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Proceedings Paper

Material decomposition in an arbitrary number of dimensions using noise compensating projection
Author(s): Thomas O'Donnell; Ahmed Halaweish; David Cormode; Rabee Cheheltani; Zahi A. Fayad; Venkatesh Mani
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Paper Abstract

Purpose: Multi-energy CT (e.g., dual energy or photon counting) facilitates the identification of certain compounds via data decomposition. However, the standard approach to decomposition (i.e., solving a system of linear equations) fails if – due to noise - a pixel’s vector of HU values falls outside the boundary of values describing possible pure or mixed basis materials. Typically, this is addressed by either throwing away those pixels or projecting them onto the closest point on this boundary. However, when acquiring four (or more) energy volumes, the space bounded by three (or more) materials that may be found in the human body (either naturally or through injection) can be quite small. Noise may significantly limit the number of those pixels to be included within. Therefore, projection onto the boundary becomes an important option. But, projection in higher than 3 dimensional space is not possible with standard vector algebra: the cross-product is not defined. Methods: We describe a technique which employs Clifford Algebra to perform projection in an arbitrary number of dimensions. Clifford Algebra describes a manipulation of vectors that incorporates the concepts of addition, subtraction, multiplication, and division. Thereby, vectors may be operated on like scalars forming a true algebra. Results: We tested our approach on a phantom containing inserts of calcium, gadolinium, iodine, gold nanoparticles and mixtures of pairs thereof. Images were acquired on a prototype photon counting CT scanner under a range of threshold combinations. Comparison of the accuracy of different threshold combinations versus ground truth are presented. Conclusions: Material decomposition is possible with three or more materials and four or more energy thresholds using Clifford Algebra projection to mitigate noise.

Paper Details

Date Published: 9 March 2017
PDF: 11 pages
Proc. SPIE 10132, Medical Imaging 2017: Physics of Medical Imaging, 101323A (9 March 2017); doi: 10.1117/12.2254077
Show Author Affiliations
Thomas O'Donnell, Siemens Healthineers (United States)
Ahmed Halaweish, Siemens Healthineers (United States)
David Cormode, Univ. of Pennsylvania (United States)
Rabee Cheheltani, Univ. of Pennsylvania (United States)
Zahi A. Fayad, Icahn School of Medicine at Mount Sinai (United States)
Venkatesh Mani, Icahn School of Medicine at Mount Sinai (United States)

Published in SPIE Proceedings Vol. 10132:
Medical Imaging 2017: Physics of Medical Imaging
Thomas G. Flohr; Joseph Y. Lo; Taly Gilat Schmidt, Editor(s)

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