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Advances in Mathematical Physics
Volume 2013, Article ID 516919, 10 pages
Research Article

External Fractional-Order Gradient Vector Perona-Malik Diffusion for Sinogram Restoration of Low-Dosed X-Ray Computed Tomography

School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China

Received 11 September 2013; Accepted 20 September 2013

Academic Editor: Ming Li

Copyright © 2013 Shaoxiang Hu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Existing fractional-order Perona-Malik Diffusion (FOPMD) algorithms are defined as fully spatial fractional-order derivatives (FSFODs). However, we argue that FSFOD is not the best way for diffusion since different parts of spatial derivative play different roles in Perona-Malik diffusion (PMD) and derivative orders should be decided according to their roles. Therefore, we adopt a novel fractional-order diffusion scheme, named external fractional-order gradient vector Perona-Malik diffusion (EFOGV-PMD), by only replacing integer-order derivatives of “external” gradient vector to their fractional-order counterparts while keeping integer-order derivatives of gradient vector for diffusion coefficients since the ability of edge indicator for 1-order derivative is demonstrated both in theory and applications. Here “external” indicates the spatial derivatives except for the derivatives used in diffusion coefficients. In order to demonstrate the power of the proposed scheme, some real sinograms of low-dosed computed tomography (LDCT) are used to compare the different performances. These schemes include PMD, regularized PMD (RPMD), and FOPMD. Experimental results show that the new scheme has good ability in edge preserving, is convergent quickly, has good stability for iteration number, and can avoid artifacts, dark resulting images, and speckle effect.