  Elasticity image, visualizing the quantitative map of tissue stiffness, can
be reconstructed by solving an inverse problem. Classical methods for magnetic
resonance elastography (MRE) try to solve a regularized optimization problem
comprising a deterministic physical model and a prior constraint as
data-fidelity term and regularization term, respectively. For improving the
elasticity reconstructions, appropriate prior about the underlying elasticity
distribution is required which is not unique. This article proposes an infused
approach for MRE reconstruction by integrating the statistical representation
of the physical laws of harmonic motions and learning-based prior. For
data-fidelity term, we use a statistical linear-algebraic model of equilibrium
equations and for the regularizer, data-driven regularization by denoising
(RED) is utilized. In the proposed optimization paradigm, the regularizer
gradient is simply replaced by the residual of learned denoiser leading to
time-efficient computation and convex explicit objective function. Simulation
results of elasticity reconstruction verify the effectiveness of the proposed
approach.
