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Proceedings Paper

PDE regularization for Bayesian reconstruction of emission tomography
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Paper Abstract

The aim of the present study is to investigate a type of Bayesian reconstruction which utilizes partial differential equations (PDE) image models as regularization. PDE image models are widely used in image restoration and segmentation. In a PDE model, the image can be viewed as the solution of an evolutionary differential equation. The variation of the image can be regard as a descent of an energy function, which entitles us to use PDE models in Bayesian reconstruction. In this paper, two PDE models called anisotropic diffusion are studied. Both of them have the characteristics of edge-preserving and denoising like the popular median root prior (MRP). We use PDE regularization with an Ordered Subsets accelerated Bayesian one step late (OSL) reconstruction algorithm for emission tomography. The OS accelerated OSL algorithm is more practical than a non-accelerated one. The proposed algorithm is called OSEM-PDE. We validated the OSEM-PDE using a Zubal phantom in numerical experiments with attenuation correction and quantum noise considered, and the results are compared with OSEM and an OS version of MRP (OSEM-MRP) reconstruction. OSEM-PDE shows better results both in bias and variance. The reconstruction images are smoother and have sharper edges, thus are more applicable for post processing such as segmentation. We validate this using a k-means segmentation algorithm. The classic OSEM is not convergent especially in noisy condition. However, in our experiment, OSEM-PDE can benefit from OS acceleration and keep stable and convergent while OSEM-MRP failed to converge.

Paper Details

Date Published: 18 March 2008
PDF: 8 pages
Proc. SPIE 6913, Medical Imaging 2008: Physics of Medical Imaging, 69132X (18 March 2008); doi: 10.1117/12.769742
Show Author Affiliations
Zhentian Wang, Tsinghua Univ. (China)
Li Zhang, Tsinghua Univ. (China)
Yuxiang Xing, Tsinghua Univ. (China)
Ziran Zhao, Tsinghua Univ. (China)

Published in SPIE Proceedings Vol. 6913:
Medical Imaging 2008: Physics of Medical Imaging
Jiang Hsieh; Ehsan Samei, Editor(s)

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