A MAP-MRF filter for phase-sensitive coil combination in autocalibrating partially parallel susceptibility weighted MRI

A statistical approach for combination of channel phases is developed for optimizing the Contrast-to-Noise Ratio (CNR) in Susceptibility Weighted Images (SWI) acquired using autocalibrating partially parallel techniques. The unwrapped phase images of each coil are filtered using local random field based probabilistic weights, derived using energy functions representative of noisy sensitivity and tissue information pertaining to venous structure in the individual channel phase images. The channel energy functions are obtained as functions of local image intensities, first or second order clique phase difference and a threshold scaling parameter dependent on the input noise level. Whereas the expectation of the individual energy functions with respect to the noise distribution in clique phase differences is to be maximized for optimal filtering, the expectation of tissue energy function decreases and noise energy function increases with increase in threshold scale parameter. The optimum scaling parameter is shown to occur at the point where expectations of both energy functions contribute to the largest possible extent. It is shown that implementation of the filter in the same lines as that of Iterated Conditional Modes (ICM) algorithm provides structural enhancement in the coil combined phase, with reduced noise amplification. Application to simulated and in vivo multi-channel SWI shows that CNR of combined phase obtained using MAP-MRF filter is higher as compared to that of coil combination using weighted average.