Locally optimal subsampling strategies for full matrix capture measurements in pipe inspection

In ultrasonic non-destructive testing, array and matrix transducers are being employed for applications that require in-field steerability or which benefit from a higher number of insonification angles. Having many transmit channels on the other hand increases the measurement time and renders the use of array transducers unfeasible for many applications. In the literature, methods for reducing the number of required channels compared to the full matrix capture scheme have been proposed. Conventionally, these are based on using only receive channels close to the transmit channel. Furthermore, Compressive Sensing based approaches have been proposed, which either use random subsampling schemes or optimize the channel configuration based on theoretic bounds derived specifically for the given measurement setup over the full imaging region. In this publication, we investigate a scenario from the field of pipe inspection, where cracks have to be detected in specific areas near the weld. Based on ray-tracing simulations which incorporate a model of the transducer directivity and beam spread at the interface we derive application specific measures of the energy distribution over the array configuration for given regions of interest. These are used to determine feasible subsampling schemes. For the given scenario, the validity/quality of the derived subsampling schemes are compared based on reconstructions using conventional total focusing method as well as sparsity driven reconstructions using the FISTA. The results can be used to effectively improve the measurement time for the given application without notable loss in defect detectability.