Sparse Recovery of Strong Reflectors with an Application to Non-Destructive Evaluation

In this paper we show that it is sufficient to recover the locations of K strong reflectors within an insonified medium from three receive elements and 2K+ 1 samples per element. The proposed approach leverages advances in sampling signals with a finite rate of innovation along each element and rank properties from the Euclidean distance matrix construction across elements. With the proposed approach, it is not necessary to construct an image in order to identify strong reflective sources, which is why much fewer receive elements are needed. However, the assumed transmit scheme still uses a standard linear array in order to excite the entire medium with sufficient energy. The approach is validated with simulated data and a measurement that emulates a scenario in non-destructive evaluation.