Noise and signal estimation in MRI: two-parametric analysis of rice-distributed data by means of the maximum likelihood approach

The paper’s subject is the elaboration of a new approach to image analysis on the basis of the maximum likelihood method. This approach allows to get simultaneous estimation of both the image noise and the signal within the Rician statistical model. An essential novelty and advantage of the proposed approach consists in reducing the task of solving the system of two nonlinear equations for two unknown variables to the task of calculating one variable on the basis of one equation. Solving this task is important in particular for the purposes of the magnetic-resonance images processing as well as for mining the data from any kind of images on the basis of the signal’s envelope analysis. The peculiarity of the consideration presented in this paper consists in the possibility to apply the developed theoretical technique for noise suppression algorithms’ elaboration by means of calculating not only the signal mean value but the value of the Rice distributed signal’s dispersion, as well. From the view point of the computational cost the procedure of the both parameters’ estimation by proposed technique has appeared to be not more complicated than one-parametric optimization. The present paper is accented upon the deep theoretical analysis of the maximum likelihood method for the two-parametric task in the Rician distributed image processing. As the maximum likelihood method is known to be the most precise, its developed two-parametric version can be considered both as a new effective tool to process the Rician images and as a good facility to evaluate the precision of other two-parametric techniques by means of their comparing with the technique proposed in the present paper.