Spatio-temporal undersampling: Recovering ultrasonic guided wavefields from incomplete data with compressive sensing

Many non-destructive evaluation techniques are based on the study and assessment of guided wavefields. Yet, the extent of the sensing region and the span of time over which wavefield data is acquired can be tremendous, resulting in an enormous amount of spatio-temporal data. As a result, reducing the burden of data acquisition and storage from undersampled data could be highly advantageous. To achieve this end, various signal processing methodologies have been proposed in the literature, many of which make use of compressive sensing. In prior work, such methodologies for effective wavefield reconstruction from incomplete data in space and in time (separately) have been demonstrated. In this paper, we combine these approaches. We present a compressive sensing based guided wave retrieval method with a two-dimensional ultrasonic guided wave model, which enables us to reconstruct wavefields that are undersampled in both the temporal and spatial domains. Results from implementing this method on a dataset consisting of experimental guided wave propagation indicate its potential for accurate wave reconstruction in the presence of spatio-temporal undersampling. We compare results for a variety of subsampling strategies and study the impact of sparsity on the reconstruction performance. Our results indicate that the proposed methodology in this paper is capable of achieving an accuracy of more than 80 percent (in terms of correlation coefficient) at a spatio-temporal undersampling ratio of about 40 percent using random sampling in space and time.