Robust 5D seismic data interpolation via memory-efficient group sparse Radon transform

Ji Li, Dawei Liu, Daniel O. Trad

The five-dimensional (5D) Radon transform holds high potential to effectively address the significant data irregularity and noise challenges presented by 5D seismic surveys. However, its direct application is impeded by prohibitive memory and computational demands. To mitigate this, we present a robust and memory-efficient 5D seismic data interpolation framework based on strong group sparsity regularization in the Radon domain. Specifically, to reconstruct missing traces and attenuate strong erratic noise, we formulate the inversion as an l₁-l₁ minimization problem that simultaneously promotes coefficient sparsity and enhances robustness against outliers. Unlike conventional sparse Radon methods, we explicitly exploit the structured coherence of seismic signals by enforcing strong group sparsity: Radon coefficients are partitioned into non-overlapping groups along slowness axes, and an energy-based greedy selection strategy is applied to identify a small subset of active groups. A key contribution of this work is developing a memory-efficient 5D Radon transform implementation, which avoids constructing the full 5D Radon cube by sequentially accumulating group energies across frequency slices and restricting coefficient updates to the selected groups only. The Radon transform is carried out in the frequency-slowness domain, enabling sharper focusing of coherent events and further improving computational efficiency. Numerical experiments on synthetic and field datasets demonstrate that the proposed method achieves higher reconstruction accuracy compared to widely used interpolation approaches such as projection onto convex sets (POCS) and damped rank-reduction (DRR), while drastically reducing both memory consumption and computational cost, thus enabling practical application of Radon-based methods to 5D seismic processing.