Narrowband Ultrasonic Detection with High Range Resolution: Separating Echoes via Compressed Sensing and Singular Value Decomposition

Abstract

It is well known that broader bandwidth leads to higher range resolution, but in ultrasonic flaw detection, the bandwidth is often limited. That is, the upper frequency of the transmitted signal is bounded by the attenuation of high-frequency ultrasound, especially when the penetration depth is large. In this case, only the band-limited signals are suitable for far-field detection. Fortunately, theoretical analysis in this paper shows that narrowband detection has greater potential for obtaining high range resolution compared with broadband detection. However, it is difficult to fully utilize this potential because of the severe overlap of narrowband echoes. As a result, we propose a novel approach for separating highly overlapping narrowband echoes in this paper to improve the resolution of range imaging. In our approach, in addition to a formulation following the emerging theory of sparse representation and compressed sensing, singular value decomposition is also employed to capture the main features of the signals, making this approach robust to moderate signal distortions. Numerous simulations and experiments on real data show that the proposed approach is able to fully utilize the potential of narrowband detection and outperforms other competitive methods in terms of stability and accuracy.