Simultaneous Reconstruction and Denoising of Seismic Data Based on Compressed Sensing and Fractional-Order Total Variation

Field seismic data are often irregular and incomplete due to environmental constraints, compromising the continuity and coherence of raw data. To achieve high-accuracy reconstruction, we propose a novel dual-regularization reconstruction method by incorporating a fractional order total variation (FOTV) regularization term into compressed sensing (CS). Compared with the traditional L1 regularization method, the proposed dual-regularization method based on CS and FOTV not only considers the sparsity of signals but also takes into account the complexity of subsurface media structures, enabling better reconstruction of seismic data. Specifically, the FOTV regularization term has the ability to balance edge preservation and noise suppression, making it suitable for processing noisy and incomplete data. We solve the proposed reconstruction model by using the alternating direction method of multipliers (ADMM). The objective function is divided into two subproblems for stepwise optimization computation, and each subproblem is solved explicitly. Testing with both synthetic and field data demonstrates that the proposed method outperforms traditional compressed sensing approaches in reconstructing complex seismic structures, while exhibiting robust noise suppression. Notably, this method enables simultaneous reconstruction and denoising, making it particularly suitable for irregularly sampled and low signal-to-noise ratio seismic data.