A high-order convex variational model for denoising MRI data corrupted by Rician noise

Rician noise removal is an essential problem in magnetic resonance imaging (MRI). Numerous variational models have been proposed in the literature dealing with Rician noise for MRI data. They, however, are first-order variational models, which suffer the staircase effect and smooth out fine structural details. In this paper, we propose a high-order convex variational model for Rician noise reduction. Unlike other works, our model employs the bounded Hessian regularizer to remedy the staircase effect and preserve small structures. The proofs for mathematical properties, including the convexity of the model, the existence and uniqueness of the solution, are provided. A split Bregman algorithm is developed to solve the proposed minimization problem. All subproblems are solved efficiently by either closed-form solutions or Newton’s method. Experimental results on simulated and real MRI data demonstrate the effectiveness of our proposed model compared with some state-of-the-art variational models for Rician noise removal.