Abstract: Spectral Computed Tomography (Spectral CT) is an emerging imaging technology that enhances material differentiation and clinical diagnostic accuracy by acquiring multi-spectral projection data. However, in sparse-angle spectral CT image reconstruction, noise suppression and edge preservation still face challenges. Regularization methods, such as Directional Probabilistic Total Variation (dTV-p) and tight wavelet frame L0, could introduce prior information to improve sparse-angle spectral CT image reconstruction quality. In this study, we propose a dTV-p and tight wavelet frame L0 regularization-based dual-regularization sparse-angle spectral CT image reconstruction algorithm to address noise suppression and edge preservation. We used the fast iterative shrinkage-thresholding algorithm (FISTA) to accelerate the algorithm. First, the dTV-p regularization is solved in the image domain using proximal mapping and FISTA. Next, the L0 regularization is solved in the wavelet domain using iterative hard thresholding. Finally, the dual variables are solved using FISTA acceleration. The experimental results demonstrated the efficacy of the proposed algorithm, revealing superior performance in edge preservation, noise suppression, and quantitative evaluation metrics compared to comparative algorithms.