Factor graphs for inverse problems: Accelerated phase contrast magnetic resonance imaging

In this work, we present a novel technique for image recovery from highly undersampled phase contrast magnetic resonance imaging (PC-MRI) data. Our approach is holistic and includes modeling of the underlying physics, optimized sampling strategies, and design of a novel inversion algorithm. We capture the unique magnitude and phase structure of PC-MRI data as a non-Gaussian conditional mixture density. We then create a factor graph that describes the joint posterior probability of the inference variables given the noisy measurements. A combination of standard belief propagation and generalized approximate message passing (GAMP) is used to form an iterative inversion algorithm capable of producing MAP or MMSE estimates of the signal of interest. Using the proposed technique, we demonstrate high-fidelity PC-MRI recovery for simulated and phantom data undersampled by a factor of ten.