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18 March 2008 PDE regularization for Bayesian reconstruction of emission tomography
Zhentian Wang, Li Zhang, Yuxiang Xing, Ziran Zhao
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Proceedings Volume 6913, Medical Imaging 2008: Physics of Medical Imaging; 69132X (2008) https://doi.org/10.1117/12.769742
Event: Medical Imaging, 2008, San Diego, California, United States
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.
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Zhentian Wang, Li Zhang, Yuxiang Xing, and Ziran Zhao "PDE regularization for Bayesian reconstruction of emission tomography", Proc. SPIE 6913, Medical Imaging 2008: Physics of Medical Imaging, 69132X (18 March 2008); https://doi.org/10.1117/12.769742
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KEYWORDS
Image segmentation
Reconstruction algorithms
Tomography
Image processing algorithms and systems
Image processing
Anisotropic diffusion
Denoising
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