  We address the estimation of seismic wavefields by means of Multidimensional
Deconvolution (MDD) for various redatuming applications. While offering more
accuracy than conventional correlation-based redatuming methods, MDD faces
challenges due to the ill-posed nature of the underlying inverse problem and
the requirement to handle large, dense, complex-valued matrices. These
obstacles have long limited the adoption of MDD in the geophysical community.
Recent interest in this technology has spurred the development of new
strategies to enhance the robustness of the inversion process and reduce its
computational overhead. We present a novel approach that extends the concept of
block low-rank approximations, usually applied to linear operators, to
simultaneously compress the operator, right-hand side, and unknowns. This
technique greatly alleviates the data-heavy nature of MDD. Moreover, since in
3d applications the matrices do not lend themselves to global low rank
approximations, we introduce a novel H2-like approximation. We aim to
streamline MDD implementations, fostering efficiency and controlling accuracy
in wavefield reconstruction. This innovation holds potential for broader
applications in the geophysical domain, possibly revolutionizing the analysis
of multi-dimensional seismic datasets.
