Granger causality (GC) is a popular method in causal linkage recovery and has been applied to various fields, such as economics and neuroscience. While the conventional Granger causality model is capable of identifying symmetrical causal relationships among variables, it is the asymmetric Granger causality that provides a more comprehensive perspective of the short- and long-term interactions between variables, which is of greater value for empirical study. Traditional vector autoregressive models lack the ability to explore multiscale information flow and are affected by the moving average component. Therefore, by combining the wavelet-based approach and state space model, we propose a new Granger causality analysis method to overcome the inherent limitation of vector autoregressive models and extend to multiscale causality exploration. Two simulations were conducted to compare the proposed approach to an existing wavelet-based method, and five evaluation indicators were utilized. The results indicate that the proposed method efficiently identifies the accurate asymmetric causalities at varying scales, while improving accuracy and reducing bias as compared to the current wavelet-based method. In conclusion, the combination of the wavelet approach and state space method enhances the multiscale causality detecting capability and can potentially contribute to multiscale Granger causality research.

Computed Tomography (CT) is a medical imaging modality that can generate more informative 3D images than 2D X-rays. However, this advantage comes at the expense of more radiation exposure, higher costs, and longer acquisition time. Hence, the reconstruction of 3D CT images using a limited number of 2D X-rays has gained significant importance as an economical alternative. Nevertheless, existing methods primarily prioritize minimizing pixel/voxel-level intensity discrepancies, often neglecting the preservation of textural details in the synthesized images. This oversight directly impacts the quality of the reconstructed images and thus affects the clinical diagnosis. To address the deficits, this paper presents a new self-driven generative adversarial network model (SdCT-GAN), which is motivated to pay more attention to image details by introducing a novel auto-encoder structure in the discriminator. In addition, a Sobel Gradient Guider (SGG) idea is applied throughout the model, where the edge information from the 2D X-ray image at the input can be integrated. Moreover, LPIPS (Learned Perceptual Image Patch Similarity) evaluation metric is adopted that can quantitatively evaluate the fine contours and textures of reconstructed images better than the existing ones. Finally, the qualitative and quantitative results of the empirical studies justify the power of the proposed model compared to mainstream state-of-the-art baselines.