MRI Denoising Using Low Rank Prior and Sparse Gradient Prior

Image priors have been successfully introduced to solve ill-posed problems, such as image denoising. In this paper, we propose a new denoising model for magnetic resonance images (MRIs) which employs the image low-rank and sparse gradient priors. First, we use a Gaussian mixture model (GMM) to guide the clustering of non-local self-similar patches by learning the structure of external noise-free MRI patches to help retain the low rank of the noisy MRI patch matrix. Second, we fit the heavy-tailed gradient of MRI with a hyper-Laplacian distribution to reduce ringing artifacts. Third, we adopt an alternating iterative algorithm. The experimental results show that our proposed algorithm outperforms many classical MRI denoising methods, such as unbiased nonlocal means (UNLM) filtering and block-matching and 3D (BM3D) filtering in both visual and numerical results.