  In electrical impedance tomography, algorithms based on minimizing a
linearized residual functional have been widely used due to their flexibility
and good performance in practice. However, no rigorous convergence results have
been available in the literature yet, and reconstructions tend to contain
ringing artifacts. In this work, we shall minimize the linearized residual
functional under a linear constraint defined by a monotonicity test, which
plays a role of a special regularizer. Global convergence is then established
to guarantee that this method is stable under the effects of noise. Moreover,
numerical results show that this method yields good shape reconstructions under
high levels of noise without appearance of artifacts.
