Bayesian approach for Rician non-local means denoising in MR images

Abstract

In this paper, we present an advanced algorithm for Rician noise reduction based on the combination of Bayesian estimation method, maximum a posteriori (MAP) and non-local mean (NLM) filtering. This algorithm is called the non-local MAP (NL-MAP) method. Our method constructs a proper prior for the unknown parameters, which is more realistic in describing actual beliefs about parameters. Moreover, we use observations, which proved to have statistically identical neighborhoods by statistical hypothesis test, in an NL neighborhood of a certain pixel to estimate its true noise free signal. We demonstrate that NL-MAP performs better than the NLM and non-local maximum likelihood estimation (NL-MLE) methods in terms of quantitative measures, especially in low signal-to-noise ratio (SNR) images; however, the NLM performs worst compared to other methods. On the other hand, NL-MAP performs well even when the SNR is high. The NL-MAP and NL-MLE methods also perform visually at a similar level, both better than the NLM method; however, the NL-MAP method performs better than the NL-MLE method through detailed comparisons with different criterion measures.

Keywords:

• Image denoising
• Magnetic resonance images
• Non-local means algorithm
• Non-local maximum likelihood estimation
• Non-local maximum a posteriori
• Rician noise