Reconstruction of missing ultrasonic phased array data using matrix completion

To acquire full matrix capture (FMC) data from an 𝑵 element array, 𝑵 individual transmissions are required. In cases where the acquisition process is lengthy and expensive (as in laser ultrasonics), it is often desirable to reduce the overall data acquisition time by decreasing the number of individual transmissions. Unfortunately, as the recording footprint of the transducer array is depleted, our ability to image with the collected data can be hindered. In this paper, we present a methodology to synthesize reflected data at points on the inspection surface not covered by an active array element, thus reconstructing the same data that would be recorded by a dense array from more sparsely distributed elements. To achieve this we apply matrix completion techniques to both the raw incomplete FMC data and incomplete scattering matrices. The matrix completed data is then compared to the complete dataset and to data reconstructed using a standard inpainting technique.