Rician nonlocal means denoising for MR images using nonparametric principal component analysis

Denoising is always a challenging problem in magnetic resonance imaging (MRI) and is important for clinical diagnosis and computerized analysis, such as tissue classification and segmentation. The noise in MRI has a Rician distribution. Unlike additive Gaussian noise, Rician noise is signal dependent, and separating the signal from the noise is a difficult task. In this paper, we propose a useful alternative of the nonlocal mean (NLM) filter that uses nonparametric principal component analysis (NPCA) for Rician noise reduction in MR images. This alternative is called the NPCA-NLM filter, and it results in improved accuracy and computational performance. We present an applicable method for estimating smoothing kernel width parameters for a much larger set of images and demonstrate that the number of principal components for NPCA is robust to variations in the noise as well as in images. Finally, we investigate the performance of the proposed filter with the standard NLM filter and the PCANLM filter on MR images corrupted with various levels of Rician noise. The experimental results indicate that the NPCA-NLM filter is the most robust to variations in images, and shows good performance at all noise levels tested.