Integer-Transform Fractional-Order Spectrum of Cumulant for Star Image Restoration

Ground-based observations are often degraded by the combined effects of spatially non-uniform, strong stray-light contamination and noise. High-fidelity restoration of ground-based star images is a prerequisite for improving the accuracy of space object detection and situational awareness. Existing restoration methods built on second-order statistics are generally ineffective under non-Gaussian noise. As a result, restored outputs frequently suffer from star loss or photometric distortion. To address these challenges, we first propose the integer-transform fractional-order spectrum of cumulant (IFOSC). By constructing an integer-transform kernel matrix for the low-rank approximation of the Mittag-Leffler transcendental function, the proposed IFOSC strictly preserves the theoretical immunity to symmetric $\alpha $ -stable (S $\alpha $ S) noise while reducing computational complexity. Building upon this foundation, an IFOSC-guided star image restoration network, termed IGIR, is further proposed, in which IFOSC is explicitly introduced as a statistical-prior prompt to guide feature extraction in the deep network. Benefiting from the sparse representational capability of IFOSC in the fractional-order domain, IGIR effectively reconstructs the underlying signal manifold in the latent space, thereby achieving precise decoupling between space targets and complex background noise. Extensive experiments demonstrate that IGIR consistently outperforms existing state-of-the-art methods in both quantitative metrics and perceptual quality, providing an efficient and robust solution for ground-based wide-field astronomical survey and monitoring systems.