Rician noise is a common noise that naturally appears in Magnetic Resonance Imaging (MRI) images. Low rank matrix approximation approaches have been widely used in image processing, which takes advantage of the non-local self-similarity between patches in a natural image. The weighted nuclear norm minimization method as a low rank matrix approximation approach has shown to be an effective approach for image denoising. Inspired by this, we propose in this paper a maximum a posteriori (MAP) model with the weighted nuclear norm as a regularization constraint to remove Rician noise. The MAP data fidelity term has a Lipschitz continuous gradient and the weighted nuclear norm can be efficiently minimized. We propose an iterative weighted nuclear norm minimization algorithm (IWNNM) to solve the proposed non-convex model and analyze the convergence of our algorithm. The computational results show that our proposed method is promising in restoring images corrupted with Rician noise.

里奇噪声是一种常见的噪声，自然会出现在磁共振成像（MRI）图像中。低秩矩阵逼近方法已广泛用于图像处理中，它利用了自然图像中各色标之间的非局部自相似性。加权核范数最小化方法作为低秩矩阵近似方法已被证明是一种有效的图像去噪方法。受此启发，我们在本文中提出了一个最大后验（MAP）模型，该模型以加权核规范作为消除Rician噪声的正则化约束。MAP数据保真度项具有Lipschitz连续梯度，加权核范数可以有效地最小化。我们提出了一种迭代加权核范数最小化算法（IWNNM），以解决所提出的非凸模型并分析该算法的收敛性。计算结果表明，我们提出的方法在恢复受Rician噪声破坏的图像方面很有前景。