Enhancing residual-based techniques with shape reconstruction features in electrical impedance tomography

TLDR: In this paper, the linearized residual functional under a linear constraint defined by a monotonicity test is minimized under high levels of noise without the appearance of artifacts, and global convergence is established to guarantee that this method is stable under the effects of noise.

Abstract: 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 are 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 the 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 the appearance of artifacts.