Dimensionality-reduced estimation of primaries by sparse inversion

Data-driven methods—such as the estimation of primaries by sparse inversion suffer from the curse of dimensionality that leads to disproportional growth in computational and storage demands when moving to realistic 3D field data. To remove this fundamental impediment, we propose a dimensionality-reduction technique where the data matrix is approximated adaptively by a randomized low-rank factorization. Compared to conventional methods, which need passes through all the data possibly including on-the-fly interpolations for each iteration, our approach has the advantage that the passes is reduced to one to three. In addition, the low-rank matrix factorization leads to considerable reductions in storage and computational costs of the matrix multiplies required by the sparse inversion. Application of the proposed formalism to synthetic and real data shows that significant performance improvements in speed and memory use are achievable at a low computational overhead required by the low-rank factorization.