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

Medical Physics
Ryan Wen LiuDefeng Wang

Abstract

Magnetic resonance imaging (MRI) often suffers from apparent noise during image acquisition and transmission. The degraded data can easily result in nonrobust postprocessing steps 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. From a statistical point of view, the magnitude MR images in the presence of noise are usually modeled using a Rician distribution. In the maximum a posteriori framework, a nonlocal total variation (NLTV)-based feature-preserving MRI Rician denoising model is proposed by taking full advantage of high degree of selfsimilarity 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 using synthetic and clinical MRI data sets as w...Continue Reading

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