12 research outputs found
A convergent algorithm for the hybrid problem of reconstructing conductivity from minimal interior data
We consider the hybrid problem of reconstructing the isotropic electric
conductivity of a body from interior Current Density Imaging data
obtainable using MRI measurements. We only require knowledge of the magnitude
of one current generated by a given voltage on the boundary
. As previously shown, the corresponding voltage potential u in
is a minimizer of the weighted least gradient problem
with . In this paper we present an
alternating split Bregman algorithm for treating such least gradient problems,
for non-negative and . We
give a detailed convergence proof by focusing to a large extent on the dual
problem. This leads naturally to the alternating split Bregman algorithm. The
dual problem also turns out to yield a novel method to recover the full vector
field from knowledge of its magnitude, and of the voltage on the
boundary. We then present several numerical experiments that illustrate the
convergence behavior of the proposed algorithm