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

Abstract 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 the 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 the development of 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. Synthetic experiments quantitatively demonstrate improved reconstruction accuracy relative to widely used interpolation approaches such as projection onto convex sets (POCS) and damped rank-reduction (DRR), while the field-data example shows improved apparent continuity and limited overall spectral distortion. The proposed implementation also drastically reduces the memory required for the 5D Radon representation and remains computationally practical for large 5D datasets.