The maximum spacing noise estimation in single-coil background MRI data

This paper presents new noise level estimation technique in single-coil background MRI data based on the maximum spacing estimation (MSP) principle. We derive new MSP estimator for Rayleigh distribution using the Kullback-Leibler divergence approximation, which in comparison with maximum likelihood approach, is based on spacings between successive order statistics. Moreover, we generalize the MSP estimator into higher order spacings and derive subsequent MSP estimators inferring from different statistical distances, i.e., J-divergence, Rényi divergence and Vajda´s measure. We validate our approach both on synthetic brain and real cardiac MRI data in comparison with literature reports. The experimental results show that the MSP estimator has a comparatively low bias and reach Cramér-Rao lower bound on the variance. Finally, we assess properties of MSP estimators derived from different statistical distances with each other.