2D Elasticity Reconstruction With Bi-Convex Alternating Direction Method of Multipliers

Elastography produces images of mechanical properties of tissue such as elasticity, which is a clinically significant biomarker of different pathologies such as liver fibrosis and cancer. However, elastography reconstruction is a highly ill-conditioned problem that requires the use of spatial filtering and regularizers. These leads to results that depend on the filter parameters and on optimization problems that are not provably convergent to an optimal solution. We have formulated the 2D elasticity reconstruction as a bi-convex optimization problem with bi-affine equality constraints. We also proposed a solver using the alternating direction method of multipliers (ADMM) and total variation (TV) regularization. ADMM provides simple closed-form updates of the elasticity with one forward solution and one direct inversion and converges faster compared to other gradient-based methods. The proposed method does not require separate data filtering and provides better convergence and superior performance to other algorithms for both numerical and experimental data.