  Model-based computational elasticity imaging of tissues can be posed as
solving an inverse problem over finite elements spanning the displacement
image. As most existing quasi-static elastography methods count on
deterministic formulations of the forward model resulting in a constrained
optimization problem, the impact of displacement observation errors has not
been well addressed. To this end, we propose a new statistical technique that
leads to a unified optimization problem for elasticity imaging. Our statistical
model takes the imperfect nature of the displacement measurements into account,
and leads to an observation model for the Young's modulus that involves signal
dependent colored noise. To solve the resulting regularized optimization
problem, we propose a fixed-point algorithm that leverages proximal splitting
methods. Preliminary qualitative and quantitative results demonstrate the
effectiveness and robustness of the proposed methodology.
