Although data-driven machine learning methods have been successfully applied to predict complex nonlinear dynamics, forecasting future evolution based on incomplete past information remains a significant challenge. This paper proposes a novel data-driven approach that leverages the dynamical relationships among variables. By integrating Non-Stationary Transformers with LightGBM, we construct a robust model where LightGBM builds a fitting function to capture and simulate the complex coupling relationships among variables in dynamically evolving chaotic systems. This approach enables the reconstruction of missing data, restoring sequence completeness and overcoming the limitations of existing chaotic time series prediction methods in handling missing data. We validate the proposed method by predicting the future evolution of variables with missing data in both dissipative and conservative chaotic systems. Experimental results demonstrate that the model maintains stability and effectiveness even with increasing missing rates, particularly in the range of 30% to 50%, where prediction errors remain relatively low. Furthermore, the feature importance extracted by the model aligns closely with the underlying dynamic characteristics of the chaotic system, enhancing the method’s interpretability and reliability. This research offers a practical and theoretically sound solution to the challenges of predicting chaotic systems with incomplete datasets.

We developed a novel method based on self-supervised learning to improve the ghost imaging of occluded objects. In particular, we introduced a W-shaped neural network to preprocess the input image and enhance the overall quality and efficiency of the reconstruction method. We verified the superiority of our W-shaped self-supervised computational ghost imaging (WSCGI) method through numerical simulations and experimental validations. Our results underscore the potential of self-supervised learning in advancing ghost imaging.

Ghost imaging (GI) has been received more and more attention in past thirty years. However, it has some limitations in the resolution. In this paper, we propose a scheme to improve the resolution of GI by a new imaging information, i.e. the coefficient of skewness coming from the fluctuations of the second-order correlation function, and put forward an enhanced GI protocol exploiting those fluctuations. We demonstrate experimentally that the additional information obtained from the new information makes it possible to improve resolution compared to the traditional GI scheme.

Multi-wavelength ghost imaging usually involves extensive data processing and faces challenges such as poor reconstructed image quality. In this paper, we propose a multi-wavelength computational ghost imaging method based on feature dimensionality reduction. This method not only reconstructs high-quality color images with fewer measurements but also achieves low-complexity computation and storage. First, we utilize singular value decomposition to optimize the multi-scale measurement matrices of red, green, and blue components as illumination speckles. Subsequently, each component image of the target object is reconstructed using the second-order correlation function. Next, we apply principal component analysis to perform feature dimensionality reduction on these reconstructed images. Finally, we successfully recover a high-quality color reconstructed image. Simulation and experimental results show that our method not only improves the quality of the reconstructed images but also effectively reduces the computational and storage burden. When extended to multiple wavelengths, our method demonstrates greater advantages, making it more feasible to handle large-scale data.

Ghost imaging (GI) has shown potential in low-light and complex scenes, but its performance is limited by noise and low-quality reconstruction under extreme sampling rates. This paper proposes a deep learning method combining dual attention mechanism with orthogonal regularization, called Dual Attention Orthogonal Optimization Ghost Imaging (DAOGI). The method uses the AttentionBlock module to enhance local feature extraction and the Transformer module to capture global dependencies. Meanwhile, the orthogonal regularization term is employed to strengthen the orthogonality of the modulation pattern matrix, thereby improving imaging quality at extremely low sampling rates and effectively reducing artifacts and noise. The DAOGI method can significantly outperform traditional ghost imaging methods at a sampling rate of 1.56$\%$, achieving high-quality image reconstruction with few samples. The feasibility and effectiveness of the proposed method are verified through numerical simulations and optical experiments, providing a new direction for ghost imaging.