A wavefield reconstruction method using sparse representation and dictionary learning for RTM

Reverse time migration (RTM) is a well-established imaging technique that uses the two-way wave equation to achieve high-resolution imaging of complex subsurface media. However, when using RTM for reverse time extrapolation, a source wavefield needs to be stored for cross-correlation with the backward wavefield. This requirement results in a significant storage burden on computer memory. This paper introduces a wavefield reconstruction method that combines sparse representation to compress a substantial amount of crucial information in the source wavefield. The method uses the K-SVD algorithm to train an adaptive dictionary, learned from a training dataset consisting of wavefield image patches. For each timestep, the source wavefield is divided into image patches, which are then transformed into a series of sparse coefficients using the trained dictionary via the batch-orthogonal matching pursuit algorithm, known for its accelerated sparse coding process. This novel method essentially attempts to transform the wavefield domain into the sparse domain to reduce the storage burden. We used several evaluation metrics to explore the impact of parameters on performance. We conducted numerical experiments using acoustic RTM and compared two RTM methods using checkpointing techniques with two strategies from our proposed method. Additionally, we extended the application of our method to elastic RTM. The conducted tests demonstrate that the method proposed in this paper can efficiently compress wavefield data, while considering both computational efficiency and reconstruction accuracy.