  This paper deals with the problem of reconstructing a depth map from a
sequence of differently focused images, also known as depth from focus or shape
from focus. We propose to state the depth from focus problem as a variational
problem including a smooth but nonconvex data fidelity term, and a convex
nonsmooth regularization, which makes the method robust to noise and leads to
more realistic depth maps. Additionally, we propose to solve the nonconvex
minimization problem with a linearized alternating directions method of
multipliers (ADMM), allowing to minimize the energy very efficiently. A
numerical comparison to classical methods on simulated as well as on real data
is presented.
