Magnitude MR image denoising via CURE-optimized non-local means

During their acquisition, magnetic resonance (MR) images are affected by random noise, causing the observed magnitude image samples to be Rician distributed. In order to reduce the noise level while preserving the relevant image features, we develop an optimized Non-Local Means (NLM) denoising algorithm. The most sensitive parameters of the proposed NLM estimator are optimized on the squared-magnitude image, which follows a non-central chi-square distribution on two degrees of freedom. This minimum MSE optimization is performed via the minimization of the so-called chi-square unbiased risk estimate (CURE). Taking advantage of some acceleration techniques involving convolutions and parallel computation, we show that the proposed CURE-optimized NLM outperforms some state-of-the-art NLM algorithms with no increase in computation time.