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Proceedings Paper

A Kullback-Leibler approach for 3D reconstruction of spectral CT data corrupted by Poisson noise
Author(s): Tom Hohweiller; Nicolas Ducros; Françoise Peyrin; Bruno Sixou
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Paper Abstract

While standard computed tomography (CT) data do not depend on energy, spectral computed tomography (SPCT) acquire energy-resolved data, which allows material decomposition of the object of interest. Decompositions in the projection domain allow creating projection mass density (PMD) per materials. From decomposed projections, a tomographic reconstruction creates 3D material density volume. The decomposition is made possible by minimizing a cost function. The variational approach is preferred since this is an ill-posed non-linear inverse problem. Moreover, noise plays a critical role when decomposing data. That is why in this paper, a new data fidelity term is used to take into account of the photonic noise. In this work two data fidelity terms were investigated: a weighted least squares (WLS) term, adapted to Gaussian noise, and the Kullback-Leibler distance (KL), adapted to Poisson noise. A regularized Gauss-Newton algorithm minimizes the cost function iteratively. Both methods decompose materials from a numerical phantom of a mouse. Soft tissues and bones are decomposed in the projection domain; then a tomographic reconstruction creates a 3D material density volume for each material. Comparing relative errors, KL is shown to outperform WLS for low photon counts, in 2D and 3D. This new method could be of particular interest when low-dose acquisitions are performed.

Paper Details

Date Published:
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Proc. SPIE 10391, Developments in X-Ray Tomography XI, 103911E; doi: 10.1117/12.2273649
Show Author Affiliations
Tom Hohweiller, Univ. Lyon, INSA-Lyon, Univ. Claude Bernard Lyon 1, CNRS (France)
Univ. Jean Monnet Saint-Etienne (France)
CREATIS (France)
Nicolas Ducros, Univ. Lyon, INSA-Lyon, Univ. Claude Bernard Lyon 1, CNRS (France)
Univ. Jean Monnet Saint-Etienne (France)
CREATIS (France)
Françoise Peyrin, Univ. Lyon, INSA-Lyon, Univ. Claude Bernard Lyon 1, CNRS (France)
Univ. Jean Monnet Saint-Etienne (France)
CREATIS (France)
Bruno Sixou, Univ. Lyon, INSA-Lyon, Univ. Claude Bernard Lyon 1, CNRS (France)
Univ. Jean Monnet Saint-Etienne (France)
CREATIS (France)


Published in SPIE Proceedings Vol. 10391:
Developments in X-Ray Tomography XI
Bert Müller; Ge Wang, Editor(s)

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