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

• Published in: Mathematical Problems in Engineering Vol. 2012; no. 2012; pp. 1 - 13
• Main Authors: Hu, Shaoxiang, Chen, Wufan, Liao, Zhiwu
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Limiteds 01.01.2012; Hindawi Publishing Corporation; Hindawi Limited
• Subjects: Anisotropy; Computed tomography; Derivatives; Diffusion; Fractional calculus; Integers; Mathematical models; Mean square errors; Medical research; Noise; Nonlinearity; Normal distribution; Partial differential equations; Restoration; Sample variance; Staircases; Studies; Visual effects; China
• ISSN: 1024-123X; 1563-5147
• DOI: 10.1155/2012/391050

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).