Image reconstruction based on nonconvex overlapping group sparse regularization for planar ECT defect detection

Composite materials have been widely applied in aerospace, automotive, and construction industries, making the non-destructive testing of these materials crucial. Planar electrical capacitance tomography (ECT), as a permittivity visualization technology, holds significant potential for development in the field of non-destructive testing. However, the underdetermination of its inverse problem often poses a key challenge to the imaging quality. To alleviate the underdetermination of the inverse problem and improve the image reconstruction quality of planar ECT, an image reconstruction method based on nonconvex overlapping group sparsity (NOGS) regularization is proposed. Firstly, the l_2,1 overlapping group sparse regularization model for normalized permittivity is established. Secondly, nonconvex functions are utilized as the external functions of the l_2,1 norm to form a NOGS regularization model. Finally, a Fast Non-Convex Overlapping Group Sparse Algorithm (FaNogSa) based on the LBP solution is proposed to solve the model for image reconstruction. To validate the effectiveness of this method, simulations, and experiments are conducted, and comparisons are made with the Tikhonov algorithm, Landweber algorithm, l₁ norm method, Laplace Prior-Based Efficient Sparse Bayesian Learning (L-ESBL), student's T Prior-Based Efficient Sparse Bayesian Learning (S-ESBL), and method by combining the density-based spatial clustering of applications with noise clustering algorithm and self-adaptive alternating direction method of multipliers (DBSCAN-SADMM) algorithm. Results demonstrate that NOGS outperforms other algorithms in terms of reconstruction accuracy, convergence time, and robustness. Among NOGS, NOGS (atan) performs the best, NOGS (abs) performs the worst, and NOGS (log) falls in between.