Fractional Optimization With the Learnable Prior for Electrical Capacitance Tomography

Despite the impressive potential of electrical capacitance tomography technology in the process industry, its application is hampered by low-quality images. To unleash its potential, we propose a new fractional optimization model with the semi-supervised learning prior (SSLP) for imaging, which synergizes the physical mechanism of measurement with semi-supervised learning. An efficient optimizer is developed to solve the proposed fractional optimization imaging model. In order to infer the SSLP, we propose a physics-constrained semi-supervised broad learning system with the potential to reduce the challenges associated with sample collection. The training is formulated by a fractional optimization model that integrates the physical mechanism of measurement as a constraint to ensure that predictions adhere to the underlying physical significance. The evaluation results using both noisy and noiseless capacitance data validate that the proposed imaging method outperforms popular imaging algorithms in terms of noise immunity, detail recovery and artifact removal. The fractional optimization imaging method makes effective use of available data, improves the ability to cope with reconstruction tasks, and unlocks the synergistic potential between the physical laws of measurement and semi-supervised learning to improve reconstruction fidelity.