Total variation regularized Acousto-Electric Tomography with Neumann conditionsMS54

We consider the Acousto-Electric Tomography problem with interior power density data together with Neumann boundary conditions for BV-constrained conductivities. We tackle this problem by reformulation as a PDE-constrained TV-regularized optimization problem and attack this by linearization and Langragian formulation. The resulting TV-term is approximated by a lagged diffusivity step. Compuations are done using the FEniCS package for Python by iteratively updating the linearization. In conclusion this algorithm provides a reconstruction scheme, when not violating approximations.

This presentation is part of Minisymposium “MS54 - Hybrid Approaches that Combine Deterministic and Statistical Regularization for Applied Inverse Problems (4 parts)
organized by: Cristiana Sebu (University of Malta) , Taufiquar Khan (Clemson University) .

Bjørn Christian Skov Jensen (Technical University of Denmark)
image reconstruction, inverse problems, nonlinear optimization, partial differential equation models