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Wen Lu

Publications and source records attributed to Wen Lu.

At least 37 records · Page 2Linked to original sources

Bergman kernels and equidistribution for sequences of line bundles on Kähler manifolds

Given a sequence of positive Hermitian holomorphic line bundles $(L_p,h_p)$ on a Kähler manifold $X$, we establish the asymptotic expansion of the Bergman kernel of the space of global holomorphic sections of $L_p$, under a natural convergence assumption on the sequence of curvatures $c_1(L_p,h_p)$. We then apply this to study the asymptotic distribution of common zeros of random sequences of $m$-tuples of sections of $L_p$ as $p\to\infty$.

math.CV↗

Optimal convergence speed of Bergman metrics on symplectic manifolds

It is known that a compact symplectic manifold endowed with a prequantum line bundle can be embedded in the projective space generated by the eigensections of low energy of the Bochner Laplacian acting on high $p$-tensor powers of the prequantum line bundle. We show that the Fubini-Study forms induced by these embeddings converge at speed rate $1/p^{2}$ to the symplectic form. This result implies the generalization to the almost-Kähler case of the lower bounds on the Calabi functional given by Donaldson for Kähler manifolds, as shown by Lejmi and Keller.

math.DG↗

Interpretable Detail-Fidelity Attention Network for Single Image Super-Resolution

Benefiting from the strong capabilities of deep CNNs for feature representation and nonlinear mapping, deep-learning-based methods have achieved excellent performance in single image super-resolution. However, most existing SR methods depend on the high capacity of networks which is initially designed for visual recognition, and rarely consider the initial intention of super-resolution for detail fidelity. Aiming at pursuing this intention, there are two challenging issues to be solved: (1) learning appropriate operators which is adaptive to the diverse characteristics of smoothes and details; (2) improving the ability of model to preserve the low-frequency smoothes and reconstruct the high-frequency details. To solve them, we propose a purposeful and interpretable detail-fidelity attention network to progressively process these smoothes and details in divide-and-conquer manner, which is a novel and specific prospect of image super-resolution for the purpose on improving the detail fidelity, instead of blindly designing or employing the deep CNNs architectures for merely feature representation in local receptive fields. Particularly, we propose a Hessian filtering for interpretable feature representation which is high-profile for detail inference, a dilated encoder-decoder and a distribution alignment cell to improve the inferred Hessian features in morphological manner and statistical manner respectively. Extensive experiments demonstrate that the proposed methods achieve superior performances over the state-of-the-art methods quantitatively and qualitatively. Code is available at https://github.com/YuanfeiHuang/DeFiAN.

cs.CV↗

AIM 2020 Challenge on Efficient Super-Resolution: Methods and Results

This paper reviews the AIM 2020 challenge on efficient single image super-resolution with focus on the proposed solutions and results. The challenge task was to super-resolve an input image with a magnification factor x4 based on a set of prior examples of low and corresponding high resolution images. The goal is to devise a network that reduces one or several aspects such as runtime, parameter count, FLOPs, activations, and memory consumption while at least maintaining PSNR of MSRResNet. The track had 150 registered participants, and 25 teams submitted the final results. They gauge the state-of-the-art in efficient single image super-resolution.

eess.IV↗

NTIRE 2020 Challenge on Perceptual Extreme Super-Resolution: Methods and Results

This paper reviews the NTIRE 2020 challenge on perceptual extreme super-resolution with focus on proposed solutions and results. The challenge task was to super-resolve an input image with a magnification factor 16 based on a set of prior examples of low and corresponding high resolution images. The goal is to obtain a network design capable to produce high resolution results with the best perceptual quality and similar to the ground truth. The track had 280 registered participants, and 19 teams submitted the final results. They gauge the state-of-the-art in single image super-resolution.

eess.IV↗

AIM 2019 Challenge on Real-World Image Super-Resolution: Methods and Results

This paper reviews the AIM 2019 challenge on real world super-resolution. It focuses on the participating methods and final results. The challenge addresses the real world setting, where paired true high and low-resolution images are unavailable. For training, only one set of source input images is therefore provided in the challenge. In Track 1: Source Domain the aim is to super-resolve such images while preserving the low level image characteristics of the source input domain. In Track 2: Target Domain a set of high-quality images is also provided for training, that defines the output domain and desired quality of the super-resolved images. To allow for quantitative evaluation, the source input images in both tracks are constructed using artificial, but realistic, image degradations. The challenge is the first of its kind, aiming to advance the state-of-the-art and provide a standard benchmark for this newly emerging task. In total 7 teams competed in the final testing phase, demonstrating new and innovative solutions to the problem.

cs.CV↗

Distilling with Residual Network for Single Image Super Resolution

Recently, the deep convolutional neural network (CNN) has made remarkable progress in single image super resolution(SISR). However, blindly using the residual structure and dense structure to extract features from LR images, can cause the network to be bloated and difficult to train. To address these problems, we propose a simple and efficient distilling with residual network(DRN) for SISR. In detail, we propose residual distilling block(RDB) containing two branches, while one branch performs a residual operation and the other branch distills effective information. To further improve efficiency, we design residual distilling group(RDG) by stacking some RDBs and one long skip connection, which can effectively extract local features and fuse them with global features. These efficient features beneficially contribute to image reconstruction. Experiments on benchmark datasets demonstrate that our DRN is superior to the state-of-the-art methods, specifically has a better trade-off between performance and model size.

cs.CV↗

A Gated Peripheral-Foveal Convolutional Neural Network for Unified Image Aesthetic Prediction

Learning fine-grained details is a key issue in image aesthetic assessment. Most of the previous methods extract the fine-grained details via random cropping strategy, which may undermine the integrity of semantic information. Extensive studies show that humans perceive fine-grained details with a mixture of foveal vision and peripheral vision. Fovea has the highest possible visual acuity and is responsible for seeing the details. The peripheral vision is used for perceiving the broad spatial scene and selecting the attended regions for the fovea. Inspired by these observations, we propose a Gated Peripheral-Foveal Convolutional Neural Network (GPF-CNN). It is a dedicated double-subnet neural network, i.e. a peripheral subnet and a foveal subnet. The former aims to mimic the functions of peripheral vision to encode the holistic information and provide the attended regions. The latter aims to extract fine-grained features on these key regions. Considering that the peripheral vision and foveal vision play different roles in processing different visual stimuli, we further employ a gated information fusion (GIF) network to weight their contributions. The weights are determined through the fully connected layers followed by a sigmoid function. We conduct comprehensive experiments on the standard AVA and Photo.net datasets for unified aesthetic prediction tasks: (i) aesthetic quality classification; (ii) aesthetic score regression; and (iii) aesthetic score distribution prediction. The experimental results demonstrate the effectiveness of the proposed method.

cs.CV↗

Donaldson's $Q$-operators for symplectic manifolds

We prove an estimate for Donaldson's $Q$-operator on a prequantized compact symplectic manifold. This estimate is an ingredient in the recent result of Keller and Lejmi about a symplectic generalization of Donaldson's lower bound for the $L^2$-norm of the Hermitian scalar curvature.

math.DG↗

Backward stochastic Volterra integral equations associated with a Levy process and applications

In this paper, we study a class of backward stochastic Volterra integral equations driven by Teugels martingales associated with an independent Lévy process and an independent Brownian motion (BSVIELs). We prove the existence and uniqueness as well as stability of the adapted M-solutions for those equations. Moreover, a duality principle and then a comparison theorem are established. As an application, we derive a class of dynamic risk measures by means of M-solutions of certain BSVIELs.

math.PR↗

Mean-field backward stochastic differential equations on Markov chains

In this paper, we deal with a class of mean-field backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We obtain the existence and uniqueness theorem and a comparison theorem for solutions of one-dimensional mean-field BSDEs under Lipschitz condition.

math.PR↗

Mean-field backward stochastic differential equations with subdifferrential operator and its applications

In this paper, we deal with a class of mean-field backward stochastic differential equations with subdifferrential operator corresponding to a lower semi-continuous convex function. By means of Yosida approximation, the existence and uniqueness of the solution is established. As an application, we give a probability interpretation for the viscosity solutions of a class of nonlocal parabolic variational inequalities.

math.PR↗

Multivalued backward doubly stochastic differential equations with time delayed coefficients

In this paper, we deal with a class of multivalued backward doubly stochastic differential equations with time delayed coefficients. Based on a slight extension of the existence and uniqueness of solutions for backward doubly stochastic differential equations with time delayed coefficients, we establish the existence and uniqueness of solutions for these equations by means of Yosida approximation.

math.PR↗

A Thom-Smale-Witten theorem on manifolds with boundary

Given a smooth compact manifold with boundary, we show that the subcomplex of the deformed de Rham complex consisting of eigenspaces of small eigenvalues of the Witten Laplacian is canonically isomorphic to the Thom-Smale complex constructed by Laudenbach. Our proof is based on Bismut-Lebeau's analytic localization techniques. As a by-product, we obtain Morse inequalities for manifolds with boundary.

math.DG↗

Equivariant Morse inequalities and applications

In this paper, we prove equivariant Morse inequalities via Bismut-Lebeau's analytic localization techniques. As an application, we obtain Morse inequalities on compact manifold with nonempty boundary by applying equivariant Morse inequalities to the doubling manifold.

math.DG↗