%0 Journal Article
%T Low-Dosed X-Ray Computed Tomography Imaging by Regularized Fully Spatial Fractional-Order Perona-Malik Diffusion
%A Zhiwu Liao
%J Advances in Mathematical Physics
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/371868
%X Existing fractional-order Perona-Malik Diffusion (FOPMD) algorithms used in noise suppressing suffer from undesired artifacts and speckle effect, which hamper FOPMD used in low-dosed X-ray computed tomography (LDCT) imaging. In this paper, we propose a new FOPMD method for low-dose computed tomography (LDCT) imaging, which is called regularized fully spatial FOPMD (RFS-FOPMD), whose numerical scheme is also given based on Gr¨¹nwald-Letnikov derivative (G-L derivative). Here, fully spatial FOPMD represents all the integer-order derivatives (IODs) in the right hand of Perona-Malik Diffusion (PMD) which are replaced by fractional-order derivatives (FODs). Since the new scheme has advantages of both regularization and FOPMD, it has good abilities in singularities preserving while suppressing noise. Some real sinogram of LDCT are used to compare the different performances not only for some classical but also for some state-of-art diffusion schemes. These schemes include PMD, regularized PMD (RPMD), and FOPMD in (Hu et al. 2012). Experimental results show that besides good ability in edge preserving, the new scheme also has good stability for iteration number and can avoid artifacts and speckle effect with suitable parameters. 1. Introduction Perona-Malik diffusion (PMD) proposed in 1990 is a popular technique in image denoising and it is defined as [1] where is the initial gray scale image, is the smoothed gray scale image at time , denotes the gradient, is the divergence operator, and is the diffusion coefficient. In 1992, Catt¨¦ et al. indicated that PMD is ill-posed and they propose a new well-posed method named regularized Perona-Malik diffusion (RPMD), by replacing the gradient in diffusion coefficients by the smoothed version [2]. Thus, the RPMD can be represented as Here is defined as: which is a Gaussian function and is a constant. In order to eliminate undesired ¡°staircase¡± of PMD and RPMD, high-order PDEs (typically fourth-order PDEs) for image restoration have been introduced in [3, 4]. Though these methods can eliminate the staircase effect efficiently, they often leave the image with isolated black and white speckles (so-called speckle effect) [5]. Recently, fractional-order PMD (FOPMD) has been studied in image denoising [5¨C14], whose fractional order is , , which is a ¡°natural interpolation¡± between PMD and fourth-order PDEs. Therefore, it has the benefits of both of PMD and high order PDEs. Bai and Feng proposed a FSFOD method for image denoising with Euler-Lagrange equations of a cost functional and using Fourier-domain to compute the
%U http://www.hindawi.com/journals/amp/2013/371868/