Cramér-Rao Bounds for Flaw Localization in Subsampled Multistatic Multichannel Ultrasound NDT Data

The localization of defects is a prevalent task in ultrasound nondestructive testing. Multi-channel techniques like Full Matrix Capture (FMC) measurements are employed in this regard for their better spatial accuracy compared to single-channel synthetic aperture measurements at the expense of larger data volumes and increased measurement time. In this paper, we analyze a compressed sensing scenario in which location parameters of point-like scatterers are estimated from subsampled FMC data. Particularly, the impact of the specific choice of Tx and Rx elements is studied by means of the Cramér-Rao Bound (CRB). We derive the CRB of lateral and vertical position of the scatterers estimated from FMC data, as well as expressions for the CRB that arise in the far-field scenario. These expressions are useful for two reasons. First, they provide insights about the impact of number and location of channels on the localization performance. Second, we can use them to optimize the sensor positions in the subsampled array, which we demonstrate by introducing a CRB-based array design technique. The far-field expressions reveal that only two channels are required for the CRB of the lateral case to become finite, and also indicate a far-field gain when using a larger subsampled array.