Seismic bandwidth extension using restarted FISTA and an improved thresholding operator

Conventional seismic data often suffer from narrow bandwidth and limited resolution due to subsurface absorption and acquisition constraints, hindering the precise characterization of thin-interbedded reservoirs and subtle lithologic traps. Traditional compressed sensing-based bandwidth extension methods typically employ $$L_{1}$$ norm regularization and soft-thresholding operators. However, these approaches often exhibit a “constant bias” defect, which complicates the balance between noise suppression and amplitude fidelity. Furthermore, the Fast Iterative Soft-Thresholding Algorithm (FISTA) is prone to convergence oscillations, leading to increased computational overhead. To address these challenges, this study proposes a seismic bandwidth extension method based on a Restarted FISTA framework. This study introduce a non-convex “limited shrinkage” thresholding operator, categorized into three functional zones—denoising, transition, and amplitude preservation—to optimize the trade-off between noise attenuation and signal fidelity. Concurrently, a restart mechanism is integrated to stabilize the convergence trajectory and mitigate momentum-induced oscillations. Numerical simulations and field data applications demonstrate that the proposed method achieves faster convergence with fewer iterations than standard FISTA. Moreover, the method yields a lower normalized root-mean-square error (NRMSE) under noisy conditions. Field results confirm a significant broadening of the effective frequency range while maintaining physical amplitude consistency.