Heydari Mostafa, Karami Mohammad Reza
Department of Biomedical Engineering, Faculty of Electrical and Computer Engineering, Babol University of Technology, Mazandaran, Iran.
J Med Signals Sens. 2015 Oct-Dec;5(4):201-9.
Although there are many methods for image denoising, but partial differential equation (PDE) based denoising attracted much attention in the field of medical image processing such as magnetic resonance imaging (MRI). The main advantage of PDE-based denoising approach is laid in its ability to smooth image in a nonlinear way, which effectively removes the noise, as well as preserving edge through anisotropic diffusion controlled by the diffusive function. This function was first introduced by Perona and Malik (P-M) in their model. They proposed two functions that are most frequently used in PDE-based methods. Since these functions consider only the gradient information of a diffused pixel, they cannot remove noise in noisy images with low signal-to-noise (SNR). In this paper we propose a modified diffusive function with fractional power that is based on pixel similarity to improve P-M model for low SNR. We also will show that our proposed function will stabilize the P-M method. As experimental results show, our proposed function that is modified version of P-M function effectively improves the SNR and preserves edges more than P-M functions in low SNR.
虽然图像去噪方法众多，但基于偏微分方程（PDE）的去噪方法在医学图像处理领域（如磁共振成像（MRI））备受关注。基于PDE的去噪方法的主要优势在于其能够以非线性方式平滑图像，这既能有效去除噪声，又能通过扩散函数控制的各向异性扩散来保留边缘。该函数最早由佩罗纳和马利克（P-M）在其模型中引入。他们提出了两种在基于PDE的方法中最常用的函数。由于这些函数仅考虑扩散像素的梯度信息，所以它们无法去除低信噪比（SNR）噪声图像中的噪声。在本文中，我们提出一种基于像素相似度的分数幂修正扩散函数，以改进低信噪比情况下的P-M模型。我们还将表明，我们提出的函数能使P-M方法更稳定。实验结果表明，我们提出的作为P-M函数改进版本的函数在低信噪比情况下比P-M函数能更有效地提高信噪比并保留边缘。
