Augmented Lagrangian and Total Variation Methods for Recovering Discontinuous Coeecients from Elliptic Equations

Estimation of coeecients of partial diierential equations is ill-posed. Output-least-squares method is often used in practice. Convergence of the commonly used minimization algorithms for the inverse problem is often very slow. By using the augmented Lagrangian method, the inverse problem is reduced to a coupled linear algebraic system, which can be solved eeciently. Total variation techniques have been successfully used in image processing. Here, we use it with the augmented Lagrangian approach to recover discontinuous coeecients. The numerical results show that our approach can recover discontinuous coeecients with large jumps from noisy observations.