3D Gaussian Splatting (3DGS) has revolutionized novel view synthesis with real-time rendering and high-quality reconstruction. However, its performance degrades under varying scales, causing aliasing and dilation artifacts. To address these challenges, we introduce Msa-Splatting, an enhanced adaptive Gaussian splatting method designed for high-fidelity multi-scale novel view synthesis. Our approach reimagines the Gaussian adaptive control process with a novel multi-fold splitting and cloning mechanism, which optimizes Gaussian properties and reduces spurious artifacts by halving the densification frequency. We further mitigate aliasing in scaled-down renderings with a weighted alpha blending sampling technique, ensuring accurate representation of high-frequency details. To eliminate scale-mismatch artifacts, we introduce 2D variable dilation Gaussians, which dynamically adjust dilation based on the rendering scale. Msa-Splatting significantly enhances the fidelity and adaptability of Gaussian-based rendering, achieving state-of-the-art performance in multi-scale novel view synthesis. Extensive quantitative and qualitative evaluations demonstrate the efficacy of our approach, showcasing its ability to produce perceptually superior renderings with reduced artifacts across varying scales, thus establishing a robust framework for future advancements in scalable rendering technologies.

Abstract. Deep learning-based image denoising models demonstrate remarkable performance, but their lack of robustness analysis remains a significant concern. A major issue is that these models are susceptible to adversarial attacks, where small, carefully crafted perturbations to input data can cause them to fail. Surprisingly, perturbations specifically crafted for one model can easily transfer across various models, including convolutional neural networks, transformers, unfolding models, and plug-and-play models, leading to failures in those models as well. Such high adversarial transferability is not observed in classification models. We analyze the possible underlying reasons behind the high adversarial transferability through a series of hypotheses and validation experiments. By characterizing the manifolds of Gaussian noise and adversarial perturbations using the concept of a typical set and the asymptotic equipartition property, we prove that adversarial samples deviate slightly from the typical set of the original input distribution, causing the models to fail. Based on these insights, we propose a novel adversarial defense method: the out-of-distribution typical set sampling (TSS) training strategy. TSS training strategy not only significantly enhances the model’s robustness but also marginally improves denoising performance compared to the original model.

The rapid development of deep learning has significantly advanced Synthetic Aperture Radar (SAR) despeckling techniques. However, as the uncertainty and vulnerability of the network structure is ignited by the fuse of adversarial attacks, its authenticity and widespread applicability are subsequently drawn into question. This study examines the robustness and performance of deep learning-based image despeckling models under a denoising-PGD adversarial attack. Furthermore, we investigate the impact of varying feature extraction approaches on model performance, with the goal of providing reliable guidelines for model training.

Pansharpening, as a widely used technique, plays a crucial role in the field of remote sensing image processing. In this letter, we propose a novel structure tensor-driven block-based variational pansharpening model with adaptive coefficients. First, a structure descriptor derived from the structure tensor of the panchromatic (PAN) image is integrated into the regularization term. It can not only effectively capture the edge information of the PAN image, but also contribute to better preserving the spatial details of the PAN image in the fused product. Furthermore, we partition the degraded PAN image and the upsampled multispectral (MS) image into several equal-sized blocks and utilize a regression-based approach to calculate the adaptive coefficients within each block. As a result, a more accurate constraint relationship between the PAN image and the high-resolution MS image can be established. Then, by incorporating the regularization term and the fidelity term, the proposed variational model is formulated. An explicit finite difference scheme is employed to efficiently solve the gradient descent flow of the proposed model. Experiments conducted on different datasets demonstrate that the proposed pansharpening method outperforms the state-of-the-art techniques in both qualitative and quantitative evaluations.

Various kinds of heart diseases pose a serious threat to human health. To effectively treat and prevent these diseases, accurate segmentation of the entire heart structure is crucial for medical research and application. At present, the solution to this problem still needs to rely on a lot of manpower. Not only is this time-consuming, but accuracy is sometimes difficult to guarantee. In the deep learning methods for medical image segmentation, large labeled images are difficult to obtain. Typically, the large databases have several thousand images, of which only a few hundred have been annotated, and the number of individual patients is even smaller. In this article, we focus on a small part of the dataset to minimize the cost of manual labeling and maximize the accurate segmentation results. The small part of the dataset contains more representative and informative images, avoiding doctors to repeatedly label images with similar information. We proposed a balanced distribution active learning (BDAL) framework for MRI cardiac multistructures segmentation based on reinforcement learning. The deep Q-network framework can learn an effective policy to select some informative and representative images to be labeled from a large number of the unlabeled dataset. We consider the shape features of images and the balance of different class distributions to build new state and action representation, which can help the agent to identify informative and representative images for annotation. Our BDAL method provides an agent to improve the ability of AL to select images to improve the accuracy of segmentation. Moreover, experiments and results show that our BDAL method significantly outperforms all baselines and other AL-based methods under the same amount of annotation budget on MRI cardiac multistructures segmentation in datasets$\mathbf {ACDC}$and$\mathbf {M \& Ms}$.

Recently, deep learning (DL) is widely used to detect physical phenomena and has obtained encouraging results. Several works have shown that it can learn quantum phenomenon. Subsequently, quantum machine learning (QML) has been paid more attention by academia and industry. Quantum drift-diffusion (QDD) is a commonplace physical phenomenon, which is a macroscopic description of electrons and holes in a semiconductor. They are commonly used to attain an understanding of the property of semiconductor devices in physics and engineering. We are motivated by the relaxation-time limit from the quantum-Navier-Stokes-Poisson system (QNSP) to the QDD equation and the existence of finite energy weak solutions to the QDD equation has been proved. Therefore, in this work, the quantum drift-diffusion learning neural network (QDDLNN) is proposed to investigate the quantum drift phenomena from limited observations. Furthermore, a piece of numerical evidence is found that the NNs can describe quantum transport phenomena by simulating the quantum confinement transport equation-quantum Navier-Stokes equation.

Under the background of the wanton spread of the coronavirus disease (COVID-19), the pandemic is changing and hitting lives all over the world. Fortunately, Spatio-temporal processes bear essential importance in many applied scientific fields. And the disease pandemic can be viewed as Spatio-temporal dynamics processes. Generally, partial differential equations (PDEs) have been widely used to investigate interfacial dynamic processes. In this work, we use a physical-constraint neural network learning the Spatio-temporal mean-field dynamics to control the propagation of epidemics. Also, we use the AI-based algorithm physical-constraint learning (PCL) to solve the minimization problems of the mean-field game (MFG) and control (MFC) problems instead of the traditional computational method. In PCL, the PDEs are encoded into the loss function, where partial derivatives can be obtained through automatic differentiation (AD). We demonstrate how they can be applied in practice by considering the problem of controlling the propagation of epidemics. Numerical experiments on different input data are implemented to demonstrate the effectiveness and superiority of the proposed models compared to the state-of-the-art approach and illustrate how to separate the infected patients in a spatial domain effectively.

Magnetic resonance (MR) images have great importance to assist doctors in diagnosing diseases, however, the long MR images scan duration remains the primary obstacle in clinical medicine. Compressed sensing reconstructed technique in MR imaging (CS‐MRI) makes it possible to reconstruct a faithful MR image from very few measurements data, which helps to reduce the scan time. The purpose of this study is to improve the accuracy and efficiency of the CS‐MRI. The authors propose a fast compressed sensing reconstruction model for MR images that can alleviate the aliasing artefacts that come from the reconstruction process by jointly minimising a total variation term, a fitting data term and a median filter term. Moreover, they accelerate the proposed algorithm by applying the split Bregman method to solve the proposed model. Then, the proposed model is applied to reconstruct a large number of MR images. They also compare the performance of the proposed model with another model. It can be observed from the experimental results that the proposed model has shown higher precision in reconstructing image quality and much more efficiency than the other one. Additionally, they also give a discussion on how to choose proper parameters in the proposed model to obtain more satisfactory results.

Multiplicative noise removal problems have attracted much attention in recent years. Unlike additive noise removal problems, multiplicative noise destroys almost all information of the original image, especially for texture images. In this paper, a fractional-order nonlinear diffusion model is proposed to denoise the texture images corrupted by multiplicative noise. In the model, a gray level indicator is introduced to remove multiplicative noise and preserve structure details for texture images. By virtue of the discrete Fourier transform, the model is solved by an iterative scheme in the frequency domain. Then an algorithm in the spatial domain is developed based on the definition of the Grünwald--Letnikov fractional-order derivative. Inspired by the discrepancy principle used for additive noise, we develop a new stopping criterion based on the mean and variance of the noise. Numerical examples are presented to demonstrate the effectiveness and efficiency of the proposed method. Experimental results show that the proposed model can handle multiplicative noise removal and texture preservation quite well.

This paper considers colorization-based image compression in RGB color space. In compression, we store only the compressed luminance component of the original color image and a few representative pixels extracted from the original color image. In decompression, by explicitly introducing the relation between the luminance component and the original color image into diffusion equations, a linear reaction-diffusion system with Perona--Malik type diffusion coefficient is proposed to reconstruct R, G, and B channels simultaneously. The Perona--Malik type diffusion coefficient is a function of the luminance component and leads to interior degenerations, in general. It yields anisotropic smoothing in the restored color image and constrains the geometry of the restored image to follow the geometry of the luminance component. The existence and uniqueness of solutions for the proposed system with a specific class of diffusion coefficients are proved in a weighted Sobolev space. The selection of representative pixels has a big impact on reconstruction results. We also propose a local-optimal strategy that splits the original color image into a series of different size subimages and searches the optimal representative pixel in each subimage. Comparisons with recent colorization-based image compression methods, as well as transform-based JPEG and JPEG2000 standards, are performed to show the potential for successful compression applications of the proposed method.

Multiplicative noise removal is a challenging task in image processing. Inspired by the impressive performance of nonlinear diffusion models in additive noise removal, we address this problem in the view of nonlinear diffusion equation theories rather than the traditional variation methods. We develop a nonlinear diffusion filter denoising framework, which considers not only the information of the gradient of the image, but also the information of gray levels of the image. Furthermore, under this framework, we propose a doubly degenerate diffusion model for multiplicative noise removal, which is analyzed with respect to some of its properties and behavior in denoising process. In numerical aspects, we present an efficient scheme which uses a stabilization by fast explicit diffusion for the implementation of the multiplicative noise removal model. Finally, the experimental results illustrate effectiveness and efficiency of the proposed model.

This paper presents an improved active contour model for fast multiphase image segmentation based on the piecewise constant Vese-Chan model and the split Bregman method. We first define a new energy functional by applying the globally convex image segmentation technique to the Vese-Chan energy functional and incorporating the edge information with a non-negative edge detector function. Then we apply the split Bregman method to fast minimize the new energy functional. The efficiency of the improved model compared with the Vese-Chan model is demonstrated by experimental results. This is the main advantage of our improved model over the Vese-Chan model.

In this paper, we propose an efficient active contour model for multiphase image segmentation in a variational level set formulation. By incorporating the globally convex segmentation idea and the split Bregman method into the multiphase formulation of the local and global intensity fitting energy model, our new model improved the original local and global intensity fitting energy model in the following aspects. First, we propose a new energy functional using the globally convex segmentation method to guarantee fast convergence. Second, we incorporate information from the edge into the energy functional by using a non-negative edge detector function to detect boundaries more easily. Third, instead of a constant value to control the influence of the local and global intensity fitting terms, we use a weight function varying with the locations of the image to balance the weights between the local and the global fitting terms dynamically. Lastly, the special structure of our energy functional enables us to apply the split Bregman method to minimize the energy much more efficiently. We have applied our model to synthetic images and real brain MR images with promising results. Experimental results demonstrate the efficiency and superiority of our model.

This paper introduces a class of adaptive Perona-Malik (PM) diffusion, which combines the PM equation with the heat equation. The PM equation provides a potential algorithm for image segmentation, noise removal, edge detection, and image enhancement. However, the defect of traditional PM model is tending to cause the staircase effect and create new features in the processed image. Utilizing the edge indicator as a variable exponent, we can adaptively control the diffusion mode, which alternates between PM diffusion and Gaussian smoothing in accordance with the image feature. Computer experiments indicate that the present algorithm is very efficient for edge detection and noise removal.