Mathematical Problems Of Thermoacoustic Tomography

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Mathematical Problems of Thermoacoustic Tomography

Author : Linh V. Nguyen
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (686 download)

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Book Synopsis Mathematical Problems of Thermoacoustic Tomography by : Linh V. Nguyen

Download or read book Mathematical Problems of Thermoacoustic Tomography written by Linh V. Nguyen and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Thermoacoustic tomography (TAT) is a newly emerging modality in biomedical imaging. It combines the good contrast of electromagnetic and good resolution of ultrasound imaging. The mathematical model of TAT is the observability problem for the wave equation: one observes the data on a hyper-surface and reconstructs the initial perturbation. In this dissertation, we consider several mathematical problems of TAT. The first problem is the inversion formulas. We provide a family of closed form inversion formulas to reconstruct the initial perturbation from the observed data. The second problem is the range description. We present the range description of the spherical mean Radon transform, which is an important transform in TAT. The next problem is the stability analysis for TAT. We prove that the reconstruction of the initial perturbation from observed data is not Hölder stable if some observability condition is violated. The last problem is the speed determination. The question is whether the observed data uniquely determines the ultrasound speed and initial perturbation. We provide some initial results on this issue. They include the unique determination of the unknown constant speed, a weak local uniqueness, a characterization of the non-uniqueness, and a characterization of the kernel of the linearized operator.

Mathematical Problems of Thermoacoustic and Compton Camera Imaging

Author : Yulia Nekova Georgieva-Hristova
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (76 download)

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Book Synopsis Mathematical Problems of Thermoacoustic and Compton Camera Imaging by : Yulia Nekova Georgieva-Hristova

Download or read book Mathematical Problems of Thermoacoustic and Compton Camera Imaging written by Yulia Nekova Georgieva-Hristova and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The results presented in this dissertation concern two different types of tomographic imaging. The first part of the dissertation is devoted to the time reversal method for approximate reconstruction of images in thermoacoustic tomography. A thorough numerical study of the method is presented. Error estimates of the time reversal approximation are provided. In the second part of the dissertation a type of emission tomography, called Compton camera imaging is considered. The mathematical problem arising in Compton camera imaging is the inversion of the cone transform. We present three methods for inversion of this transform in two dimensions. Numerical examples of reconstructions by these methods are also provided. Lastly, we turn to a problem of significance in homeland security, namely the detection of geometrically small, low emission sources in the presence of a large background radiation. We consider the use of Compton type detectors for this purpose and describe an efficient method for detection of such sources. Numerical examples demonstrating this method are also provided.

Spherical Radon Transforms and Mathematical Problems of Thermoacoustic Tomography

Author : Gaik Ambartsoumian
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (69 download)

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Book Synopsis Spherical Radon Transforms and Mathematical Problems of Thermoacoustic Tomography by : Gaik Ambartsoumian

Download or read book Spherical Radon Transforms and Mathematical Problems of Thermoacoustic Tomography written by Gaik Ambartsoumian and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The spherical Radon transform (SRT) integrates a function over the set of all spheres with a given set of centers. Such transforms play an important role in some newly developing types of tomography as well as in several areas of mathematics including approximation theory, integral geometry, inverse problems for PDEs, etc. In Chapter I we give a brief description of thermoacoustic tomography (TAT or TCT) and introduce the SRT. In Chapter II we consider the injectivity problem for SRT. A major breakthrough in the 2D case was made several years ago by M. Agranovsky and E.T. Quinto. Their techniques involved microlocal analysis and known geometric properties of zeros of harmonic polynomials in the plane. Since then there has been an active search for alternative methods, which would be less restrictive in more general situations. We provide some new results obtained by PDE techniques that essentially involve only the finite speed of propagation and domain dependence for the wave equation. In Chapter III we consider the transform that integrates a function supported in the unit disk on the plane over circles centered at the boundary of this disk. As is common for transforms of the Radon type, its range has an in finite co-dimension in standard function spaces. Range descriptions for such transforms are known to be very important for computed tomography, for instance when dealing with incomplete data, error correction, and other issues. A complete range description for the circular Radon transform is obtained. In Chapter IV we investigate implementation of the recently discovered exact backprojection type inversion formulas for the case of spherical acquisition in 3D and approximate inversion formulas in 2D. A numerical simulation of the data acquisition with subsequent reconstructions is made for the Defrise phantom as well as for some other phantoms. Both full and partial scan situations are considered.

Thermoacoustic Tomography

Author : Huabei Jiang
Publisher :
ISBN 13 : 9780750331647
Total Pages : 152 pages
Book Rating : 4.3/5 (316 download)

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Book Synopsis Thermoacoustic Tomography by : Huabei Jiang

Download or read book Thermoacoustic Tomography written by Huabei Jiang and published by . This book was released on 2020-03-26 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first of its kind to cover the underlying principles and biomedical applications of thermoacoustic tomography (TAT). Written in a tutorial format, it describes the fundamentals of TAT; details advanced approaches for quantitative TAT; explores the development of several image enhancing schemes including both software and hardware approaches; examines array-based TAT systems; considers high-resolution TAT approaches and combinations of TAT with other imaging methods; addresses contrast agent-based molecular TAT; and discusses clinical applications and animal studies in the areas of brain, breast, joint, thyroid, liver and vascular imaging. It is a valuable resource for students, academics, and industry specialists, including biomedical engineers, electrical engineers, physicists and mathematicians.

Handbook of Mathematical Methods in Imaging

Author : Otmar Scherzer
Publisher : Springer Science & Business Media
ISBN 13 : 0387929193
Total Pages : 1626 pages
Book Rating : 4.3/5 (879 download)

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Book Synopsis Handbook of Mathematical Methods in Imaging by : Otmar Scherzer

Download or read book Handbook of Mathematical Methods in Imaging written by Otmar Scherzer and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Microlocal Analysis and Inverse Problems in Tomography and Geometry

Author : Eric Todd Quinto
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111337480
Total Pages : 198 pages
Book Rating : 4.1/5 (113 download)

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Book Synopsis Microlocal Analysis and Inverse Problems in Tomography and Geometry by : Eric Todd Quinto

Download or read book Microlocal Analysis and Inverse Problems in Tomography and Geometry written by Eric Todd Quinto and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-09-23 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Microlocal Analysis has proven to be a powerful tool for analyzing and solving inverse problems; including answering questions about stability, uniqueness, recovery of singularities, etc. This volume, presents several studies on microlocal methods in problems in tomography, integral geometry, geodesic transforms, travel time tomography, thermoacoustic tomography, Compton CT, cosmology, nonlinear inverse problems, and others.

Mathematical and Numerical Approaches for Multi-Wave Inverse Problems

Author : Larisa Beilina
Publisher : Springer Nature
ISBN 13 : 3030486346
Total Pages : 147 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Mathematical and Numerical Approaches for Multi-Wave Inverse Problems by : Larisa Beilina

Download or read book Mathematical and Numerical Approaches for Multi-Wave Inverse Problems written by Larisa Beilina and published by Springer Nature. This book was released on 2020-06-30 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume gathers peer-reviewed, selected papers presented at the “Mathematical and Numerical Approaches for Multi-Wave Inverse Problems” conference at the Centre Internacional de Rencontres Mathématiques (CIRM) in Marseille, France, in April 2019. It brings the latest research into new, reliable theoretical approaches and numerical techniques for solving nonlinear and inverse problems arising in multi-wave and hybrid systems. Multi-wave inverse problems have a wide range of applications in acoustics, electromagnetics, optics, medical imaging, and geophysics, to name but a few. In turn, it is well known that inverse problems are both nonlinear and ill-posed: two factors that pose major challenges for the development of new numerical methods for solving these problems, which are discussed in detail. These papers will be of interest to all researchers and graduate students working in the fields of nonlinear and inverse problems and its applications.

Tomography and Inverse Transport Theory

Author : Guillaume Bal
Publisher : American Mathematical Soc.
ISBN 13 : 0821853015
Total Pages : 194 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Tomography and Inverse Transport Theory by : Guillaume Bal

Download or read book Tomography and Inverse Transport Theory written by Guillaume Bal and published by American Mathematical Soc.. This book was released on 2011 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains research and review articles written by participants of two related international workshops ``Mathematical Methods in Emerging Modalities of Medical Imaging'' (October 2009) and ``Inverse Transport Theory and Tomography'' (May 2010), which were held at the Banff International Research Station in Banff, Canada. These workshops brought together mathematicians, physicists, engineers, and medical researchers working at the cutting edge of medical imaging research and addressed the demanding mathematical problems arising in this area. The articles, written by leading experts, address important analytic, numerical, and physical issues of the newly developing imaging modalities (e.g., photoacoustics, current impedance imaging, hybrid imaging techniques, elasticity imaging), as well as the recent progress in resolving outstanding problems of more traditional modalities, such as SPECT, ultrasound imaging, and inverse transport theory. Related topics of invisibility cloaking are also addressed.

Inverse Problems and Applications

Author : Gunther Uhlmann
Publisher : Cambridge University Press
ISBN 13 : 1107032016
Total Pages : 593 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Inverse Problems and Applications by : Gunther Uhlmann

Download or read book Inverse Problems and Applications written by Gunther Uhlmann and published by Cambridge University Press. This book was released on 2013 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems lie at the heart of contemporary scientific inquiry and technological development. Applications include a variety of medical and other imaging techniques, which are used for early detection of cancer and pulmonary edema, location of oil and mineral deposits in the Earth's interior, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes, and modeling in the life sciences among others. The expository survey essays in this book describe recent developments in inverse problems and imaging, including hybrid or couple-physics methods arising in medical imaging, Calderon's problem and electrical impedance tomography, inverse problems arising in global seismology and oil exploration, inverse spectral problems, and the study of asymptotically hyperbolic spaces. It is suitable for graduate students and researchers interested in inverse problems and their applications.

Inverse Problems and Applications

Author : Plamen Stefanov
Publisher : American Mathematical Soc.
ISBN 13 : 1470410796
Total Pages : 322 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Inverse Problems and Applications by : Plamen Stefanov

Download or read book Inverse Problems and Applications written by Plamen Stefanov and published by American Mathematical Soc.. This book was released on 2014-05-05 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of two conferences on Inverse Problems and Applications, held in 2012, to celebrate the work of Gunther Uhlmann. The first conference was held at the University of California, Irvine, from June 18-22, 2012, and the second was held at Zhejiang University, Hangzhou, China, from September 17-21, 2012. The topics covered include inverse problems in medical imaging, scattering theory, geometry and image processing, and the mathematical theory of cloaking, as well as methods related to inverse problems.

The Radon Transform, Inverse Problems, and Tomography

Author : Gestur Ólafsson
Publisher : American Mathematical Soc.
ISBN 13 : 0821839306
Total Pages : 176 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Radon Transform, Inverse Problems, and Tomography by : Gestur Ólafsson

Download or read book The Radon Transform, Inverse Problems, and Tomography written by Gestur Ólafsson and published by American Mathematical Soc.. This book was released on 2006 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their emergence in 1917, tomography and inverse problems remain active and important fields that combine pure and applied mathematics and provide strong interplay between diverse mathematical problems and applications. The applied side is best known for medical and scientific use, in particular, medical imaging, radiotherapy, and industrial non-destructive testing. Doctors use tomography to see the internal structure of the body or to find functional information, such asmetabolic processes, noninvasively. Scientists discover defects in objects, the topography of the ocean floor, and geological information using X-rays, geophysical measurements, sonar, or other data. This volume, based on the lectures in the Short Course The Radon Transform and Applications to InverseProblems at the American Mathematical Society meeting in Atlanta, GA, January 3-4, 2005, brings together articles on mathematical aspects of tomography and related inverse problems. The articles cover introductory material, theoretical problems, and practical issues in 3-D tomography, impedance imaging, local tomography, wavelet methods, regularization and approximate inverse, sampling, and emission tomography. All contributions are written for a general audience, and the authors have includedreferences for further reading.

The Radon Transform and Medical Imaging

Author : Peter Kuchment
Publisher : SIAM
ISBN 13 : 1611973295
Total Pages : 238 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis The Radon Transform and Medical Imaging by : Peter Kuchment

Download or read book The Radon Transform and Medical Imaging written by Peter Kuchment and published by SIAM. This book was released on 2014-01-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Problems of Tomography

Author : Izrailʹ Moiseevich Gelʹfand
Publisher : American Mathematical Society(RI)
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Problems of Tomography by : Izrailʹ Moiseevich Gelʹfand

Download or read book Mathematical Problems of Tomography written by Izrailʹ Moiseevich Gelʹfand and published by American Mathematical Society(RI). This book was released on 1990 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: As early as 1917, Radon derived an explicit formula for the reconstruction of a function on the plane, given its integrals over all lines. In the late 1960s, the first applications of the Radon formula appeared, in radio astronomy and then in electron micrography. The use of the Radon formula for constructing tomograms, made possible by the advent of the computer, saw its first use in clinical medicine in 1970 and earned its developers the Nobel Prize in medicine.

Microlocal Analysis and Inverse Problems in Tomography and Geometry

Author : Eric Todd Quinto
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111338010
Total Pages : 252 pages
Book Rating : 4.1/5 (113 download)

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Book Synopsis Microlocal Analysis and Inverse Problems in Tomography and Geometry by : Eric Todd Quinto

Download or read book Microlocal Analysis and Inverse Problems in Tomography and Geometry written by Eric Todd Quinto and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-09-23 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Microlocal Analysis has proven to be a powerful tool for analyzing and solving inverse problems; including answering questions about stability, uniqueness, recovery of singularities, etc. This volume, presents several studies on microlocal methods in problems in tomography, integral geometry, geodesic transforms, travel time tomography, thermoacoustic tomography, Compton CT, cosmology, nonlinear inverse problems, and others.

The Mathematical Legacy of Leon Ehrenpreis

Author : Irene Sabadini
Publisher : Springer Science & Business Media
ISBN 13 : 8847019478
Total Pages : 391 pages
Book Rating : 4.8/5 (47 download)

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Book Synopsis The Mathematical Legacy of Leon Ehrenpreis by : Irene Sabadini

Download or read book The Mathematical Legacy of Leon Ehrenpreis written by Irene Sabadini and published by Springer Science & Business Media. This book was released on 2012-04-23 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Author : Ke Chen
Publisher : Springer Nature
ISBN 13 : 3030986616
Total Pages : 1981 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging by : Ke Chen

Download or read book Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging written by Ke Chen and published by Springer Nature. This book was released on 2023-02-24 with total page 1981 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Models, Methods and Applications

Author : Abul Hasan Siddiqi
Publisher : Springer
ISBN 13 : 9812879730
Total Pages : 309 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Mathematical Models, Methods and Applications by : Abul Hasan Siddiqi

Download or read book Mathematical Models, Methods and Applications written by Abul Hasan Siddiqi and published by Springer. This book was released on 2015-12-14 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume contains invited talks of 11th biennial conference on “Emerging Mathematical Methods, Models and Algorithms for Science and Technology”. The main message of the book is that mathematics has a great potential to analyse and understand the challenging problems of nanotechnology, biotechnology, medical science, oil industry and financial technology. The book highlights all the features and main theme discussed in the conference. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world.