In this paper, a new filtering method is presented to remove the Rician noise from magnetic resonance images (MRI) acquired using single coil MRI acquisition system. This filter is based on nonlocal neutrosophic set (NLNS) approach of Wiener filtering. A neutrosophic set (NS), a part of neutrosophy theory, studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Now, we apply the neutrosophic set into image domain and define some concepts and operators for image denoising. First, the nonlocal mean is applied to the noisy MRI. The resultant image is transformed into NS domain, described using three membership sets: true (T), indeterminacy (I) and false (F). The entropy of the neutrosophic set is defined and employed to measure the indeterminacy. The ω-Wiener filtering operation is used on T and F to decrease the set indeterminacy and to remove the noise. The experiments have been conducted on simulated MR images from Brainweb database and clinical MR images. The results show that the NLNS Wiener filter produces better denoising results in terms of qualitative and quantitative measures compared with other denoising methods, such as classical Wiener filter, the anisotropic diffusion filter, the total variation minimization and the nonlocal means filter. The visual and the diagnostic quality of the denoised image are well preserved. 
MRI denoising using nonlocal neutrosophic set approach of Wiener filtering