A two-step optimization approach for nonlocal total variation-based Rician noise reduction in magnetic resonance images

Purpose: Magnetic resonance imaging (MRI) often suffers from apparent noise during image acquisition and transmission. The degraded data can easily result in nonrobust postprocessing teps in medical image analysis. The purpose of this study is to eliminate noise effects and improve image quality using a nonlocal feature-preserving denoising method. Methods: From a statistical point of view, the magnitude MR images in the presence of noise are usually modeled using a Rician istribution. In the maximum a posteriori framework, a nonlocal total variation (NLTV)-based feature-reserving MRI Rician denoising model is proposed by taking full advantage of high degree of elfsimilarity and redundancy within MR images. However, the nonconvex data-fidelity term and nonsmooth NLTV regularizer make the denoising problem difficult to solve. To guarantee solution stability, a piecewise convex function is first introduced to approximate the nonconvex version. In what follows, a two-step optimization approach is developed to solve the resulting convex denoising model. In each step of this approach, the subproblem can be efficiently solved using existing optimization algorithms. The method performance is evaluated sing synthetic and clinical MRI data sets as well as one diffusion tensor MRI (DTI) data set. Extensive experiments are conducted to compare the proposed method with several state-of-the-art denoising methods. Results: For the synthetic and clinical MRI data sets, the proposed method considerably outperformed other competing denoising methods in terms of both quantitative and visual quality evaluations. It was capable of effectively removing noise in MR images and enhancing tissue characterization. The advantage of the proposed method became more significant as the noise level increased. For the DTI data set, compared with other denoising methods, the proposed method not only preserved the apparent diffusion coefficient but also generated more regular fractional anisotropy (FA) and color-coded FA without obvious visual artifacts. Conclusions: This study describes and validates a nonlocal feature-preserving method for Rician noise reduction on synthetic and real MRI data sets. By exploiting the feature-preserving capability of NLTV regularizer, the proposed method maintains a good balance between noise reduction and fine detail preservation. The experiments have demonstrated a huge potential of the proposedmethod for routine clinical practice.