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Exploring and modeling rain generation mechanism is critical for augmenting paired data to ease training of rainy image processing models. Against this task, this study proposes a novel deep learning based rain generator, which fully takes the physical generation mechanism underlying rains into consideration and well encodes the learning of the fundamental rain factors (i.e., shape, orientation, length, width and sparsity) explicitly into the deep network. Its significance lies in that the generator not only elaborately design essential elements of the rain to simulate expected rains, like conventional artificial strategies, but also finely adapt to complicated and diverse practical rainy images, like deep learning methods. By rationally adopting filter parameterization technique, we first time achieve a deep network that is finely controllable with respect to rain factors and able to learn the distribution of these factors purely from data. Our unpaired generation experiments demonstrate that the rain generated by the proposed rain generator is not only of higher quality, but also more effective for deraining and downstream tasks compared to current state-of-the-art rain generation methods. Besides, the paired data augmentation experiments, including both in-distribution and out-of-distribution (OOD), further validate the diversity of samples generated by our model for in-distribution deraining and OOD generalization tasks.

Recently, it has been found that a $Q$-ball can amplify waves incident upon it, due to rotation in the internal space and the interaction of the two modes in the complex scalar field. While the spherically symmetric 3D case has been investigated previously, here we explore the 3D axi-symmetric case, which is numerically much more challenging. The difficulty comes because a partial wave expansion is needed, and the different partial waves can not be separated, for either the background spinning Q-ball solution or the perturbative scattering on top of it. A relaxation method and a high dimensional shooting method are applied to compute the Q-ball solutions and the amplification factors respectively. We also classify the behavior of the amplification factors and we discuss their bounds and the superradiance criteria., Comment: 20 pages, 14 figures

The deep unfolding approach has attracted significant attention in computer vision tasks, which well connects conventional image processing modeling manners with more recent deep learning techniques. Specifically, by establishing a direct correspondence between algorithm operators at each implementation step and network modules within each layer, one can rationally construct an almost ``white box'' network architecture with high interpretability. In this architecture, only the predefined component of the proximal operator, known as a proximal network, needs manual configuration, enabling the network to automatically extract intrinsic image priors in a data-driven manner. In current deep unfolding methods, such a proximal network is generally designed as a CNN architecture, whose necessity has been proven by a recent theory. That is, CNN structure substantially delivers the translational invariant image prior, which is the most universally possessed structural prior across various types of images. However, standard CNN-based proximal networks have essential limitations in capturing the rotation symmetry prior, another universal structural prior underlying general images. This leaves a large room for further performance improvement in deep unfolding approaches. To address this issue, this study makes efforts to suggest a high-accuracy rotation equivariant proximal network that effectively embeds rotation symmetry priors into the deep unfolding framework. Especially, we deduce, for the first time, the theoretical equivariant error for such a designed proximal network with arbitrary layers under arbitrary rotation degrees. This analysis should be the most refined theoretical conclusion for such error evaluation to date and is also indispensable for supporting the rationale behind such networks with intrinsic interpretability requirements.

The physics of individual Q-balls and interactions between multiple Q-balls are well-studied in classical numerical simulations. Interesting properties and phenomena have been discovered, involving stability, forces, collisions and swapping of charge between different components of multi-Q-ball systems. We investigate these phenomena in quantum field theory, including quantum corrections to leading order in a 2PI coupling expansion, the inhomogeneous Hartree approximation. The presence of quantum modes and new decay channels allows the mean-field Q-ball to exchange charge with the quantum modes, and also alters the charge swapping frequencies of the composite Q-balls. It is also observed that the periodic exchanges between the mean-field and quantum modes tend to be quenched by collisions between Q-balls. We illustrate how the classical limit arises through a scaling of the Q-ball potential, making quantum corrections negligible for large-amplitude Q-balls., Comment: 29 pages, 18 figures

With translation equivariance, convolution neural networks (CNNs) have achieved great success in retinal vessel segmentation. However, some other symmetries of the vascular morphology are not characterized by CNNs, such as rotation and scale symmetries. To embed more equivariance into CNNs and achieve the accuracy requirement for retinal vessel segmentation, we construct a novel convolution operator (FRS-Conv), which is Fourier parameterized and equivariant to rotation and scaling. Specifically, we first adopt a new parameterization scheme, which enables convolutional filters to arbitrarily perform transformations with high accuracy. Secondly, we derive the formulations for the rotation and scale equivariant convolution mapping. Finally, we construct FRS-Conv following the proposed formulations and replace the traditional convolution filters in U-Net and Iter-Net with FRS-Conv (FRS-Nets). We faithfully reproduce all compared methods and conduct comprehensive experiments on three public datasets under both in-dataset and cross-dataset settings. With merely 13.9% parameters of corresponding baselines, FRS-Nets have achieved state-of-the-art performance and significantly outperform all compared methods. It demonstrates the remarkable accuracy, generalization, and clinical application potential of FRS-Nets.

Recently, it has been realized that in some systems internal space rotation can induce energy amplification for scattering waves, similar to rotation in real space. Particularly, it has been shown that energy extraction is possible for a Q-ball, a stationary non-topological soliton that is coherently rotating in its field space. In this paper, we generalize the analysis to the case of boson stars, and show that the same energy extraction mechanism still works for boson stars., Comment: 10 pages, 6 figures; v2: refs added and clarified

During X-ray computed tomography (CT) scanning, metallic implants carrying with patients often lead to adverse artifacts in the captured CT images and then impair the clinical treatment. Against this metal artifact reduction (MAR) task, the existing deep-learning-based methods have gained promising reconstruction performance. Nevertheless, there is still some room for further improvement of MAR performance and generalization ability, since some important prior knowledge underlying this specific task has not been fully exploited. Hereby, in this paper, we carefully analyze the characteristics of metal artifacts and propose an orientation-shared convolution representation strategy to adapt the physical prior structures of artifacts, i.e., rotationally symmetrical streaking patterns. The proposed method rationally adopts Fourier-series-expansion-based filter parametrization in artifact modeling, which can better separate artifacts from anatomical tissues and boost the model generalizability. Comprehensive experiments executed on synthesized and clinical datasets show the superiority of our method in detail preservation beyond the current representative MAR methods. Code will be available at \url{https://github.com/hongwang01/OSCNet}

Q-balls are non-topological solitons that coherently rotate in field space. We show that these coherent rotations can induce superradiance for scattering waves, thanks to the fact that the scattering involves two coupled modes. Despite the conservation of the particle number in the scattering, the mismatch between the frequencies of the two modes allows for the enhancement of the energy and angular momentum of incident waves. When the Q-ball spins in real space, additional rotational superradiance is also possible, which can further boost the enhancements. We identify the criteria for the energy and angular momentum superradiance to occur., Comment: 9 pages, 12 figures. Published version in PRL

Two types of excited oscillons are investigated. We first focus on spherical symmetry and find that there are a tower of spherical oscillons with higher energies. Despite having multiple approximate "nodes" in their energy density profiles, these oscillons are long-lived. We find that during the lifetime of a highly excited oscillon it will cascade down all the lower energy levels before its disintegration. We also point out the existence of excited oscillons with higher approximate multipoles, which generally have shorter lifespans than the spherical ones. Apart from performing nonlinear simulations with absorbing boundary conditions, we also apply a perturbative method to analyze some features of these excited oscillons., Comment: 27 pages, 17 figures

Channel state information (CSI) plays a critical role in achieving the potential benefits of massive multiple input multiple output (MIMO) systems. In frequency division duplex (FDD) massive MIMO systems, the base station (BS) relies on sustained and accurate CSI feedback from the users. However, due to the large number of antennas and users being served in massive MIMO systems, feedback overhead can become a bottleneck. In this paper, we propose a model-driven deep learning method for CSI feedback, called learnable optimization and regularization algorithm (LORA). Instead of using l1-norm as the regularization term, a learnable regularization module is introduced in LORA to automatically adapt to the characteristics of CSI. We unfold the conventional iterative shrinkage-thresholding algorithm (ISTA) to a neural network and learn both the optimization process and regularization term by end-toend training. We show that LORA improves the CSI feedback accuracy and speed. Besides, a novel learnable quantization method and the corresponding training scheme are proposed, and it is shown that LORA can operate successfully at different bit rates, providing flexibility in terms of the CSI feedback overhead. Various realistic scenarios are considered to demonstrate the effectiveness and robustness of LORA through numerical simulations.

Although current deep learning-based methods have gained promising performance in the blind single image super-resolution (SISR) task, most of them mainly focus on heuristically constructing diverse network architectures and put less emphasis on the explicit embedding of the physical generation mechanism between blur kernels and high-resolution (HR) images. To alleviate this issue, we propose a model-driven deep neural network, called KXNet, for blind SISR. Specifically, to solve the classical SISR model, we propose a simple-yet-effective iterative algorithm. Then by unfolding the involved iterative steps into the corresponding network module, we naturally construct the KXNet. The main specificity of the proposed KXNet is that the entire learning process is fully and explicitly integrated with the inherent physical mechanism underlying this SISR task. Thus, the learned blur kernel has clear physical patterns and the mutually iterative process between blur kernel and HR image can soundly guide the KXNet to be evolved in the right direction. Extensive experiments on synthetic and real data finely demonstrate the superior accuracy and generality of our method beyond the current representative state-of-the-art blind SISR methods. Code is available at: https://github.com/jiahong-fu/KXNet., Comment: Accepted by ECCV2022

Deep generative models have achieved tremendous success in designing novel drug molecules in recent years. A new thread of works have shown the great potential in advancing the specificity and success rate of in silico drug design by considering the structure of protein pockets. This setting posts fundamental computational challenges in sampling new chemical compounds that could satisfy multiple geometrical constraints imposed by pockets. Previous sampling algorithms either sample in the graph space or only consider the 3D coordinates of atoms while ignoring other detailed chemical structures such as bond types and functional groups. To address the challenge, we develop Pocket2Mol, an E(3)-equivariant generative network composed of two modules: 1) a new graph neural network capturing both spatial and bonding relationships between atoms of the binding pockets and 2) a new efficient algorithm which samples new drug candidates conditioned on the pocket representations from a tractable distribution without relying on MCMC. Experimental results demonstrate that molecules sampled from Pocket2Mol achieve significantly better binding affinity and other drug properties such as druglikeness and synthetic accessibility., Comment: ICML 2022 accepted

We study charge-swapping Q-balls, a kind of composite Q-ball where positive and negative charges co-exist and swap with time, in models with a logarithmic potential that arises naturally in supersymmetric extensions of the Standard Model. We show that charge-swapping Q-balls can be copiously generated in the Affleck-Dine fragmentation process in the early universe. We find that the charge-swapping Q-balls with the logarithmic potential are extremely stable. By performing long time, parallelized lattice simulations with absorbing boundary conditions, we find that the lifetimes of such objects with low multipoles are at least $4.6 \times 10^5/m$ in 3+1D and $2.5 \times 10^7/m$ in 2+1D, where $m$ is the mass scale of the scalar field. We also chart the attractor basin of the initial conditions to form these charge-swapping Q-balls., Comment: 23 pages, 15 figures

Guided image super-resolution (GISR) aims to obtain a high-resolution (HR) target image by enhancing the spatial resolution of a low-resolution (LR) target image under the guidance of a HR image. However, previous model-based methods mainly takes the entire image as a whole, and assume the prior distribution between the HR target image and the HR guidance image, simply ignoring many non-local common characteristics between them. To alleviate this issue, we firstly propose a maximal a posterior (MAP) estimation model for GISR with two types of prior on the HR target image, i.e., local implicit prior and global implicit prior. The local implicit prior aims to model the complex relationship between the HR target image and the HR guidance image from a local perspective, and the global implicit prior considers the non-local auto-regression property between the two images from a global perspective. Secondly, we design a novel alternating optimization algorithm to solve this model for GISR. The algorithm is in a concise framework that facilitates to be replicated into commonly used deep network structures. Thirdly, to reduce the information loss across iterative stages, the persistent memory mechanism is introduced to augment the information representation by exploiting the Long short-term memory unit (LSTM) in the image and feature spaces. In this way, a deep network with certain interpretation and high representation ability is built. Extensive experimental results validate the superiority of our method on a variety of GISR tasks, including Pan-sharpening, depth image super-resolution, and MR image super-resolution., Comment: 24 pages, 16 figures

Motivated by their recent advances, deep learning techniques have been widely applied to low-light image enhancement (LIE) problem. Among which, Retinex theory based ones, mostly following a decomposition-adjustment pipeline, have taken an important place due to its physical interpretation and promising performance. However, current investigations on Retinex based deep learning are still not sufficient, ignoring many useful experiences from traditional methods. Besides, the adjustment step is either performed with simple image processing techniques, or by complicated networks, both of which are unsatisfactory in practice. To address these issues, we propose a new deep learning framework for the LIE problem. The proposed framework contains a decomposition network inspired by algorithm unrolling, and adjustment networks considering both global brightness and local brightness sensitivity. By virtue of algorithm unrolling, both implicit priors learned from data and explicit priors borrowed from traditional methods can be embedded in the network, facilitate to better decomposition. Meanwhile, the consideration of global and local brightness can guide designing simple yet effective network modules for adjustment. Besides, to avoid manually parameter tuning, we also propose a self-supervised fine-tuning strategy, which can always guarantee a promising performance. Experiments on a series of typical LIE datasets demonstrated the effectiveness of the proposed method, both quantitatively and visually, as compared with existing methods.