Inverse Problems In Dynamic Elasticity Imaging

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Inverse Problems In Dynamic Elasticity Imaging

Author : Christoph Moosbauer
Publisher : Anchor Academic Publishing (aap_verlag)
ISBN 13 : 395489906X
Total Pages : 118 pages
Book Rating : 4.9/5 (548 download)

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Book Synopsis Inverse Problems In Dynamic Elasticity Imaging by : Christoph Moosbauer

Download or read book Inverse Problems In Dynamic Elasticity Imaging written by Christoph Moosbauer and published by Anchor Academic Publishing (aap_verlag). This book was released on 2015-03-25 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the early 1990’s, elasticity imaging techniques are developed as a powerful supplement of the medical toolbox in diagnostic analysis and computer aided surgery. By solving a so-called inverse problem, information about the spatial variation of material parameters of soft (human) tissue are derived from displacement data, which can be measured noninvasively using standard imaging devices such as ultrasound or magnetic resonance tomography. The terms of quasi-static and dynamic elastography refer to the type of load situation, by which the tissue in question is excited. The extension of the theoretical formulation and implementation of the underlying inverse problem in quasi-static elastography to time-harmonic approaches poses several additional challenges, which are addressed in detail within the course of this study. We propose a robust strategy for the reconstruction, which takes advantage of the high sensitivity of the accuracy in harmonic elastography to the choice of the starting point. While not being reported in the literature up to now, the quite competing claims of quasi-static and time-harmonic elastography motivate a comprehensive comparison of these two techniques. Via a spectral decomposition of the curvature information of the underlying inverse problem, a clear explanation for an improved robustness of time- harmonic elastography in the presence of inaccuracies due to noise and/or numerical approximations can be given. Several numerical examples confirm these findings as well as the efficiency of the proposed reconstruction strategy. In particular, it is shown that for moderately low frequencies, it is sufficient to use very coarse finite element meshes, so that the only additional computational cost stems from the worse conditioning of the system matrix.

Dynamical Inverse Problems: Theory and Application

Author : Graham M. L. Gladwell
Publisher : Springer Science & Business Media
ISBN 13 : 3709106966
Total Pages : 229 pages
Book Rating : 4.7/5 (91 download)

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Book Synopsis Dynamical Inverse Problems: Theory and Application by : Graham M. L. Gladwell

Download or read book Dynamical Inverse Problems: Theory and Application written by Graham M. L. Gladwell and published by Springer Science & Business Media. This book was released on 2011-05-25 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume present an overview of the general aspects and practical applications of dynamic inverse methods, through the interaction of several topics, ranging from classical and advanced inverse problems in vibration, isospectral systems, dynamic methods for structural identification, active vibration control and damage detection, imaging shear stiffness in biological tissues, wave propagation, to computational and experimental aspects relevant for engineering problems.

Continuous Versus Discontinuous Elastic Modulus Distribution in Inverse Problems Based on Finite Element Methods

Author : Xuchen Liu
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (938 download)

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Book Synopsis Continuous Versus Discontinuous Elastic Modulus Distribution in Inverse Problems Based on Finite Element Methods by : Xuchen Liu

Download or read book Continuous Versus Discontinuous Elastic Modulus Distribution in Inverse Problems Based on Finite Element Methods written by Xuchen Liu and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Elasticity imaging, which is also known as Elastography, aims to determine the elastic property distribution of non-homogeneous deformable solids such as soft tissues. This can be done non-destructively using displacement fields measured with medical imaging modalities, such as ultrasound or magnetic resonance imaging. Elasticity imaging can potentially be used to detect tumors based on the stiffness contrast between different materials. This requires the solution of an inverse problem in elasticity. This field has been growing very fast in the past decade. One of the most useful applications of elasticity imaging may be in breast cancer diagnosis, where the tumor could potentially be detected and visualized by its stiffness contrast from its surrounding tissues. In this work the inverse problem will be solved for the shear modulus which is directly related to the Young's modulus through the Poisson's ratio. The inverse problem is posed as a constrained optimization problem, where the difference between a computed (predicted) and measured displacement field is minimized. The computed displacement field satisfies the equations of equilibrium. The material is modeled as an isotropic and incompressible material. The present work focuses on assessing the solution of the inverse problem for problem domains defined with a continuous and discontinuous shear modulus distribution. In particular, two problem domains will be considered: 1) a stiff inclusion in a homogeneous background representing a stiff tumor surrounded by soft tissues, 2) a layered ring model representing an arterial wall cross-section. The hypothetical "measured" displacement field for these problem domains will be created by solving the finite element forward problem. Additionally, noise will be added to the displacement field to simulate noisy measured displacement data. According to the results of my thesis work, the potential of the elasticity imaging in the medical field is emerging. The inclusion in problem domain 1, representing a stiffer tumor in a uniform background, can be found and located in the shear modulus reconstructions. Thus, these reconstructed images can potentially be used to detect tumors in the medical field. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/155332

Time-dependent Problems in Imaging and Parameter Identification

Author : Barbara Kaltenbacher
Publisher : Springer Nature
ISBN 13 : 3030577848
Total Pages : 464 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Time-dependent Problems in Imaging and Parameter Identification by : Barbara Kaltenbacher

Download or read book Time-dependent Problems in Imaging and Parameter Identification written by Barbara Kaltenbacher and published by Springer Nature. This book was released on 2021-02-23 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Methods in Elasticity Imaging

Author : Habib Ammari
Publisher : Princeton University Press
ISBN 13 : 1400866626
Total Pages : 240 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Mathematical Methods in Elasticity Imaging by : Habib Ammari

Download or read book Mathematical Methods in Elasticity Imaging written by Habib Ammari and published by Princeton University Press. This book was released on 2015-04-05 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Inverse Problems and Imaging

Author : Ana Carpio
Publisher : Springer Science & Business Media
ISBN 13 : 3540785450
Total Pages : 207 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Inverse Problems and Imaging by : Ana Carpio

Download or read book Inverse Problems and Imaging written by Ana Carpio and published by Springer Science & Business Media. This book was released on 2008-04-17 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the CIME Summer School on Imaging, experts in mathematical techniques and applications presented useful introductions to many aspects of the field. This volume contains updated lectures as well as additional contributions on other related topics.

Inverse Problems in Engineering Mechanics II

Author : G.S. Dulikravich
Publisher : Elsevier
ISBN 13 : 0080535151
Total Pages : 607 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Inverse Problems in Engineering Mechanics II by : G.S. Dulikravich

Download or read book Inverse Problems in Engineering Mechanics II written by G.S. Dulikravich and published by Elsevier. This book was released on 2000-12-11 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse Problems are found in many areas of engineering mechanics and there are many successful applications e.g. in non-destructive testing and characterization of material properties by ultrasonic or X-ray techniques, thermography, etc. Generally speaking, inverse problems are concerned with the determination of the input and the characteristics of a system, given certain aspects of its output. Mathematically, such problems are ill-posed and have to be overcome through development of new computational schemes, regularization techniques, objective functionals, and experimental procedures. Following the IUTAM Symposium on these topics, held in May 1992 in Tokyo, another in November 1994 in Paris, and also the more recent ISIP'98 in March 1998 in Nagano, it was concluded that it would be fruitful to gather regularly with researchers and engineers for an exchange of the newest research ideas. The most recent Symposium of this series "International Symposium on Inverse Problems in Engineering Mechanics (ISIP2000)" was held in March of 2000 in Nagano, Japan, where recent developments in inverse problems in engineering mechanics and related topics were discussed. The following general areas in inverse problems in engineering mechanics were the subjects of ISIP2000: mathematical and computational aspects of inverse problems, parameter or system identification, shape determination, sensitivity analysis, optimization, material property characterization, ultrasonic non-destructive testing, elastodynamic inverse problems, thermal inverse problems, and other engineering applications. The papers in these proceedings provide a state-of-the-art review of the research on inverse problems in engineering mechanics and it is hoped that some breakthrough in the research can be made and that technology transfer will be stimulated and accelerated due to their publication.

Inverse Problems in Finite Elasticity: an Application to Imaging the Nonlinear Elastic Properties of Soft Tissues

Author : Sevan Goenezen
Publisher :
ISBN 13 :
Total Pages : 208 pages
Book Rating : 4.:/5 (115 download)

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Book Synopsis Inverse Problems in Finite Elasticity: an Application to Imaging the Nonlinear Elastic Properties of Soft Tissues by : Sevan Goenezen

Download or read book Inverse Problems in Finite Elasticity: an Application to Imaging the Nonlinear Elastic Properties of Soft Tissues written by Sevan Goenezen and published by . This book was released on 2011 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Inverse Dynamics Problems

Author : Hamed Kalhori
Publisher : MDPI
ISBN 13 : 3036510664
Total Pages : 218 pages
Book Rating : 4.0/5 (365 download)

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Book Synopsis Inverse Dynamics Problems by : Hamed Kalhori

Download or read book Inverse Dynamics Problems written by Hamed Kalhori and published by MDPI. This book was released on 2021-06-15 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The inverse dynamics problem was developed in order to provide researchers with the state of the art in inverse problems for dynamic and vibrational systems. Contrasted with a forward problem, which solves for the system output in a straightforward manner, an inverse problem searches for the system input through a procedure contaminated with errors and uncertainties. An inverse problem, with a focus on structural dynamics, determines the changes made to the system and estimates the inputs, including forces and moments, to the system, utilizing measurements of structural vibration responses only. With its complex mathematical structure and need for more reliable input estimations, the inverse problem is still a fundamental subject of research among mathematicians and engineering scientists. This book contains 11 articles that touch upon various aspects of inverse dynamic problems.

Inverse Problems in Transcient [sic] Elastography

Author : Yat Tin Chow
Publisher :
ISBN 13 :
Total Pages : 204 pages
Book Rating : 4.:/5 (93 download)

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Book Synopsis Inverse Problems in Transcient [sic] Elastography by : Yat Tin Chow

Download or read book Inverse Problems in Transcient [sic] Elastography written by Yat Tin Chow and published by . This book was released on 2012 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-dimensional coefficient inverse problem (MCIP) in linear elasticity has found many applications, such as crack detection, oil/salt/ore detection, medical imaging. Transient elastography is among one of the most useful applications, providing a fast and safe medical imaging technique which can be used to detect tumors or abnormal tissue in fast-moving organs such as the liver. In this thesis focus is casted on two of the numerical algorithms to solve inverse problems related to transient elastography, namely the level-set inversion method and the approximate globally convergent method. The derivations of both methods and numerical results are presented. In particular, the approximate globally convergent method is a newly developed stable method to solve coefficient determination inverse problem for hyperbolic partial differential equation proposed by Beilina and Klibanov in [6]. It achieves pproximately a global convergence by avoiding construction of a least squares functional, thus averting some of the well-known problems of trapping in the neighborhoods of local minima when one minimizes such a nonlinear functional. The results of the approximate globally convergent method have shown its strong stability and robustness. This suggests a good way for the reconstruction of the distribution of the shear modulus in the coefficient inverse problem of linear elasticity.

Methods of Inverse Problems in Physics

Author : Dilip N. Ghosh Roy
Publisher : CRC Press
ISBN 13 : 9780849362583
Total Pages : 506 pages
Book Rating : 4.3/5 (625 download)

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Book Synopsis Methods of Inverse Problems in Physics by : Dilip N. Ghosh Roy

Download or read book Methods of Inverse Problems in Physics written by Dilip N. Ghosh Roy and published by CRC Press. This book was released on 1991-03-14 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This interesting volume focuses on the second of the two broad categories into which problems of physical sciences fall-direct (or forward) and inverse (or backward) problems. It emphasizes one-dimensional problems because of their mathematical clarity. The unique feature of the monograph is its rigorous presentation of inverse problems (from quantum scattering to vibrational systems), transmission lines, and imaging sciences in a single volume. It includes exhaustive discussions on spectral function, inverse scattering integral equations of Gel'fand-Levitan and Marcenko, Povzner-Levitan and Levin transforms, Møller wave operators and Krein's functionals, S-matrix and scattering data, and inverse scattering transform for solving nonlinear evolution equations via inverse solving of a linear, isospectral Schrodinger equation and multisoliton solutions of the K-dV equation, which are of special interest to quantum physicists and mathematicians. The book also gives an exhaustive account of inverse problems in discrete systems, including inverting a Jacobi and a Toeplitz matrix, which can be applied to geophysics, electrical engineering, applied mechanics, and mathematics. A rigorous inverse problem for a continuous transmission line developed by Brown and Wilcox is included. The book concludes with inverse problems in integral geometry, specifically Radon's transform and its inversion, which is of particular interest to imaging scientists. This fascinating volume will interest anyone involved with quantum scattering, theoretical physics, linear and nonlinear optics, geosciences, mechanical, biomedical, and electrical engineering, and imaging research.

Inverse Problems in Engineering Mechanics IV

Author : Mana Tanaka
Publisher : Elsevier
ISBN 13 : 0080535178
Total Pages : 545 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Inverse Problems in Engineering Mechanics IV by : Mana Tanaka

Download or read book Inverse Problems in Engineering Mechanics IV written by Mana Tanaka and published by Elsevier. This book was released on 2003-11-19 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: This latest collection of proceedings provides a state of the art review of research on inverse problems in engineering mechanics. Inverse problems can be found in many areas of engineering mechanics, and have many successful applications. They are concerned with estimating the unknown input and/or the characteristics of a system given certain aspects of its output. The mathematical challenges of such problems have to be overcome through the development of new computational schemes, regularization techniques, objective functionals, and experimental procedures. The papers within this represent an excellent reference for all in the field. Providing a state of the art review of research on inverse problems in engineering mechanics Contains the latest research ideas and related techniques A recognized standard reference in the field of inverse problems Papers from Asia, Europe and America are all well represented

Inverse Problems of Mathematical Physics

Author : V. G. Romanov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110926016
Total Pages : 248 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Inverse Problems of Mathematical Physics by : V. G. Romanov

Download or read book Inverse Problems of Mathematical Physics written by V. G. Romanov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Inverse Problems of Mathematical Physics".

Inverse Problems and Imaging

Author : Gary Francis Roach
Publisher : Chapman & Hall/CRC
ISBN 13 :
Total Pages : 290 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Inverse Problems and Imaging by : Gary Francis Roach

Download or read book Inverse Problems and Imaging written by Gary Francis Roach and published by Chapman & Hall/CRC. This book was released on 1991 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the invited papers presented at an international workship on inverse problems and imaging held at Ross Priory, University of Strathclyde, 1988.

Inverse Problems in Engineering Mechanics III

Author : G.S. Dulikravich
Publisher : Elsevier
ISBN 13 : 0080535143
Total Pages : 433 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Inverse Problems in Engineering Mechanics III by : G.S. Dulikravich

Download or read book Inverse Problems in Engineering Mechanics III written by G.S. Dulikravich and published by Elsevier. This book was released on 2001-11-20 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse Problems are found in many areas of engineering mechanics and there are many successful applications e.g. in non-destructive testing and characterization of material properties by ultrasonic or X-ray techniques, thermography, etc. Generally speaking, inverse problems are concerned with the determination of the input and the characteristics of a system, given certain aspects of its output. Mathematically, such problems are ill-posed and have to be overcome through development of new computational schemes, regularization techniques, objective functionals, and experimental procedures. This volume contains a selection of peer-reviewed papers presented at the International Symposium on Inverse Problems in Engineering Mechanics (ISIP2001), held in February of 2001 in Nagano, Japan, where recent development in inverse problems in engineering mechanics and related topics were discussed. The following general areas in inverse problems in engineering mechanics were the subjects of the ISIP2001: mathematical and computational aspects of inverse problems, parameter or system identification, shape determination, sensitivity analysis, optimization, material property characterization, ultrasonic non-destructive testing, elastodynamic inverse problems, thermal inverse problems, and other engineering applications. These papers can provide a state-of-the-art review of the research on inverse problems in engineering mechanics.

A Dynamic Finite Element Framework Built Towards the Inverse Problem of Soft Tissues

Author :
Publisher :
ISBN 13 :
Total Pages : 88 pages
Book Rating : 4.:/5 (43 download)

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Book Synopsis A Dynamic Finite Element Framework Built Towards the Inverse Problem of Soft Tissues by :

Download or read book A Dynamic Finite Element Framework Built Towards the Inverse Problem of Soft Tissues written by and published by . This book was released on 2008 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study seeks to simulate soft tissue behavior with a custom finite element analysis. It is the eventual goal of this team to explore the inverse problem of soft tissues, and this simulation study will play an integral role in that process. It is hoped that new information regarding the elastic properties of soft tissue can be used to diagnose disease processes and improve health care delivery. In this investigation, soft tissue is modeled as a linear, isotropic, elastic, and nearly incompressible material. A dynamic finite element problem was defined consistent with the experimental protocol of harmonic motion imaging, an elasticity imaging technique that utilizes acoustic radiation force to induce localized displacements within soft tissue samples. The finite element equations of motion in this investigation were solved using the Newmark method, an approach commonly used by engineers to determine the dynamic response of structures under the action of any general time-dependent loads. It was found that the displacement results obtained with the Newmark method made physical sense and agreed with the observations of other researchers in this field, suggesting that the current finite element analysis is a suitable simulation of soft tissue behavior.

Introduction to Inverse Problems in Imaging

Author : M. Bertero
Publisher : CRC Press
ISBN 13 : 9781138434042
Total Pages : pages
Book Rating : 4.4/5 (34 download)

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Book Synopsis Introduction to Inverse Problems in Imaging by : M. Bertero

Download or read book Introduction to Inverse Problems in Imaging written by M. Bertero and published by CRC Press. This book was released on 2017-07-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate textbook on the principles of linear inverse problems, methods of their approximate solution, and practical application in imaging. The level of mathematical treatment is kept as low as possible to make the book suitable for a wide range of readers from different backgrounds in science and engineering. Mathematical prerequisites are first courses in analysis, geometry, linear algebra, probability theory, and Fourier analysis. The authors concentrate on presenting easily implementable and fast solution algorithms. With examples and exercised throughout, the book will provide the reader with the appropriate background for a clear understanding of the essence of inverse problems (ill-posedness and its cure) and, consequently, for an intelligent assessment of the rapidly growing literature on these problems.