Dual-Domain Deep Unfolding Network With Implicit Regularization for Seismic Data Reconstruction

Deep unfolding networks (DUNs), which offer strong interpretability, have gradually attracted increasing attention in seismic data reconstruction. Most existing DUN approaches are limited to unfolding in the time-space (t–x) domain, making it difficult to fully exploit the multi-scale features of seismic signals, thereby decreasing reconstruction performance and often leading to the loss of fine details. To overcome the above limitation, a dual-domain optimization framework is proposed, in which the traditional iterative process is replaced by neural networks, yielding a dual-domain deep unfolding network (D3U-Net) based on implicit regularization. The proposed method combines prior information from both thet–xdomain and the wavelet domain, guiding the network to simultaneously capture spatial structural information and frequency characteristics at each stage, thus achieving cooperative reconstruction in both domains and enhancing detail recovery. Meanwhile, an implicit regularization mechanism is introduced, where a learnable neural network substitutes the conventional proximal mapping operator and does not require manual specification of the weights of the regularization term, simplifying the tuning process and endowing the network with greater flexibility and adaptability. Experiments conducted on synthetic data, the BP2004 dataset, and field marine seismic data demonstrate that D3U-Net achieves superior reconstruction accuracy and stability under both regular and random seismic-trace missing scenarios compared with current state-of-the-art methods, confirming overall advantages in reconstruction fidelity, generalization capability, and interpretability.