A weighted difference of L1 and L2 on the gradient minimization based on alternating direction method for circular computed tomography

Journal of X-ray Science and Technology
Wanli LuBin Yan

Abstract

Iterative reconstruction algorithms for computed tomography (CT) through total variation (TV) regularization can provide accurate and stable reconstruction results. TV minimization is the L1-norm of gradient-magnitude images and can be regarded as a convex relaxation method to replace the L0 norm. In this study, a fast and efficient algorithm, which is named a weighted difference of L1 and L2 (L1 - αL2) on the gradient minimization, was proposed and investigated. The new algorithm provides a better description of sparsity for the optimization-based algorithms than TV minimization algorithms. The alternating direction method is an efficient method to solve the proposed model, which is utilized in this study. Both simulations and real CT projections were tested to verify the performances of the proposed algorithm. In the simulation experiments, the reconstructions from the proposed method provided better image quality than TV minimization algorithms with only 7 views in 180 degrees, which is also computationally faster. Meanwhile, the new algorithm enabled to achieve the final solution with less iteration numbers.

References

Aug 15, 2008·Physics in Medicine and Biology·Emil Y Sidky, Xiaochuan Pan
Nov 18, 2014·IEEE Journal of Translational Engineering in Health and Medicine·Emil Y SidkyXiaochuan Pan
Aug 4, 2015·Computerized Medical Imaging and Graphics : the Official Journal of the Computerized Medical Imaging Society·Ailong CaiGuoen Hu
Jul 28, 2016·Physics in Medicine and Biology·Zheng ZhangXiaochuan Pan

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BETA
X-ray
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Windows 7
MATLAB

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