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Sinogram restoration for low-dosed $X$-ray computed tomography using fractional-order Perona-Malik diffusion. (English) Zbl 1264.94015
Summary: 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 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).
##### MSC:
 94A08 Image processing (compression, reconstruction, etc.) 35R30 Inverse problems for PDE 35R11 Fractional partial differential equations 92C55 Biomedical imaging and signal processing, tomography 35K10 Second order parabolic equations, general