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Quantitative characterization of tissue properties, known as elasticityimaging, can be cast as solving an ill-posed inverse problem. The finiteelement methods (FEMs) in magnetic resonance elastography (MRE) imaging arebased on solving a constrained optimization problem consisting of a physicalforward 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, indicatea deterministic relationship between MRE-measured data and unknown elasticitydistribution which leads to the poor and unstable elasticity distributionestimation in the presence of noise. Toward this end, we propose an efficientstatistical methodology for physical forward model refinement by formulating itas linear algebraic representation with respect to the unknown elasticitydistribution and incorporating an analytical noise model. To solve thesubsequent total variation regularized optimization task, we benefit from afixed-point scheme involving proximal gradient methods. Simulation results ofelasticity reconstruction in various SNR conditions verify the effectiveness ofthe proposed approach.

Finite Element Reconstruction Of Stiffness Images In MR Elastography Using Statistical Physical Forward Modeling And Proximal Optimization Methods