Author: Lee Patrolia
Publisher:
ISBN:
Category : Acoustooptical devices
Languages : en
Pages : 59
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Book Description
Photoacoustic tomography is a rapidly developing medical imaging technique that combines optical and ultrasound imaging to exploit the high contrast and high resolution of the respective individual modalities. Mathematically, photoacoustic tomography is divided into two steps. In the first step, one solves an inverse problem for the wave equation to determine how tissue absorbs light as a result of a boundary illumination. The second step is generally modeled by either diffusion or transport equations, and involves recovering the optical properties of the region being imaged. In this paper we, we provide an overview of mathematical progress in photoacoustic and thermoacoustic tomography, as well as inverse problems for the radiative transfer equation. We then address quantitative photoacoustic tomography modeled by the radiative transfer equation, and in particular, we show that the absorption coefficient in the stationary transport equation can be recovered given certain internal information about the solution. Our new result will consider the variable index of refraction case, which will correspond to an inverse transport problem on a Riemannian manifold with internal data and a known metric. We will prove a stability estimate for a functional of the absorption coefficient of the medium by finding a singular decomposition for the distribution kernel of the measurement operator. Finally, we will use this estimate to recover the desired absorption properties.
Author: Huabei Jiang
Publisher: CRC Press
ISBN: 1482261049
Category : Science
Languages : en
Pages : 304
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Book Description
The concept of photoacoustic tomography (PAT) emerged in the mid-1990s, and the field of PAT is now rapidly moving forward. Presenting the research of a well-respected pioneer and leading expert, Photoacoustic Tomography is a first-of-its-kind book covering the underlying principles and practical applications of PAT in a systematic manner. Written in a tutorial format, the text: Addresses the fundamentals of PAT, the theory on photoacoustic effect, image reconstruction methods, and instrumentation Details advanced methods for quantitative PAT, which allow the recovery of tissue optical absorption coefficient and/or acoustic properties Explores the development of several image-enhancing schemes, including both software and hardware approaches Examines array-based PAT systems that are the foundation for the realization of 2-D, 3-D, and 4-D PAT Discusses photoacoustic microscopy (PAM) and combinations of PAT/PAM with other imaging methods Considers contrast-agents-based molecular PAT, with both nontargeted and cell receptor–targeted methods Describes clinical applications and animal studies in breast cancer detection, osteoarthritis diagnosis, seizure localization, intravascular imaging, and image-guided cancer therapy Photoacoustic Tomography is an essential reference for graduate students, researchers, industry professionals, and those who wish to enter this exciting field.
Author: Lihong V. Wang
Publisher: CRC Press
ISBN: 1420059920
Category : Science
Languages : en
Pages : 518
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Book Description
Photoacoustics promises to revolutionize medical imaging and may well make as dramatic a contribution to modern medicine as the discovery of the x-ray itself once did. Combining electromagnetic and ultrasonic waves synergistically, photoacoustics can provide deep speckle-free imaging with high electromagnetic contrast at high ultrasonic resolution and without any health risk. While photoacoustic imaging is probably the fastest growing biomedical imaging technology, this book is the first comprehensive volume in this emerging field covering both the physics and the remarkable noninvasive applications that are changing diagnostic medicine. Bringing together the leading pioneers in this field to write about their own work, Photoacoustic Imaging and Spectroscopy is the first to provide a full account of the latest research and developing applications in the area of biomedical photoacoustics. Photoacoustics can provide functional sensing of physiological parameters such as the oxygen saturation of hemoglobin. It can also provide high-contrast functional imaging of angiogenesis and hypermetabolism in tumors in vivo. Discussing these remarkable noninvasive applications and so much more, this reference is essential reading for all researchers in medical imaging and those clinicians working at the cutting-edge of modern biotechnology to develop diagnostic techniques that can save many lives and just as importantly do no harm.
Author: Ronny Ramlau
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110560852
Category : Mathematics
Languages : en
Pages : 347
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Book Description
In 1917, Johann Radon published his fundamental work, where he introduced what is now called the Radon transform. Including important contributions by several experts, this book reports on ground-breaking developments related to the Radon transform throughout these years, and also discusses novel mathematical research topics and applications for the next century.
Author: Hélène Frisch
Publisher: Springer Nature
ISBN: 3030952479
Category : Science
Languages : en
Pages : 611
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Book Description
This book discusses analytic and asymptotic methods relevant to radiative transfer in dilute media, such as stellar and planetary atmospheres. Several methods, providing exact expressions for the radiation field in a semi-infinite atmosphere, are described in detail and applied to unpolarized and polarized continuous spectra and spectral lines. Among these methods, the Wiener–Hopf method, introduced in 1931 for a stellar atmospheric problem, is used today in fields such as solid mechanics, diffraction theory, or mathematical finance. Asymptotic analyses are carried out on unpolarized and polarized radiative transfer equations and on a discrete time random walk. Applicable when photons undergo a large number of scatterings, they provide criteria to distinguish between large-scale diffusive and non-diffusive behaviors, typical scales of variation of the radiation field, such as the thermalization length, and specific descriptions for regions close and far from boundaries. Its well organized synthetic view of exact and asymptotic methods of radiative transfer makes this book a valuable resource for both graduate students and professional scientists in astrophysics and beyond.
Author: L. A. Apresyan
Publisher: Routledge
ISBN: 1351420089
Category : Technology & Engineering
Languages : en
Pages : 272
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Book Description
The authors expound on non-traditional phenomena for transfer theory, which are nevertheless of considerable interest in wave measurements, and bring the advances of transfer theory as close as possible to the practical needs of those working in all areas of wave physics. The book opens with a historical overview of the topic, then moves on to examine the phenomenological theory of radiative transport, blending traditional theory with original ideas. The transport equation is derived from first principles, and the ensuing discussion of the diffraction content of the transport equation and non-classical radiometry is illustrated by practical examples from various fields of physics. Popular techniques of solving the transport equation are discussed, paying particular attention to wave physics and computing the coherence function. The book also examines various problems which are no longer covered by the traditional radiative transfer theory, such as enhanced backscattering and weak localization phenomena, nonlinear transport problems and kinetic equations for waves. This monograph bridges the gap between the simple power balance description in radiative transfer theory and modern coherence theory. It will be of interest to researchers and professionals working across a wide range of fields from optics, acoustics and radar theory to astrophysics, radioastronomy and remote sensing, as well as to students in these areas.
Author: Wenfeng Xia
Publisher: Springer Nature
ISBN: 3031614119
Category :
Languages : en
Pages : 608
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Book Description
Author: Maïtine Bergounioux
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110430495
Category : Mathematics
Languages : en
Pages : 621
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Book Description
With a focus on the interplay between mathematics and applications of imaging, the first part covers topics from optimization, inverse problems and shape spaces to computer vision and computational anatomy. The second part is geared towards geometric control and related topics, including Riemannian geometry, celestial mechanics and quantum control. Contents: Part I Second-order decomposition model for image processing: numerical experimentation Optimizing spatial and tonal data for PDE-based inpainting Image registration using phase・amplitude separation Rotation invariance in exemplar-based image inpainting Convective regularization for optical flow A variational method for quantitative photoacoustic tomography with piecewise constant coefficients On optical flow models for variational motion estimation Bilevel approaches for learning of variational imaging models Part II Non-degenerate forms of the generalized Euler・Lagrange condition for state-constrained optimal control problems The Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controls Controllability of Keplerian motion with low-thrust control systems Higher variational equation techniques for the integrability of homogeneous potentials Introduction to KAM theory with a view to celestial mechanics Invariants of contact sub-pseudo-Riemannian structures and Einstein・Weyl geometry Time-optimal control for a perturbed Brockett integrator Twist maps and Arnold diffusion for diffeomorphisms A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part I Index
Author: Guillaume Bal
Publisher: American Mathematical Soc.
ISBN: 0821853015
Category : Mathematics
Languages : en
Pages : 194
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Book Description
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.
Author: Yimin Zhong
Publisher:
ISBN:
Category :
Languages : en
Pages : 278
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Book Description
Inverse problems in photoacoustic imaging (PAT) have been extensively studied in recent years due to their importance in applications. This thesis addresses three important aspects of PAT inverse problems mathematically and computationally. First, we present a detailed mathematical and numerical analysis of quantitative fluorescence PAT, a variant of PAT for applications in molecular imaging. We develop uniqueness and stability theory on quantitative reconstructions based on the radiative transport model of light propagation and present numerical simulations to validate the mathematical theory. Second, we develop a fast numerical algorithm for solving the radiative transport equation, the model of light propagation in PAT applications on tissue imaging, in isotropic media. Our method is based on an integral equation formulation of the radiative transport equation and a fast multipole method for accelerating matrix-vector multiplications for the discretized system. Third, we perform mathematical analysis on PAT reconstruction problem with unknown ultrasound speed. We prove local uniqueness and stability results on the simultaneous reconstruction of the ultrasound speed, the acoustic attenuation coefficient as well as the optical absorption coefficients.
