Abstract Random noise attenuation remains challenging for seismic data containing complex small-scale geological structures, where conventional denoising methods often either leave residual noise or oversmooth subtle but geologically meaningful reflections. To address this issue, we propose a fx-domain quantum-adaptive basis denoising (fx-QABD) method for seismic random-noise suppression. The key idea is to model the fx-domain seismic amplitude as a signal-dependent potential and construct a Hamiltonian matrix whose eigenvectors form data-adaptive quantum basis (QAB) functions. In this representation, coherent seismic events become sparsely concentrated, whereas random noise remains broadly distributed, enabling more effective signal–noise separation through coefficient thresholding. Compared with fixed transform-based or conventional predictive filtering methods, the proposed method provides a representation that is intrinsically matched to local seismic characteristics and is therefore better suited to preserving weak and small-scale structural features. In addition, the 2D framework is extended to 3D seismic volumes through an iterative bidirectional implementation along the inline and crossline directions. Synthetic and field-data experiments demonstrate that the proposed method achieves stronger random-noise attenuation while preserving structural continuity and reflection fidelity. In the synthetic test, fx-QABD yields the highest post-denoising SNR and PSNR among the compared methods, confirming its superior capability for enhancing seismic data quality in structurally complex settings.
Ke et al. (Mon,) studied this question.