Reconstruction from few views is an important problem in medical imaging and applied mathematics. In this paper, a combined energy minimization is proposed for image reconstruction. l₂ energy of the image gradient is introduced in the lower density region, and it can accelerate the reconstruction speed and improve the results. Total variation of the image is introduced in the higher density region, and the image features can be preserved well. Nonlinear conjugate gradient method is introduced to solve the problem. The efficiency and accuracy of our method are shown in several numerical experiments.

In order to remove random noise in seismic data, this letter proposes a seismic data denoising method based on tensor decomposition and total variation (TDTV). Based on the self-similarity of seismic data, this method first groups similar patches into a stack, then utilizes the low-rank tensor approximation strategy to restore the structural effective information of the seismic section. Considering that the approximate seismic section obtained after CANDECOMP/PARAFAC (CP) decomposition and patch aggregation is unsmooth, this letter introduces the total variation (TV) constraint to perform anisotropic diffusion, and protects edge information while smoothing. Finally, the gradient descent method is used to solve the whole model. The TDTV method proposed in this letter can not only effectively denoise synthetic and field seismic section but also restore structural and edge information. Experimental results show that the proposed method outperforms many state-of-the-art denoising methods.

Seismic data contain a lot of information in both spatial ( t-x ) and frequency domains. In order to make full use of the effective information in multiple domains, this letter proposes a low-rank tensor minimization method for seismic data denoising. This model first uses variational mode decomposition (VMD) to decompose the seismic data in the frequency domain and constructs a seismic tensor to highlight the frequency information of the seismic data; then to make use of the spatial similarity and frequency correlation of the seismic tensor, a low rank seismic tensor is built through block matching and a low-rank tensor minimization model is established to attenuate the noise. Finally, the denoised seismic tensor is reconstructed into a seismic section. Experimental results show that compared with several denoising methods, the method proposed in this letter can obtain higher signal-to-noise ratio (SNR) and structural similarity (SSIM) and achieve better denoising effects.

High-resolution remote sensing images (HRRSI) have important theoretical and practical value in urban planning. However, current segmentation methods often struggle with issues like blurred edges and loss of detailed information due to the intricate backgrounds and rich semantics in high-resolution remote sensing images. To tackle these challenges, this paper proposes an end-to-end attention-based Convolutional Neural Network (CNN) called Double Hybrid Attention U-Net (DHAU-Net). We designed a new Double Hybrid Attention structure consisting of dual-parallel hybrid attention modules to replace the skip connections in U-Net, which can eliminate redundant information interference and enhances the collection and utilization of important shallow features. Comprehensive experiments on the Massachusetts remote sensing building dataset and the Inria aerial image labeling dataset demonstrate that our proposed method achieves effective pixel-level building segmentation in urban remote sensing images by eliminating redundant information interference and making full use of shallow features, and improves the segmentation performance without significant time costs (approximately 15%). The evaluation metrics reveal significant results, with an accuracy rate of 0.9808, precision reaching 0.9300, an F1 score of 0.9112, a mean intersection over union (mIoU) of 0.9088, and a recall rate of 0.8932.

In the present paper, we investigate a generalized differential mixed quasi-variational inequality consisting of a system of an ordinary differential equation and a generalized mixed quasi-variational inequality. By using an important result concerning the measurable selection, we prove the existence of Caratheodory weak solution to ´ the generalized differential mixed quasi-variational inequality. Then, with the existence result, we establish two stability results for the generalized differential mixed quasi-variational inequality under different conditions, i.e., upper semicontinuity and lower semicontinuity of the Caratheodory weak solution with respect to the ´ parameter, which is a perturbation of some mappings in the generalized mixed quasi-variational inequality.