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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.

A new adaptive diffusive function for magnetic resonance imaging denoising based on pixel similarity