A self-supervised L1/L2-regularized sparse Radon transform and its demultiple application

The sparse Radon transform is a widely used demultiple method, valued for high resolution. However, conventional sparse regularization often leads to significant amplitude loss, which distorts primaries and reduces the overall demultiple performance. Therefore, finding an optimal solution that balances sparsity and amplitude preservation is a critical issue. Deep learning exhibits strengths in feature extraction, but Convolutional Neural Network (CNN)-based Radon transform methods are limited by their reliance on labeled data. To address these problems, a self-supervised framework for Radon transform inversion is proposed. Within this framework, the forward Radon transform operator is embedded as a prior constraint, allowing the network to learn the inversion directly from the input data and thus overcome dependence on labeled training data. Furthermore, a scale-invariant L1/L2-regularization is designed to guide the network in achieving a better balance between sparsity and amplitude preservation. This approach adaptively encourages sparsity in the model space while avoiding penalizing weak events, thereby mitigating the overly sparse features induced by conventional methods. In addition, cascaded architectures with different numbers of stages are tested to evaluate the influence of network complexity on the proposed self-supervised Radon inversion framework. Demultiple experiments on one synthetic dataset and two field datasets confirm the effectiveness of the proposed method. It not only yields a high-fidelity and artifact-free Radon solution for accurate multiple estimation, but also significantly improves inversion efficiency by leveraging end-to-end computation. The results demonstrate clearer primary events and thorough suppression of multiple energy compared to traditional approaches.