Seminar "Tomographic Imaging of Scattering Media" by Vadim Markel (University of Pennsylvania, USA) on Wednesday, July 2, 2014, 11:00 a.m., Faculté des Sciences St Jérôme, Institut Fresnel, Room Pierre Cotton (level -1).
Abstract :
Development of three-dimensional computerized tomography about 40 years ago has revolutionized the practice of clinical medicine. Since then, the scope of tomographic techniques has greatly increased and, currently, it includes security, subsurface imaging of defects, geophysics and nanotechnology. In traditional tomographic techniques, scattering of waves or particles that are used to probe the composition and structure of samples has been traditionally viewed as a fundamental obstruction to imaging. However, in most practical cases, scattering is not negligible. Even X-rays experience noticeable scattering in human tissues. In the case of near-infrared light, multiple scattering is so strong that we can talk about the diffuse regime of propagation, when the light energy "diffuses" through the tissues like a drop of dye diffuses in water.
I will talk about tomographic modalities in which scattering is not only taken into account but also taken advantage of. These modalities can be broadly classified by the scattering regime used. In single-scattering tomography (an emerging approach to X-ray imaging), first-order scattering is taken into account and we obtain a new transform of the medium known as the broken-ray transform (BRT). Quite counter-intuitively, this transform has many advantages compared to the traditional Radon transform, which involves only straight (ballistic) rays. If more than one scattering event is taken into account, then the medium must be described by the radiative transport equation (RTE), and the associated inverse problem becomes nonlinear and, generally, very complicated. However at the extreme limit of strong multiple scattering (typically, applicable to near-IR light), a new simplified description emerges since the electromagnetic energy density is well described in this case by the relatively simple diffusion equation. The corresponding tomographic modality is known as diffuse optical tomography (DOT). One of the important questions in DOT is utilization of very large data sets and I will talk about my work in this direction. Finally, I will talk about a new approach, which we are currently developing at Penn, to solving nonlinear inverse problems in tomography. I will show numerical examples pertinent to the nonlinear problem of inverse diffraction, wherein the nonlinearity is caused by multiple scattering within the sample.
Contact :
Vadim Markel
Radiology/Bioengineering/Applied Math & Computational Science
UPenn, Philadelphia
vmarkel@mail.med.upenn.edu
Invitation : Stefan ENOCH, Institut Fresnel
ResearchGate
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