• Abstract

We propose a novel first-order non-convex model for the fusion of infrared and visible images. It maintains thermal radiation information by ensuring that the fused image has similar pixel intensities as the infrared image, and it preserves the appearance information, including the edges and texture of the source images, by enforcing similar gray gradients and pixel intensities as the visible image. Our model could effectively reduce the staircase effect and enhance the preservation of sharp edges. The maximum-minimum principle of the model with Neumann boundary condition is discussed and the existence of a minimizer of our model in $W^{1,2}(Ω)$ is also proved. We employ the augmented Lagrangian method (ALM) to design a fast algorithm to minimize the proposed model and establish the convergence analysis of the proposed algorithm. Numerical experiments are conducted to showcase the distinctive features of the model and to provide a comparison with other image fusion techniques.

• General Summary

• Abstract

Physics-Informed Neural Networks (PINNs) encounter challenges in dealing with imbalanced training losses, especially when there are sample points with extremely high losses. This can make the optimization process unstable, making it challenging to find the correct descent direction during training. In this paper, we propose a progressive learning approach based on anomaly points awareness to improve the optimization process of PINNs. Our approach comprises two primary steps: the awareness of anomaly data points and the update of training set. Anomaly points are identified by utilizing an upper bound calculated from the mean and standard deviation of the feedforward losses of all training data. In the absence of anomalies, the parameters of the PINN are optimized using the default training data; however, once anomalies are detected, a progressive exclusion method aligned with the network learning pattern is introduced to exclude potentially unfavorable data points from the training set. In addition, intermittent detection is employed, rather than performing anomaly detection in each iteration, to balance performance and efficiency. Extensive experimental results demonstrate that the proposed method leads to substantial improvement in approximation accuracy when solving typical benchmark partial differential equations. The code is accessible at https://github.com/JcLimath/Anomaly-Aware-PINN.

• General Summary

• Abstract

Radial basis function generated finite-difference (RBF-FD) methods have recently gained popularity due to their flexibility with irregular node distributions. However, the convergence theories in the literature, when applied to nonuniform node distributions, require shrinking fill distance and do not take advantage of areas with high data density. Non-adaptive approach using same stencil size and degree of appended polynomial will have higher local accuracy at high density region, but has no effect on the overall order of convergence and could be a waste of computational power. This work proposes an adaptive RBF-FD method that utilizes the local data density to achieve a desirable order accuracy. By performing polynomial refinement and using adaptive stencil size based on data density, the adaptive RBF-FD method yields differentiation matrices with higher sparsity while achieving the same user-specified convergence order for nonuniform point distributions. This allows the method to better leverage regions with higher node density, maintaining both accuracy and efficiency compared to standard non-adaptive RBF-FD methods.

• General Summary

• Abstract

Remote sensing images (RSIs) encompass abundant spatial and spectral/temporal information, finding wide applications in various domains. However, during image acquisition and transmission, RSI often encounter noise interference, which adversely affects the accuracy of subsequent applications. To address this issue, this paper proposes a novel non-local fully connected tensor network (NLFCTN) decomposition algorithm for denoising RSI, aiming to fully exploit their global correlation and non-local self-similarity (NSS) characteristics. FCTN, as a recently developed tensor decomposition technique, exhibits remarkable capability in capturing global correlations and minimizing information loss. In addition, we introduce an efficient algorithm based on proximal alternating minimization (PAM) to efficiently solve the model and prove the convergence. The effectiveness of the proposed method is validated through denoising experiments on both simulated and real RSI data, employing objective evaluation metrics and subjective visual assessments. The results of the experiment show that the proposed method outperforms other RSI denoising techniques in terms of denoising performance.

• General Summary