A new non-local maximum likelihood estimation method for Rician noise reduction in magnetic resonance images using the Kolmogorov–Smirnov test

• An NLML method for denoising MRI based on Kolmogorov-Smirnov (KS) similarity test is proposed.
• The proposed method is statistically convincing and performs better than the conventional NLML method.
• Through the proposed approach the samples for ML estimation can be selected in an adaptive way.
• Quantitative analysis at various noise levels based on the various similarity measures, shows that the proposed method is more effective than conventional NLML.

Denoising algorithms play an important role in the enhancement of magnetic resonance (MR) images. Effective denoising is vital for proper analysis and accurate quantitative measurements from MR images. Maximum Likelihood (ML) estimation methods were proved to be very effective in denoising MR images. Among the ML based methods, the recently proposed non-local maximum likelihood (NLML) approach gained much attention. In the NLML method, the samples for the ML estimation of the true underlying intensity are selected in a non-local way based on the intensity similarity of the pixel neighborhoods. This similarity is generally measured using the Euclidean distance. A drawback of this approach is the usage of a fixed sample size for the ML estimation resulting in over- or under-smoothing. In this work, we propose an NLML estimation method for denoising MR images in which the samples are selected in an adaptive and statistically supported way using the Kolmogorov–Smirnov (KS) similarity test. The method has been tested both on simulated and real data, showing its effectiveness.