  For electrical impedance tomography (EIT), most practical reconstruction
methods are based on linearizing the underlying non-linear inverse problem.
Recently, it has been shown that the linearized problem still contains the
exact shape information. However, the stable reconstruction of shape
information from measurements of finite accuracy on a limited number of
electrodes remains a challenge.
  In this work we propose to regularize the standard linearized reconstruction
method (LM) for EIT using a non-iterative shape reconstruction method (the
factorization method). Our main tool is a discrete sensitivity-based variant of
the factorization method (herein called S-FM) which allows us to formulate and
combine both methods in terms of the sensitivity matrix. We give a heuristic
motivation for this new method and show numerical examples that indicate its
good performance in the localization of anomalies and the alleviation of
ringing artifacts.
