Iterative ADMM for inverse FE-BI problem

An iterative alternating direction method of multipliers (ADMM) is proposed for inverse finite-element boundary-integral (FE-BI) problem with total variation (TV) regularization. The inverse FE-BI fits to a wide class of penetrable sensing applications. TV regularizer enforces sparsity on the gradient of reconstructed permittivity which agrees well with the `piecewise constant' reality of `rocks embedded in soil' scenario. For largescale asteroid problem, the distributed ADMM algorithm is adapted to solve the linear TV inversion at each iteration. The 2D inversion is validated with the Fresnel Institute measurement data. The proposed iterative ADMM can also be applied to similar penetrable imaging applications.