Fast Adaptive Weighting with Local Support Density Awareness for 3D Seismic Data Reconstruction

This paper addresses the limitation of fixed weighting in the Weighted Projection Onto Convex Sets (WPOCS) method based on prior support sets for 3D seismic data reconstruction, which fails to adapt to spatial heterogeneity. We propose a Fast Adaptive Weighted Projection Onto Convex Sets (FAWPOCS) method in the shearlet domain that utilizes density-aware local support sets. Within the Fast Projection Onto Convex Sets (FPOCS) framework, the proposed method incorporates prior support set information derived from shearlet coefficients of adjacent time slices. Unlike fixed-weight strategies, our approach precisely calculates the support set density characteristics within the local neighborhood of each non-support-set coefficient point through convolution operations. Based on this analysis, the data region is adaptively partitioned into high-, medium-, and low-density zones. Furthermore, the method dynamically assigns differentiated attenuation weights to different density regions through an exponential weighting model, achieving a refined balance between noise suppression and detail preservation. Both synthetic and field data tests demonstrate that the AWPOCS method outperforms the WPOCS method in terms of reconstruction Signal-to-Noise Ratio (SNR) and convergence rate. Moreover, it eliminates the need for manual weight parameter tuning, significantly enhancing the adaptability and practicality of the method, thereby providing a reliable solution for high-precision seismic data reconstruction.