A strategy for inverse problem solving in coplanar capacitive imaging: the alternating direction method of multipliers framework with adaptive optimization

In the detection of invisible defects at multilayer composite bonding interfaces, Coplanar Array Capacitive Sensors (CACS) exhibit significant potential. However, the nonlinear relationship between internal defects and dielectric responses in multilayer structures makes image reconstruction highly challenging, often causing feature loss and reconstruction artifacts. To address this inverse imaging problem, this study proposes a novel reconstruction framework based on an improved Alternating Direction Method of Multipliers (ADMM). The proposed method combines sparse regularization and Bayesian inference, reformulating coplanar array capacitive imaging as an optimization problem to improve reconstruction fidelity. To alleviate the ill-conditioning of the inverse model, a hybrid regularization strategy integrating sparse constraints with Bayesian priors is developed, enhancing both stability and reconstruction accuracy. In addition, an adaptive step-size scheme and a dynamic penalty-factor updating mechanism are incorporated into the ADMM framework, enabling the original optimization task to be decomposed into tractable subproblems while accelerating convergence and improving computational efficiency. Experimental results demonstrate that the proposed ADMM-based framework consistently outperforms conventional imaging algorithms in both reconstruction quality and computational efficiency. The proposed method provides a reliable and efficient solution for defect detection in complex bonded structures and shows strong potential for practical non-destructive testing applications.