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A Note on Analytic Recovery of Transition Probabilities in Three Dimensional Diffuse Tomography

Year: 1994

Type: article

Abstract: The word ``tomography`` refers to imaging an object by slices. X rays, for example, have high energy and travel straight through the body. Data analysis is linear and yields a scalar valued function. The oxymoron diffuse tomography refers to low energy imaging in which the paths of the radiant energy are not necessarily straight and are unknown. Data analysis in diffuse tomography is highly nonlinear and yields a vector valued function. Problems in diffuse tomography are highly nonlinear because low energy is used. Clinical applications such as neonatal imaging and annual mammograms are not amenable to high energy techniques which might overexpose the patient to harmful radiation. Experimentalists in the medical arena are presently working with near infrared radiation; mathematicians have done preliminary mathematical analysis of diffuse tomographic methods. An analytic algorithm for recovering Markov transition probabilities from boundary value data for the smallest nontrivial problem in three dimensions is outlined in this paper.

Source: eScholarship (California Digital Library)

Author: S. K. Patch

Language: English

Topic: Optical Imaging and Spectroscopy Techniques

Subfield: Radiology, Nuclear Medicine and Imaging

Field: Medicine

Domain: Health Sciences

Open Access status: green

Funders: National Science Foundation, U.S. Department of Energy, National Aeronautics and Space Administration, Division of Mathematical Sciences, Air Force Office of Scientific Research

Awards: G1398330795, G1643223109, G193590374, Mathematical Sciences: Classical and Applied Analysis, G8099852790

OpenAlex ID: W180226575

FWCI:

Cites: 6

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Related to: 10