In this paper, we propose a novel method for removing noise from MRI data by exploiting regularisation techniques combined with variational mode decomposition. Variational mode decomposition is a new decomposition technique for sparse decomposition of a 1D or 2D signal into a set of modes. In turn, regularisation is a method that can translate the ill-posed problem (e.g., image denoising) into a well-posed problem.

The proposed method aims to remove the noise from the image in two steps. In the first step, the MR imaging data are decomposed by the 2D variational mode decomposition algorithm. In the second step, for effective suppression of Rician noise from MRI data, we used the fused lasso signal approximator with all modes acquired from the medical scan.

The performance of the proposed approach was compared with state-of-the-art reference methods based on different metrics, that is, the peak signal-to-noise ratio, the structural similarity index metrics, the high-frequency error norm, the quality index based on local variance, and the sharpness index. The experiments were performed on the basis of both simulated and real images. The presented results prove the high denoising performance of the proposed algorithm; particularly under heavy noise conditions.