Atomic library optimization for pulse ultrasonic sparse signal decomposition and reconstruction

Abstract

Compressive sampling of pulse ultrasonic NDE signals could bring significant savings in the data acquisition process. Sparse representation of these signals using an atomic library is key to their interpretation and reconstruction from compressive samples. However, the obstacles to practical applicability of such representations are: large size of the atomic library and computational complexity of the sparse decomposition and reconstruction. To help solve these problems, we develop a method for optimizing the ranges of parameters of traditional Gabor-atom library to match a real pulse ultrasonic signal in terms of correlation. As a result of atomic-library optimization, the number of the atoms is greatly reduced. Numerical simulations compare the proposed approach with the traditional method. Simulation results show that both the time efficiency and signal reconstruction energy error are superior to the traditional one even with small-scale atomic library. The performance of the proposed method is also explored under different noise levels. Finally, we apply the proposed method to real pipeline ultrasonic testing data, and the results indicate that our reduced atomic library outperforms the traditional library.