Sparse Blind Deconvolution with Nonconvex Optimization for Ultrasonic NDT Application

In the field of ultrasonic nondestructive testing (NDT), robust and accurate detection of defects is a challenging task because of the attenuation and noising of the ultrasonic wave from the structure. For determining the reflection characteristics representing the position and amplitude of ultrasonic detection signals, sparse blind deconvolution methods have been implemented to separate overlapping echoes when the ultrasonic transducer impulse response is unknown. This letter introduces the ℓ1/ℓ2 ratio regularization function to model the deconvolution as a nonconvex optimization problem. The initialization influences the accuracy of estimation and, for this purpose, the alternating direction method of multipliers (ADMM) combined with blind gain calibration is used to find the initial approximation to the real solution, given multiple observations in a joint sparsity case. The proximal alternating linearized minimization (PALM) algorithm is embedded in the iterate solution, in which the majorize-minimize (MM) approach accelerates convergence. Compared with conventional blind deconvolution algorithms, the proposed methods demonstrate the robustness and capability of separating overlapping echoes in the context of synthetic experiments.