Electrical capacitance tomography using an accelerated proximal gradient algorithm.

Area of Science:

• Process Engineering
• Imaging Science
• Computational Mathematics

Background:

• Image reconstruction in Electrical Capacitance Tomography (ECT) is an ill-posed inverse problem.
• Existing methods face challenges in achieving high image quality for complex flow patterns.

Purpose of the Study:

• To improve image quality in ECT for two-phase flow imaging.
• To adapt and enhance the accelerated proximal gradient (APG) singular value thresholding algorithm for ECT applications.

Main Methods:

• Applied an accelerated proximal gradient (APG) singular value thresholding algorithm, originally for matrix completion, to ECT image reconstruction.
• Utilized nuclear norm-based regularization to address the ill-posed nature of the inverse problem.
• Implemented a novel sensitivity matrix updating technique.

Main Results:

• The APG algorithm with an updated sensitivity matrix yielded superior image quality compared to using a standard sensitivity matrix.
• Successfully reconstructed both typical and complex two-phase flow distributions (e.g., 'sun-rise', cross-shape).
• Achieved good quality reconstructed images with relatively fast computation speeds in simulations and experiments.

Conclusions:

• The developed APG algorithm with sensitivity matrix updating effectively enhances ECT image reconstruction for two-phase flow.
• The method offers a promising approach for achieving high-fidelity and computationally efficient imaging in ECT.