Bayesian MRI denoising in complex domain

Abstract

In recent years, several efforts have been done for producing Magnetic Resonance Image scanner with higher magnetic field strength mainly for increasing the Signal to Noise Ratio and the Contrast to Noise Ratio of the acquired images. However, denoising methodologies still play an important role for achieving images neatness. Several denoising algorithms have been presented in literature. Some of them exploit the statistical characteristics of the involved noise, some others project the image in a transformed domain, some others look for geometrical properties of the image. However, the common denominator consists in working in the amplitude domain, i.e. on the gray scale, real valued image. Within this manuscript we propose the idea of performing the noise filtering in the complex domain, i.e. on the real and on the imaginary parts of the acquired images. The advantage of the proposed methodology is that the statistical model of the involved signals is greatly simplified and no approximations are required, together with the full exploitation of the whole acquired signal. More in detail, a Maximum A Posteriori estimator developed for the handling complex data, which adopts Markov Random Fields for modeling the images, is proposed. First results and comparison with other widely adopted denoising filters confirm the validity of the method.

Keywords: Bayesian estimation; Complex decomposition; MRI denoising; Markov random fields; Maximum a posteriori; Statistical signal processing.