A Modified Low Rank Learning Based on Iterative Nuclear Weighting in Ripplet Transform for Denoising MR Images

In recent studies, several methods have been suggested to decrease noise of magnetic resonance image (MRI) in order to raise the peak signal-to-noise ratio (PSNR) and the structural similarity index (SSIM). In this paper, we propose a novel method based on a minimization problem in Ripplet domain that uses singular value decomposition (SVD) in low rank learning to eliminate the noise of MRI images. We reschedule the weighted nuclear norm minimization (WNNM) problem in any edges of Ripplet domain transform and using an adaptive weighting structure to denoise the patches of Ripplet component matrix. The parameters of the proposed method are divided into two groups, some of them are calculated systematically based on the WNNM problem in input MR images, and some others are defined according to the problem situations. The proposed method is compared with recent state-of-the-art denoising methods by the synthetic and actual MR image datasets in the presence of the Rician and Gaussian noises. The three experimental outcomes investigate the ability of the proposed method in reducing the noise in PSNR-range [0.5-3] dB and enhance the similarity performance with range [1]–[10] percent in comparison to the other methods.