Sinogram Restoration for Low‐Dosed X‐Ray Computed Tomography Using Fractional‐Order Perona‐Malik Diffusion

Shaoxiang Hu,Zhiwu Liao,Wufan Chen

doi:10.1155/2012/391050

Abstract

Existing integer‐order Nonlinear Anisotropic Diffusion (NAD) used in noise suppressing will produce undesirable staircase effect or speckle effect. In this paper, we propose a new scheme, named Fractal‐order Perona‐Malik Diffusion (FPMD), which replaces the integer‐order derivative of the Perona‐Malik (PM) Diffusion with the fractional‐order derivative using G‐L fractional derivative. FPMD, which is a interpolation between integer‐order Nonlinear Anisotropic Diffusion (NAD) and fourth‐order partial differential equations, provides a more flexible way to balance the noise reducing and anatomical details preserving. Smoothing results for phantoms and real sinograms show that FPMD with suitable parameters can suppress the staircase effects and speckle effects efficiently. In addition, FPMD also has a good performance in visual quality and root mean square errors (RMSE).

Highlights

Radiation exposure and associated risk of cancer for patients receiving CT examination have been an increasing concern in recent years
Smoothing results for phantoms and real sinograms show that Fractional-Order PM Diffusion (FPMD) with suitable parameters can suppress the staircase effects and speckle effects efficiently
Nonlinear Anisotropic Diffusion NAD, called Perona-Malik diffusion PMD, is a technique aiming at reducing image details without removing significant parts of the image contents, typically edges, lines, or textures, which are important for the image 50

Summary

Introduction

Radiation exposure and associated risk of cancer for patients receiving CT examination have been an increasing concern in recent years. Li and Zhao investigate relation between the data of cyber-physical networking systems and power laws and suggest that power-law-type data may be governed by stochastically differential equations of fractional order 45 They propose that one-dimensional random functions with long-range dependence LRD based on a specific class of processes called the Cauchy-class CC process maybe a possible model of sea level data 46. Bai and Feng proposed a class of fractional-order anisotropic diffusion equations based on PM equation for image denoising using Fourier-domain fractional derivative in 49.

Noise Models

Poisson Model and Signal-Dependent Gaussian Model

Perona-Malik Diffusion

Experiments and Discussion

Conclusions