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

Abstract

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 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.

Monotonicity-Based Regularization for Phantom Experiment Data in Electrical Impedance Tomography

“…This result raises a question that whether to regularize the linearized-data-fit functional such that the corresponding minimizer yields a good approximation of the conductivity contrast. An affirmative answer has been proved in [19] for the continuum boundary data. In the present paper, we shall apply this new algorithm to the real electrode setting and test with standard arXiv:1610.05718v2 [math.AP] 19 Oct 2016 phantom experiment data.…”

“…An affirmative answer has been proved in [19] for the continuum boundary data. In the present paper, we shall apply this new algorithm to the real electrode setting and test with standard arXiv:1610.05718v2 [math.AP] 19 Oct 2016 phantom experiment data. Numerical results later on show that this new algorithm helps to improve the quality of the reconstructed images as well as reduce the ringing artifacts.…”

“…Thus one-step linearization methods are principally capable of reconstructing the correct (outer) support of the conductivity difference even though they ignore the non-linearity of the EIT measurement process. In [19] the authors developed a monotonicity-based regularization method for the linearized EIT equation for which (in the continuum model) it can be guaranteed that the regularized solutions converge against a function that shows the correct outer shape. In this section, we formulate and analyze this new method for real electrode measurements, and in the next section we will apply it to real data from a phantom experiment and compare it with the GREIT method.…”

“…Following [19] we then solve the linearized EIT equation (3) using the monotonicity constraints β k . We minimize the Euclidean norm of the residuum…”

“…For the continuum model, and under the assumption that D has connected complement, the authors [19] showed that for exact data this monotonicity-constrained minimization of the linearized EIT residuum admits a unique solution and that the support of the solution agrees with the anomalies support D up to the pixel partition. Moreover, [19] also shows that for noisy data and using the regularized constraints β δ k , minimizers exist and that, for δ → 0, they converge to the minimizer with the correct support. Since practical electrode measurements can be regarded as an approximation to the continuum model, we therefore expect that the above approach will also well approximate the anomaly support for real electrode data.…”