within a material from acoustic or electromagnetic measurements at its surface is an essential problem of non-destructive evaluation. The concept of inverse problems precisely originates from the idea of inverting the laws of physics to recover a quantity of interest from measurable data. Unfortunately, most inverse problems are ill-posed, which means that precise and stable solutions are not easy to devise. Regularization is the key concept to solve inverse problems. The goal of this book is to deal with inverse problems and regularized solutions using the Bayesian statistical tools, with a particular view to signal and image estimation. The first three chapters bring the theoretical notions that make it possible to cast inverse problems within a mathematical framework. The next three chapters address the fundamental inverse problem of deconvolution in a comprehensive manner. Chapters 7 and 8 deal with advanced statistical questions linked to image estimation. In the last five chapters, the main tools introduced in the previous chapters are put into a practical context in important applicative areas, such as astronomy or medical imaging.

Download or read book Waves and Imaging through Complex Media written by P. Sebbah and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent advances in wave propagation in random media are certainly consequences of new approaches to fundamental issues, as well as of a strong interest in potential applications. A collective effort has been made to present in this book the state of the art in fundamental concepts, as well as in biomedical imaging techniques. As an example, the recent introduction of wave chaos, and more specifically random matrix theory - an old tool from nuclear physics - to the study of multiple scattering, has pointed the way to a deeper understanding of wave coherence in complex media. At the same time, efficient new approaches for retrieving information from random media promise to allow wave imaging of small tumors in opaque tissues. Review chapters are written by experts in the field, with the aim of making the book accessible to the widest possible scientific audience: graduate students and research scientists in theoretical and applied physics, optics, acoustics, and biomedical physics.

Download or read book Mathematics and Computation in Imaging Science and Information Processing written by Say Song Goh and published by World Scientific. This book was released on 2007 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: The explosion of data arising from rapid advances in communication, sensing and computational power has concentrated research effort on more advanced techniques for the representation, processing, analysis and interpretation of data sets. In view of these exciting developments, the program OC Mathematics and Computation in Imaging Science and Information ProcessingOCO was held at the Institute for Mathematical Sciences, National University of Singapore, from July to December 2003 and in August 2004 to promote and facilitate multidisciplinary research in the area. As part of the program, a series of tutorial lectures were conducted by international experts on a wide variety of topics in mathematical image, signal and information processing. This compiled volume contains survey articles by the tutorial speakers, all specialists in their respective areas. They collectively provide graduate students and researchers new to the field a unique and valuable introduction to a range of important topics at the frontiers of current research. Sample Chapter(s). Foreword (46 KB). Chapter 1: Subdivision on Arbitrary Meshes: Algorithms and Theory (771 KB). Contents: Subdivision on Arbitrary Meshes: Algorithms and Theory (D Zorin); High Order Numerical Methods for Time Dependent Hamilton-Jacobi Equations (C-W Shu); Theory and Computation of Variational Image Deblurring (T F Chan & J Shen); Data Hiding OCo Theory and Algorithms (P Moulin & R Koetter); Image Steganography and Steganalysis: Concepts and Practice (M Kharrazi et al.); The Apriori Algorithm OCo A Tutorial (M Hegland). Readership: Graduate students and researchers in mathematical image, signal and information processing."

Download or read book Dissertation Abstracts International written by and published by . This book was released on 2008 with total page 946 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Index Medicus written by and published by . This book was released on 2004 with total page 2520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vols. for 1963- include as pt. 2 of the Jan. issue: Medical subject headings.

Download or read book Handbook of Small Animal Imaging written by George C. Kagadis and published by CRC Press. This book was released on 2018-09-03 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of small animal models in basic and preclinical sciences constitutes an integral part of testing new pharmaceutical agents prior to their application in clinical practice. New imaging and therapeutic approaches need to be tested and validated first in animals before application to humans. Handbook of Small Animal Imaging: Preclinical Imaging, Therapy, and Applications collects the latest information about various imaging and therapeutic technologies used in preclinical research into a single source. Useful to established researchers as well as newcomers to the field, this handbook shows readers how to exploit and integrate these imaging and treatment modalities and techniques into their own research. The book first presents introductory material on small animal imaging, therapy, and research ethics. It next covers ionizing radiation and nonionizing radiation methods in small animal imaging, hybrid imaging, and imaging agents. The book then addresses therapeutic research platforms and image quantification, explaining how to ensure accurate measurements of high-quality data. It concludes with an overview of many small animal imaging and therapy applications that demonstrate the strength of the techniques in biomedical fields.

Download or read book Optics Letters written by and published by . This book was released on 2005 with total page 1002 pages. Available in PDF, EPUB and Kindle. Book excerpt: