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A theoretical framework of x-ray dark-fieldtomography
Journal article   Peer reviewed

A theoretical framework of x-ray dark-fieldtomography

Weimin Han, Joseph A Eichholz, Xiaoliang Cheng and Ge Wang
SIAM Journal on Applied Mathematics, Vol.71(5), pp.1557-1577
2011
DOI: 10.1137/100809039
url
https://vtechworks.lib.vt.edu/bitstreams/d46cb915-32f1-4fb4-8ead-a259f955b67b/downloadView
Open Access

Abstract

X-ray mammography is currently the most prevalent imaging modality for screening and diagnosis of breast cancers. However, its success is limited by the poor differentiation between healthy and diseased tissues in the mammogram. A potentially prominent imaging modality is based on the significant difference of x-ray scattering behaviors between tumor and normal tissues. Driven by major practical needs for better x-ray imaging, exploration into contrast mechanisms other than attenuation has been active for decades, e.g., in terms of scattering, which is also known as dark-field tomography. This paper provides a preliminary theoretical study of x-ray dark-field tomography (XDT) assuming the spectral x-ray detection technology. For XDT, the modified Leakeas–Larsen equation (MLLE) is an appropriate approximation of the radiative transfer equation (RTE) for a highly forward-peaked medium with small but sufficient amounts of large-angle scattering. Properties of the MLLE are studied, such as existence of a uniq...

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