  Quantitative characterization of tissue properties, known as elasticity
imaging, can be cast as solving an ill-posed inverse problem. The finite
element methods (FEMs) in magnetic resonance elastography (MRE) imaging are
based on solving a constrained optimization problem consisting of a physical
forward model and a regularizer as the data-fidelity term and the prior term,
respectively. In existing formulation for the elasticity forward model,
physical laws that arise from equilibrium equation of harmonic motion, indicate
a deterministic relationship between MRE-measured data and unknown elasticity
distribution which leads to the poor and unstable elasticity distribution
estimation in the presence of noise. Toward this end, we propose an efficient
statistical methodology for physical forward model refinement by formulating it
as linear algebraic representation with respect to the unknown elasticity
distribution and incorporating an analytical noise model. To solve the
subsequent total variation regularized optimization task, we benefit from a
fixed-point scheme involving proximal gradient methods. Simulation results of
elasticity reconstruction in various SNR conditions verify the effectiveness of
the proposed approach.
