A matching pursuit method for approximating overlapping ultrasonic echoes

Ultrasonic pulse-echo methods have been used extensively in measuring the thickness of layered structures as well as those of thin adhesive interface layers. When acoustically measuring thin layers, the resulting echoes from two successive interfaces overlap in time, limiting the minimum thickness that can be resolved using conventional pulse-echo techniques. In this paper, we propose a method, named support matching pursuit (SMP), for resolving the individual echoes. The method is based on the concept of sparse signal approximation in an overcomplete dictionary composed of Gabor atoms (elementary functions). Although the dictionary enables highly flexible approximations, it is also overcomplete, which implies that the approximation is not unique. We propose a method for approximation in which each ultrasonic echo is principally represented by a single atom and therefore has a physical interpretation. SMP operates similarly to the sparse matching pursuit (MP) method. It iteratively improves the approximation by adding, at each iteration, a single atom to the solution set. However, our atom selection criterion utilizes the time localization nature of ultrasonic echoes, which causes portions of a multi-echo ultrasonic signal to be composed mainly from a single echo. This leads to accurate approximations in which each echo is characterized by a set of physical parameters that represent the composing ultrasonic echoes. In the current research we compare SMP to other sparse approximation methods such as MP and basis pursuit (BP). We perform simulations and experiments on adhesively bonded structures which clearly demonstrate the superior performance of the SMP method over the MP and BP methods.