Learnable bilevel optimization method for electrical capacitance tomography

Abstract

The positive role of electrical capacitance tomography technology depends on high-precision tomographic images. Despite its success, one of the main barriers is the low-quality tomogram. A new learnable bilevel optimization imaging method is proposed to address this problem in this study, in which the image prior and model parameters can be learned from the collected datasets. The upper level optimization problem learns the regularization parameter under the constraint of the lower level optimization problem that implements image reconstruction. A new lower level optimization problem with the introduced machine learning prior is built, which leverages the prior knowledge from collected datasets, imaging targets and imaging mechanisms. The machine learning prior is learned through extreme learning machine, and the training is reformulated into a fractional optimization problem with the physical mechanisms of imaging as a constraint. A new optimizer is proposed to solve the learnable bilevel optimization imaging problem. The effectiveness has been demonstrated by the reconstruction of higher precision images and better noise immunity in comparison with advanced imaging techniques. The new imaging method unifies imaging mechanisms and machine learning, and promotes the complementarity of image priors, which offers new opportunities to unlock the potential of the measurement technique.