Rician noise and intensity nonuniformity correction (NNC) model for MRI data. (March 2019) - Liu, Lu; Yang, Huan; Fan, Jiyun; Liu, Ryan Wen; Duan, Yuping
Highlights: We propose a novel image restoration model based on maximum a posteriori estimation for MRI data, which are corrupted by both Rician noise and intensity nonuniformity. We develop an efficient optimization algorithm based on ADMM, where all subproblems can be solved by either Newton's method or closed-form solution. We disclosure that the existence of intensity nonuniformity may lead to an underestimation of the noise, which illustrates the importance of simultaneously dealing with Rician noise and intensity nonuniformity. Numerical experiments on both synthetic and real MR data confirm the robustness of the proposed method and its better performance for MR data restoration. Abstract: Rician noise and intensity nonuniformity are two common artifacts and usually coexist in magnetic resonance imaging (MRI) data. Many methods have been proposed in the literature dealing with either Rician noise or intensity nonuniformity individually. We numerically verify that the existence of intensity nonuniformity may lead to the underestimation of noise, which means intensity nonuniformity influences the performance of denoising and vice versa. Thus, we propose a novel restoration model via a maximum a posteriori (MAP) estimator by regarding MRI data as a combination of two multiplicative components, namely, the true intensity and the bias field, and a noise followed a Rician distribution. We also guarantee that the proposed model has at least one positive nontrivial solution theoretically. An efficient algorithm based on alternating minimization method is developed, all subproblems of which can be solved effectively by either Newton's method or closed-form solutions. Intensive numerical results on synthetic and real MRI data confirm the robustness of the method and its better performance for MRI data restoration.