Laterally constrained low-rank seismic data completion via cyclic-shear transform

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.