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", which leads to disproportional growth in computational and storage demands when moving to realistic 3-D 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 approximation. Compared to conventional methods, our approach has the advantage that the cost of the low-rank approximation is reduced significantly, which may lead to considerable reductions in storage and computational costs of the sparse inversion. Application of the proposed formalism to synthetic data shows that significant improvements are achievable at low computational overhead required to compute the low-rank approximations.