Multitasking optimization for the imaging problem in electrical capacitance tomography

Electrical capacitance tomography excels in measuring multiphase flows, but it faces challenges in reconstructing high-accuracy images. To tap into the potential of this measurement technique, we model the image reconstruction problem as a bilevel multitasking optimization problem, aiming to enhance imaging quality via effective knowledge transfer and integration across various tasks. This new imaging model consists of a target optimization problem and an auxiliary optimization problem, facilitating knowledge transfer and fusion between tasks. We design a new algorithm to solve the target optimization problem and integrate it with an autoencoder used for the cross-task knowledge transfer, forming a new multitasking optimizer to solve this proposed bilevel multitasking optimization imaging model. The extreme learning machine is developed for the prediction of learnable prior images by introducing a novel bilevel optimization framework that enables concurrent parameter selection and model training. A novel nested algorithm, designed to efficiently address optimization problems structured hierarchically, is developed to solve the training model. Evaluation results show that the new imaging algorithm outperforms popular imaging methods in terms of reconstruction accuracy and robustness, while also demonstrating stable performance. This proposed imaging algorithm achieves cross-task knowledge transfer and fusion, integrates measurement physics and machine learning, mines and integrates effective image priors, adaptively learns model parameters, alleviates the ill-posed property of the image reconstruction problem, increase the automation of the model, and improves imaging quality, robustness and performance stability, which provides a comprehensive solution to mitigate challenges in imaging.