  A crucial step in seismic data processing consists in reconstructing the
wavefields at spatial locations where faulty or absent sources and/or receivers
result in missing data. Several developments in seismic acquisition and
interpolation strive to restore signals fragmented by sampling limitations;
still, seismic data frequently remain poorly sampled in the source, receiver,
or both coordinates. An intrinsic limitation of real-life dense acquisition
systems, which are often exceedingly expensive, is that they remain unable to
circumvent various physical and environmental obstacles, ultimately hindering a
proper recording scheme. In many situations, when the preferred reconstruction
method fails to render the actual continuous signals, subsequent imaging
studies are negatively affected by sampling artefacts. A recent alternative
builds on low-rank completion techniques to deliver superior restoration
results on seismic data, paving the way for data kernel compression that can
potentially unlock multiple modern processing methods so far prohibited in 3D
field scenarios. In this work, we propose a novel transform domain revealing
the low-rank character of seismic data that prevents the inherent matrix
enlargement introduced when the data are sorted in the midpoint-offset domain
and develop a robust extension of the current matrix completion framework to
account for lateral physical constraints that ensure a degree of proximity
similarity among neighbouring points. Our strategy successfully interpolates
missing sources and receivers simultaneously in synthetic and field data.
