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

Abstract

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 integerorder 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.

Partial Discharge Signal De-noising Method Based on EMD and High Order PDE

“…Following the classical P-M anisotropic diffusion equation proposed by PERONA et al [4]. In 2000, the following four order partial differential equation was put forward by Yu-Li et al:…”

A New Definition of Fractional Derivatives Based on Truncated Left-Handed Grünwald-Letnikov Formula with0<α<1and Median Correction

“…Partial differential equations (PDEs) and related methods are very important tools for signal processing [1][2][3][4][5][6][7][8][9][10][11][12][13]. Especially, in recent years progress was achieved in the theory of fractional calculus as a useful tool to handle applications in the area of physics, chemistry, and engineering sciences [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

“…Therefore, some integer-order PDE methods cannot be modified to their fractional-order counterparts directly. Hu noticed the problem in 2013 and proposed a new fractional-order PDE with different orders of different parts for fractional-order PM method [13]. However, he did not give the analysis in theory.…”

Low-Dosed X-Ray Computed Tomography Imaging by Regularized Fully Spatial Fractional-Order Perona-Malik Diffusion

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