Abstract Rank reduction techniques have been found to be extensively used in seismic data processing, particularly for interpolation and denoising applications. Although effective, most existing methods rely on nuclear norm optimization, which incurs substantial computational costs. A novel seismic interpolation method based on non-convex regularization is proposed to address this limitation. Within the Multichannel Singular Spectrum Analysis (MSSA) framework, an arctangent function is employed to construct a non-convex objective function, enabling a more accurate capture of the essence of rank minimization. The differentiable objective function allows efficient gradient calculation, enabling a gradient-based projection-prediction algorithm to speed up iterative optimization. Numerical experiments on both 2D and 3D field datasets demonstrate that a comparable or superior signal-to-noise ratio (SNR) is maintained. Furthermore, the computation time is reduced to half of that required by conventional soft‑thresholding techniques, thereby significantly enhancing the processing efficiency for large‑scale seismic data.
Zhu et al. (Mon,) studied this question.