召集人：Tai   Xuecheng（Norwegian Research Center）、庞志峰（河南大学）、常慧宾（天津师范大学）、孔德兴（浙江大学）

时间：2024.09.29—2024.10.05

会议日程

报告题目、摘要和简介

（按姓氏首字母排序）

 Virtual Nodes based Heterogeneous Graph Convolutional Neural Network for Efficient Long-Range Information Aggregation

蔡佳

摘要：Heterogeneous Graph Neural Networks (HGNNs) have shown powerful performance on heterogeneous graph learning. However, existing heterogeneous graph related models may confront with three major challenges: (1) Predefined meta-paths are required to capture the semantic relations between nodes from different types; (2). Existing models have to stack too many layers to learn long-range dependencies; (3) Performance degradation and semantic confusion may happen with the growth of the network depth. In this talk, we introduce two models to deal with the above-mentioned challenges. Specifically, we develop an end-to-end Dense connected Heterogeneous Graph Convolutional Network to learn node representations (Dense-HGCN). Dense-HGCN computes the attention weights between different nodes and incorporates the information of previous layers into each layer’s aggregation process via a specific fuse function. Furthermore, we develop a Virtual Nodes based Heterogeneous Graph Convolutional Network (VN-HGCN), which uses virtual nodes to enhance the information flow in the graph. Virtual nodes are auxiliary nodes that are connected to all the nodes of a certain type in the graph, thus enabling efficient aggregation of long-range information across different types of nodes and edges. By modifying the graph structure with virtual nodes, VN-HGCN can aggregate the information of each node of a graph with 4 layers.

个人简介：蔡佳，广东财经大学，教授，博士生导师。2009年-2015年曾数次访问香港城市大学，2017年2月-2018年2月访问美国纽约州立大学奥尔巴尼分校。2013年2月-2016年12月获聘为广东财经大学“卓越青年教师”校长特聘教授，2019年6月破格晋升为教授，2019年12月入选广东省省级人才计划。现担任中国工业与应用数学学会大数据与人工智能专委会委员、金融科技与算法专委会常务委员，广东省计算数学学会常务理事，广东省计算机学会大数据专委会委员。已在国内外著名期刊《IEEE Transactions on Neural Networks and Learning Systems》，《Neural Networks》，《Neural Computation》,《Journal of Multivariate Analysis》，《Engineering Applications of Artificial Intelligence》，《Neurocomputing》, 《Cognitive Computation》，《中国科学》(中英文版)等发表SCI、EI 检索论文近 30 篇。主持和承担国家自科(青年，面上)、国家社科重点项目、国家统计局重点项目，广东省自然科学基金等合计20余项。(邮箱：jiacai1999@gdufe.edu.cn)

Region-based Min-Cut Geodesic Models for Image Segmentation

陈达

摘要：Geodesic models have been used for long to address the problems of image seg- mentation, where the features of interest, i.e, object boundaries, can be modeled as geodesic paths. As an important advantage, the geodesic model is capable of finding the global minimum of a well-designed curve energy, thus can avoid unexpected local minima. The solutions to the segmentation problems can be regarded as a way to find a simple closed curve globally minimizing the associated curve energy, done by solving the corresponding Hamiltonian-Jacobi-Bellman PDE using the efficient Fast Marching method. In contrast to finding the global minimum of a simplified curve energy that consists of edge-based features, we have recently established the relationship with the classical continuous min-cut problem, allowing to extend the geodesic model to cover region- and edge-based terms in conjunction with convexity and star convexity shape priors. By designing adequate geodesic metrics, we now are able to compute optimal paths according to various active contours terms, involving curvature penalization, region-based statistical term and shape prior constraints. We will present the mathematical background as well as concrete applications to biomedical and natural images. 

个人简介：陈达，齐鲁工业大学副研究员，硕士生导师，2017年获得法国巴黎文理研究大学的应用数学博士学位，2016年底至2019年3月在巴黎多芬纳大学和巴黎国立眼科医院从事博士后研究工作，2019年5月通过高层次人才引进计划全职加入山东省人工智能研究院，齐鲁工业大学（山东省科学院），并作为课题组负责人组建了图像智能分析团队，着力于解决图像分析和视觉计算领域存在的重点与难点问题。山东省优秀青年基金获得者，同时主持国家自然科学基金青年项目1项，作为骨干人员参与国家自然基金面上项目和国家重点研发计划项目各1项。共发表学术论文30余篇，其中以第一作者身份发表PNAS、TPAMI、IJCV、TIP等CCF-A类顶级期刊会议论文9篇，共申请授权发明专利20多项。(邮箱：dachen.cn@hotmail.com)

Multiscale approach for variational problem joint diffeomorphic image registration and intensity correction

韩欢

摘要：In real life problems, images may be affected by the imaging environment, such as varying illumination and noise during the process of imaging acquisition. This may lead to the local intensity distortion, which makes it meaningless to minimize the intensity difference in the traditional registration framework. To address this problem, we propose a variational model for joint image registration and intensity correction. Based on this model, a related greedy matching problem is solved by introducing a multiscale approach for joint image registration and intensity correction. Several theoretical results and numerical tests are performed to validate the efficiency of the proposed model. This is a joint work with Peng Chen, Ke Chen and Daoping Zhang.

个人简介：韩欢，武汉理工大学副教授，硕导，主要从事医学图像反问题相关的变分理论与数值算法研究。主持国家自然科学基金青年基金、湖北省自然科学基金面上项目、波谱与原子分子物理国家重点实验室开放基金等项目，参与国家重点研发计划项目。已在SIAM J. Multiscale Model. Simul.、SIAM J. Imaging Sci.、ESAIM: Math. Model. Numer. Anal.、IEEE Trans. Multimedia、Inverse Probl. Imag.等国际权威期刊发表论文20余篇。(邮箱：hanhuan11@whut.edu.cn)

核医学智能成像与分析

胡战利

摘要：核医学是将核技术应用于医学，利用放射性核素发出的射线对疾病进行诊断、治疗和研究的一门学科。由于单光子发射计算机断层（SPECT）和正电子发射计算机断层（PET）技术的发展，以及放射性药物的创新和开发，使核医学显像技术取得突破性进展。在智能技术迅猛演进的背景下，核医学正在迈向更加精准、高效和安全的未来。报告综述了人工智能和大模型的发展现状，分析了人工智能在核医学中的临床应用，重点关注分割、去噪和校正三个关键领域。

个人简介：胡战利，中国科学院深圳先进技术研究院·劳特伯生物医学成像研究中心的研究员、博士生导师、国自然优秀青年基金获得者、科技部国家重点研发计划首席科学家、国自然数学天元重点专项负责人、广东省特支计划青年拔尖人才、深圳市杰出青年基金获得者，研究领域为医学 PET/MR 与 PET/CT 成像、人工智能医学影像。先后荣获“中国科学院科技促进发展奖”、“中国体视学学会青年科学技术奖”、“中国图象图形学学会技术发明奖”。以通讯/第一作者在 EJNMMI,European Radiology, EJR, IEEE TMI/JBHI/TBME/TCI/TRPMS, Medical Physics, PMB 等本领域国际权威期刊发表 SCI 论文 100 余篇。以第一发明人授权国家发明专利 30 余项、美国专利 2 项。研究成果以发明专利和软件著作权先后转让到企业，相关技术转化到了高端医疗器械龙头企业【上海联影公司】，落地到了国产 PET/MR、PET/CT 和 CT 产品中。先后主持国自然优秀青年基金、数学天元重点专项、面上项目，国家重点研发计划（首席科学家），广东省自然科学基金卓越青年团队项目、国际合作项目，深圳市杰青项目、重点项目、国际合作项目，深圳医科院原创探索项目，企业横向项目多项。(邮箱：zl.hu@siat.ac.cn)

A New SVTV-Stokes Model with Bayesian Optimization for Color Image Denoising

贾志刚

摘要：In this talk, a new model is proposed for color image denoising, which combines tangential field smoothing techniques, image reconstruction techniques, and Bayesian optimization methods. Firstly, the smooth tangential vector field method is used to process the color image, and the “texture” information of the denoised image is obtained by using the anisotropic TV-Stokes model to effectively improve the smoothness of the image. Secondly, combined with the regularization characteristics of the SVTV model, the image after preliminary processing is further color smoothing and detail preservation, in order to eliminate noise to the maximum extent and maintain the natural appearance of the image. Bayesian optimization methods are then used to optimize the parameters, improving the algorithm’s performance. Numerical experimental results demonstrate that the proposed method can effectively capture details in color images, exhibiting superior denoising effects. The new model proposed in this paper brings innovation and effective solutions to the field of color image denoising, offering important insights and guidance for research and applications in image processing. This model is expected to provide reliable technical support for enhancing image quality and information extraction in practical applications.

个人简介：贾志刚，江苏师范大学数学与统计学院、数学研究院，教授。2009年毕业于华东师范大学数学系，获理学博士学位；2017年晋升教授；2023年入选江苏高校“青蓝工程”中青年学术带头人；2024年起担任 Numerical Algorithms 期刊编委。主要研究方向为数值代数与图像处理，至今已在IEEE Trans. Image Process.，SIAM J. Matrix Anal. Appl., SIAM J. Sci. Comput., SIAM J. Imaging Sci. 等期刊上发表学术论文40余篇，在科学出版社出版英文专著1部（独立作者），主持国家自然科学基金项目3项（青年1项、面上2项）和省高校自然科学研究重大项目1项，参加国家自然科学基金重大项目1项和国家重点研发计划课题1项。2023 年荣获江苏省高等学校科学技术研究成果奖（自然科学奖）三等奖 (排名1/5)和第十届淮海科学技术奖（科技创新奖）一等奖(排名1/8)。曾先后到英国曼彻斯特大学、香港浸会大学、澳门大学等高校数学系进行学术访问。(邮箱：zhgjia@jsnu.edu.cn)

Quaternion Nuclear Norm minus Frobenius Norm Minimization for Color Image Reconstruction

金其余

摘要：Color image restoration methods typically represent images as vectors in Euclidean space or combinations of three monochrome channels. However, they often overlook the correlation between these channels, leading to color distortion and artifacts in the reconstructed image. To address this, we present Quaternion Nuclear Norm Minus Frobenius Norm Minimization (QNMF), a novel approach for color image reconstruction. QNMF utilizes quaternion algebra to capture the relationships among RGB channels comprehensively. By employing a regularization technique that involves nuclear norm minus Frobenius norm, QNMF approximates quaternion low-rank matrices, resulting in more accurate color image estimation. Theoretical proofs are provided to ensure the method's mathematical integrity. Demonstrating versatility and efficacy, the QNMF regularizer excels in various color low-level vision tasks, including denoising, deblurring, inpainting, and random impulse noise removal, achieving state-of-the-art results.

个人简介：金其余，内蒙古大学教授、博导。法国南布列塔尼大学应用数学博士，巴黎六大、上海交通大学博士后，巴黎-萨克雷高等师范学校访问学者，内蒙古自治区“青年科技英才支持计划”青年科技领军人才，中国运筹学会数学规划分会理事，内蒙古自治区数学学会理事。长期与国内外多所大学保持合作，包括法国巴黎-萨克雷高等师范学校、巴黎六大、Centre Inria Rennes等。研究领域包括：图像处理、计算机视觉与最优化。相应成果发表于SIAM Journal on Imaging Sciences、Cell子刊Structure、Journal of scientific computing、Journal of Mathematical Imaging and Vision，TIP，Inverse problems等期刊。主持国家自然科学基金、内蒙古自然科学基金等项目多项。(邮箱：qyjin2015@aliyun.com)

Regularized CNNs Based on Geodesic Active Contour and Edge Predictor for Image Segmentation

金正猛

摘要：In this talk, I will introduce a novel regularized convolutional neural network (CNN) based on geodesic active contour (GAC) and edge predictor (EP) for image segmentation. The main idea is to establish a variational problem which integrates the Heaviside function such that the GAC prior is easily added into the problem. Furthermore, an edge predictor module is designed to predict the edges of target objects and an edge predictor function (EPF) is generated instead of the traditional edge indicator function in the GAC. Besides, an iterative convolution soft thresholding module (ICSTM) is developed to numerically solve the GAC and EPF based variational problem, and merged into an existing CNN to generate our new end-to-end network. It is also proved that the ICSTM algorithm is unconditionally stable. Finally, experimental results on synthetic, MRI and CT images show that the proposed method is quite competitive with the other state-of-the-art segmentation methods especially in segmenting noisy images with low contrast.

个人简介：金正猛，南京邮电大学教授、博士生导师。入选江苏省“333 高层次人才培育工程”培养对象、江苏省“青蓝工程”优秀青年骨干教师培养对象。中国兵工学会应用数学专委会委员，江苏省运筹学会常务理事。长期从事非线性偏微分方程及其在图像处理中的应用研究，先后主持国家自然科学基金项目 3 项，在 SIAM Journal on Imaging Sciences、Journal of Mathematical Imaging and Vision、数学学报、应用数学学报、数学年刊等国内外重要学术期刊上发表论文 40 余篇。曾获江苏省工与应用数学学会“青年科技奖”、江苏省教学成果二等奖等。(邮箱：jinzhm@njupt.edu.cn)

超声成像新进展及应用

孔德兴

个人简介：孔德兴，浙江大学求是特聘教授，博士生导师，浙江师范大学数理医学院院长。兼任国家卫生健康委能力建设和继续教育中心超声大数据创新应用中心主任、国家卫生健康委《医学图像标准数据库》工作组副组长、国家药监局器审中心人工智能医疗器械创新合作平台管委会副主任兼数据治理工作组组长；中国人民解放军总医院、国防科技大学、上海交通大学、英国NorthumbriaUniversity等高校客座教授；中国生物医学工程学会医学人工智能分会主任委员、中国医疗装备协会超声大数据与人工智能专委会主任委员、中国工业与应用数学学会数学与医学交叉学科专委会主任委员、中国甲状腺与乳腺超声人工智能联盟名誉主任委员、中国医学装备人工智能联盟专家委员会委员、浙江省数理医学学会理事长、国家自然科学基金委重大项目首席科学家、国家自然科学基金委重大研究计划集成项目首席科学家等。提出了“数理医学”的概念，取得了一系列重要成果。主持研发三项医疗设备，并获得医疗许可证，成功实现产业化。在著名学术期刊上发表论文160多篇；由科学出版社出版专著2部、日本数学会出版英文专著1部、由高等教育出版社出版教材2部；申请国家发明专利20余项；以第一完成人获省部级科技奖项3项；入选浙江省万人计划科技创新领军人才、浙江省151人才工程第一层次培养人员、教育部新世纪优秀人才支持计划等人才计划；承担包括国家自然科学基金重大研究计划集成项目在内的十余项国家自然科学基金项目及浙江省重大科技专项等科技项目。(邮箱：dxkong@zju.edu.cn)

Learning Pseudo-Contractive Denoisers for Inverse Problems

黎芳

摘要：Deep denoisers are highly effective for solving inverse problems but usually require strict Lipschitz conditions, such as non-expansiveness, to ensure convergence, which can degrade recovery performance. To address this issue, we propose a weaker constraint called pseudo-contractiveness. We derive several effective algorithms using pseudo-contractive denoisers, including those based on gradient descent and Ishikawa process, half-quadratic splitting, and forward-backward splitting. These algorithms demonstrate strong convergence to a fixed point. Extensive experiments demonstrate that the proposed methods outperform existing techniques in solving image inverse problems.

个人简介：黎芳，华东师范大学数学科学学院，教授，博士生导师，主要研究方向为基于变分法、深度学习等方法的图像处理。在IEEE Trans Image Process、IEEE Trans. Neural Netw、SIAM J. Imaging Sci、ICCV、ECCV、ICML等国际著名期刊和会议上发表论文 60 余篇，google学术统计引用2400多次。担任Software Impacts副主编。近年来主持和参与了多项国家自然科学基金项目、国家重点研发计划等。(邮箱：fli@math.ecnu.edu.cn)

Nonconvex low-rank regularization method for video snapshot compressive imaging

李敏

摘要：The reconstruction of snapshot compressive imaging (SCI) presents a significant challenge in signal processing. The primary goal of SCI is to employ a low-dimensional sensor to capture high-dimensional data in a compressed form. As a result, compared to traditional compressive sensing, SCI emphasizes capturing structural information and enhancing the reconstruction quality of high-dimensional videos and hyperspectral images. This paper proposes a novel SCI reconstruction method by integrating non-convex regularization approximation in conjunction with rank minimization. Furthermore, we address the characterization of structural information by leveraging nonlocal self-similarity across video frames to improve the reconstruction quality. We also develop an optimization algorithm based on the alternating direction method of multipliers (ADMM) to solve the model and provide a convergence algorithm analysis. Extensive experiments demonstrate that the proposed approach can potentially reconstruct SCI effectively.

个人简介：李敏，深圳大学数学科学学院副教授。主要研究图像处理中的数学问题、模式识别和智能计算。目前在国内外重要学术期刊与会议发表论文 30 余篇，合作出版专著 1 部。先后主持国家自然科学基金 3 项，省市级项目 6项。(邮箱：limin800@szu.edu.cn)

Exploring Structural Sparsity of Coil Images from 3-Dimensional Directional Tight Framelets for SENSE Reconstruction

李炎然

摘要：Each coil image in a parallel magnetic resonance imaging (pMRI) system is an imaging slice modulated by the corresponding coil sensitivity. These coil images, structurally similar to each other, are stacked together as a 3-dimensional (3D) image data and their sparsity property can be explored via 3D directional Haar tight framelets. The features of the 3D image data from the 3D framelet systems are utilized to regularize sensitivity encoding (SENSE) pMRI reconstruction. Accordingly, a so-called SENSE3d-algorithm is proposed to reconstruct images of high quality from the sampled k-space data with a high acceleration rate by decoupling effects of the desired image (slice) and sensitivity maps.Since both the imaging slice and sensitivity maps are unknown, this algorithm repeatedly performs a slice-step followed by a sensitivity-step by using updated estimations of the desired image and the sensitivity maps. In the slice-step, for the given sensitivity maps, the estimation of the desired image is viewed as the solution to a convex optimization problem regularized by the sparsity of its 3D framelet coefficients of coil images. This optimization problem, involved  data from the complex field, is solved by a primal-dual-three-operator splitting (PD3O) method. In the sensitivity-step, the estimation of sensitivity maps is modelled as the solution to a Tikhonov-type optimization problem that favours the smoothness of the sensitivity maps. This corresponding problem is nonconvex, and could be solved by a forward-backward splitting method. Experiments on real phantoms and in-vivo data show that the proposed SENSE3d-algorithm can explore the sparsity property of the imaging slices and efficiently produce reconstructed images of high quality with reducing aliasing artifacts caused by high acceleration rate, additive noise, as well as the inaccurate estimation of each coil sensitivity. To provide a comprehensive picture of the overall performance of our SENSE3d model, we provide quantitative index (HaarPSI) and comparisons to some deep learning methods such as VarNet and fastMRI-UNet.

个人简介：李炎然，深圳大学计算机与软件学院副教授，2009年6月毕业于中山大学通信与信息系统专业，获工学博士学位。2009年9月至今在深圳大学从事科研和教学工作。目前担任IEEE TIP, IEEE TMM, J MATH IMAGING VIS, SIGNAL PROCESS IMAGE等期刊的审稿人。主持过国家自然科学基金青年项目、广东省自然科学基金项目和深圳市基础研究计划项目。在SIAM Journal on Imaging Sciences，IEEE Transactions on Image Processing，IEEE Transactions on Circuits and Systems for Video Technology等国际期刊发表高水平学术成果。主要研究方向：紧框架理论分析及其在图像分析与处理、医学图像重建中的应用研究。(邮箱：lyran@szu.edu.cn)

CurvPnP: Plug-and-play blind image restoration with deep curvature denoiser

李雨桐

摘要：Due to the development of deep learning-based denoisers, the plug-and-play strategy has achieved great success in image restoration problems. However, existing plug-and-play image restoration methods are designed for non-blind Gaussian denoising, the performance of which visibly deteriorate for unknown noises. To push the limits of plug-and-play image restoration, we propose a novel framework with blind Gaussian prior, which can deal with more complicated image restoration problems in the real world. More specifically, we build up a new image restoration model by regarding the noise level as a variable, which is implemented by a two-stage blind Gaussian denoiser consisting of a noise estimation subnetwork and a denoising subnetwork, where the noise estimation subnetwork provides the noise level to the denoising subnetwork for blind noise removal. We also introduce the curvature map into the encoder-decoder architecture and the supervised attention module to achieve a highly flexible and effective convolutional neural network. The experimental results on image denoising, deblurring and single-image super-resolution are provided to demonstrate the advantages of our deep curvature denoiser and the resulting plug-and-play blind image restoration method over the state-of-the-art model-based and learning-based methods. Our model is shown to be able to recover the fine image details and tiny structures even when the noise level is unknown for different image restoration tasks.

个人简介：李雨桐，2023年博士毕业于天津大学，现为天津师范大学讲师。研究方向为基于变分和深度学习的图像处理。目前在国际主流期刊如IEEE Trans. Image Processing和国际重要会议如 CVPR, ICIP等发表论文多篇。(邮箱：yutong_li@tjnu.edu.cn)

Variational Method for Structure-Preserving Priors in Data-Driven Large Segmentation Models

刘君

摘要：Most current data-driven segmentation methods rely on CNN/Transformer architectures, including large segmentation models like the Segment Anything Model (SAM). These methods often employ convolution and downsampling operations that can inadvertently discard fine details and structural information, which are crucial for the accurate segmentation of medical and remote sensing images. In this presentation, we will delve into how to seamlessly integrate structural priors—such as boundaries, skeletons, shapes, and topology—into the framework of data-driven large model image segmentation, employing variational methods and techniques in an end-to-end manner. Through a series of numerical experiments, we will highlight the critical role of structure preservation in enhancing the segmentation quality for both medical and remote sensing imagery.

个人简介：刘君，北京师范大学副教授，博士生导师。2011年博士毕业于北京师范大学。主要研究方向为变分法、深度学习、强化学习相关的图像处理算法与应用。曾先后访问过新加坡南洋理工大学、香港科技大学、香港浸会大学、美国UCLA等高校。一些研究工作发表在图像处理、计算机视觉、计算数学等领域权威期刊如IJCV、IEEE TIP、SIIMS、IP、JSC等。研究成果曾获教育部高等学校优秀科研成果二等奖(团体），北京市科技进步二等奖(团体)。主持参与多项国家科研项目。(邮箱：jliu@bnu.edu.cn)

A Fast Minimization Algorithm for the Euler Elastica Model Based on a Bilinear Decomposition

刘志方

摘要：Euler elastica (EE), as a regulariser for the curvature and length of the image surface's level lines, can effectively suppress the staircase artifacts of traditional regulariser and has attracted lots of attention in image processing. However, developing fast and stable algorithms for optimizing the EE energy is a great challenge due to its nonconvexity, strong nonlinearity, and singularity. This talk will present a novel, fast, globally convergent hybrid alternating minimization method (HALM) algorithm for the Euler elastica model based on a bilinear decomposition. The HALM algorithm comprises three sub­minimization problems, and each is either solved in the closed form or approximated by fast solvers, making the new algorithm highly accurate and efficient. Numerical experiments show that the new algorithm produces good results with much-improved efficiency compared to other state­of-the-art algorithms for the EE model. This work is joint with Baochen Sun, Xue-Cheng Tai, Qi Wang, and Huibin Chang.

个人简介：刘志方，天津师范大学数学科学学院讲师。2019年在南开大学获得博士学位，博士期间曾公派到新加坡国立大学数学系联合培养。2019年加入天津师范大学数学科学学院。主要研究兴趣包括图像重建、数值优化等。在国际图像科学及计算数学知名杂志比如SIAM J. Imaging Sciences, SIAM J. Scientific Computing, Math. Comput.等上发表多篇学术论文, 主持国家自然科学基金青年科学基金项目1项，参与多项国家自然科学基金项目。(邮箱：matlzhf@tjnu.edu.cn)

基于梯度一致性的图像分割模型与算子分裂算法

罗守胜

摘要：近年来，基于形状先验的分割方法受到越来越多的关注和研究，如基于星形先验、凸形先验的分割方法。首先，本报告总结常用的形状先验刻画方法，进而建立统一的梯度一致性数学模型。该模型要求分割目标边界的外法向与给定的向量场具有一定的一致性，可以覆盖星形先验、刺猬（hedgehog）形等形状先验。其次，基于算子分裂算法框架，本报告给出模型的快速求解算法。最后，针对不同图像的数值实验验证了算法的有效性。

个人简介：罗守胜，浙江师范大学数理医学院，副教授，2013年博士毕业于北京大学数学科学院。2016年9月-2017年8月受国家留学基金委资助访问佐治亚理工大学数学学院，2017年12月-2019年11月在北京计算科学研究中心、香港科技大学做博士后研究，2019年12月-2020年2月访问香港浸会大学。主要研究方向为CT图像重建模型与算法、带有图先验的图像分割方法，在Inverse Problems and Imaging, ICCV等期刊和会议上发表论文多篇，主持完成国家自然科学基金面上项目一项、河南省科技厅科技攻关项目一项。(邮箱：luo_ssheng@henu.edu.cn)

推荐算法研究

彭亚新

摘要：推荐算法在人工智能领域，有着广泛的应用。本报告将介绍一些跨域推荐和基于强化学习的推荐算法。

个人简介：彭亚新，上海大学理学院、教授、博导，主要从事几何变分模型、统计学习理论、多模态数据智能算法和强化学习泛化性研究等；提出将统计、几何和语义等结构正则性引入到跨域数据建模和表征中，并与大模型技术和优化算法结合，应用于机器人的智能感知、决策和规划。目前，在国内外有影响的国际SCI期刊和会议上接收/发表学术论文50余篇，包括中科院一区TOP期刊IEEE Trans. on Neural Networks and Learning Systems、Trans. on Image Processing、Tran. on MultiMedia、Neural Network、Expert Systems with Applications、Chaos, Solitons & Fractals  和AAAI、IJCAI、ECCV 等顶会；已主持5项国家自然科学基金项目及多项校企合作手术、家居机器人项目。(邮箱：yaxin.peng@shu.edu.cn)

Geometric Analysis of Unconstrained Feature Models with $d=K$

沈益

摘要: Recently, interesting empirical phenomena known as Neural Collapse have been observed during the final phase of training deep neural networks for classification tasks. We examine this issue when the feature dimension $d$ is equal to the number of classes $K$. We demonstrate that two popular unconstrained feature models are strict saddle functions, with every critical point being either a global minimum or a strict saddle point that can be exited using negative curvatures. The primary findings conclusively confirm the conjecture on the unconstrained feature models.

个人简介：沈益，浙江理工大学数学科学系教授，浙江省应用数学研究会副理事长，毕业于浙江大学数学系获应用数学博士学位 ( 导师：李松教授 ) 。从事应用调和分析，逼近论相关领域的研究。研究内容为信号处理，数据分析中的数学问题与方法。主持国家自然科学基金面上项目，优秀青年科学基金项目，浙江省杰出青年基金项目等省部级项目。在 Appl Comput Harmon A 、IEEE T Inform Thoery 、IEEE T Signal Proces 、Comput Aided Geom D 等期刊发表论文 20 余篇。(邮箱：yshen@qq.com)

多模态图像融合

石玉英

摘要：多模态图像融合可以有效地整合图像信息，显示更多的图像细节特征，应用到医学领域可以使医生更容易观察到病变区域。图像融合的通用框架通常分为三个步骤：图像分解，融合系数，图像重建。众所周知，大多数真实图像被不同类型的噪声污染，那么如何使图像在去除噪声的同时进行融合就是我们要考虑的问题。数值实验表明所提出的方法在视觉效果上具有良好的性能。

个人简介：石玉英，华北电力大学数理学院教授，2006年博士毕业于中国科学院数学与系统科学研究院。中国工业与应用数学学会理事，北京计算数学学会理事。主要研究偏微分方程数值解和图像恢复、边界检测及其在医学和能源等相关领域的数学理论与算法，曾获北京市优秀人才培养资助计划，主持国家自然科学基金3项，教育部中央高校基金重大项目1项，北京市自然科学基金重点研究专题子课题1项，出版专著一部。(邮箱：yyshi@ncepu.edu.cn)

A stochastic preconditioned Douglas-Rachford splitting method for saddle-point problems

孙鸿鹏

摘要：In this article, we propose and study a stochastic preconditioned Douglas-Rachford splitting method to solve saddle-point problems that have separable dual variables. We prove the almost sure convergence of the iteration sequences in Hilbert spaces for a class of convex-concave and nonsmooth saddle-point problems. We also provide the sublinear convergence rate for the ergodic sequence concerning the expectation of the restricted primal-dual gap functions. Numerical experiments show the high efficiency of the proposed stochastic preconditioned Douglas-Rachford splitting methods. This is a joint work with Yakun Dong and Kristian Bredies.

个人简介：孙鸿鹏，中国人民大学，教授，博士生导师，2012年博士毕业于中科院数学科学研究院数学所，2012-2014年于奥地利格拉茨大学(University of Graz)数学与科学计算研究所做博士后，研究方向为反问题和图像处理。目前主持国家自然科学基金面上项目，北京市自然科学基金重点子课题，科技部新一代人工智能国家科技重大专项子课题，已主持国家自然科学基金青年项目，德国洪堡基金等项目，在国内外有影响的期刊和会议上发表学术论文30余篇。(邮箱：hpsun@amss.ac.cn)

Double-well Net for image segmentation

台雪成

摘要：In this study, our goal is to integrate classical mathematical models with deep neural networks by introducing two novel deep neural network models for image segmentation known as Double-well Nets. Drawing inspirations from the Potts model, our models leverage neural networks to represent a region force functional. We extend the well-know MBO (Merriman-Bence-Osher) scheme to solve the Potts model. The widely recognized Potts model is approximated using a double-well potential and then solved by an operator-splitting method, which turns out to be an extension of the well-known MBO scheme. Subsequently, we replace the region force functional in the Potts model with a UNet-type network, which is data-driven and is designed to capture multiscale features of images, and also introduce control variables to enhance

effectiveness. The resulting algorithm is a neural network activated by a function that minimizes the double-well potential. What sets our proposed Double-well Nets apart from many existing deep learning methods for image segmentation is their strong mathematical foundation. They are derived from the network approximation theory and employ the MBO scheme to approximately solve the Potts model. By incorporating mathematical principles, Double-well Nets bridge the MBO scheme and neural networks, and offer an alternative perspective for designing networks with mathematical backgrounds. Through comprehensive experiments, we demonstrate the performance of Double-well Nets, showcasing their superior accuracy and robustness

compared to state-of-the-art neural networks. Overall, our work represents a valuable contribution to the field of image segmentation by combining the strengths of classical variational models and deep neural networks. The Double-well Nets introduce an innovative approach that leverages mathematical foundations to enhance segmentation performance.

个人简介：台雪成，挪威研究中心的首席科学家，曾任挪威卑尔根大学教授和香港浸会大学讲座教授和系主任，第 8 届“冯康”计算数学奖获得者。研究领域主要包括数值 PDE、优化技术、计算机视觉以及图像处理等，在 SIAM, IJCV, IEEE Trans. (TIP, TOG)等国际顶级杂志以及 CVPR、ECCV 等国际顶级会议共发表论文 100 多篇（Google Scholar: citations 11740, h-index 51）。担任多个国际会议的大会主席，并多次应邀做大会报告，担任 Inverse Problems and Imaging、International Journal of Numerical analysis and modelling、Advances in Continuous and Discrete Models: Theory and Applications、Advances in Numerical Analysis, SIAM Journal on Imaging Sciences、Journal of Mathematical Imaging and Vision、SIAM numerical analysis 等多个国际知名期刊的编辑及执行编辑。(邮箱：xtai@norceresearch.no)

基于神经隐式学习的表面重建

陶文兵

摘要：从三维点云中获取网格表达是计算机视觉和计算机图形学的重要任务。在表面重建中，如何使重建的表面能够充分表达物体的三维细节信息，以及如何使得用尽可能少的三角面片来表达网格一直都是一对矛盾，目前典型的方法均是先重建具有足够精度的三角网格表面，然后采用表面重建算法对表面进行简化，这种简化通常为丢失较多的表面细节信息。本报告采用神经隐式学习算法构建一个端到端的神经网络，将表面重建和网格简化统一到一个网络架构中，输入点云经过网络处理后，直接生成简化的表面网格，与以往的算法相比，本方法在不降低表面重建质量的情况下，所需要的三角网格面片的数量降低了10倍，大量的实验结果验证了方法的性能。

个人简介：陶文兵，华中科技大学人工智能与自动化学院及多谱智能信息处理技术全国重点实验室教授/博士生导师，现担任华中科技大学与杭州市共建的杭州运河人工智能研究院首任执行院长筹备研究院。曾连续6年入选爱思唯尔中国高被引学者，以第一作者和通讯作者在TPAMI, IJCV, TIP, TVCG, ICCV, CVPR, NeurIPS, AAAI等期刊和会议上发表论文100余篇，授权发明专利50余项，多项研究成果已在企业成功转化应用，产生重大经济价值。近年来研究工作主要集中在以下几个方面：1）提出一系列多视图重建算法在公开数据集上评测取得领先的性能，为工业界广泛采用（代码已开源）；2）提出几种深度学习表面重建算法解决了大规模点云表面重建问题，并取得与传统几何算法相当的性能（代码已开源）；3）在点云配准领域提出若干性能SOTA的算法（代码已开源）。(邮箱：wenbingtao@hust.edu.cn)

基于多模态结构相似度的短时PET-CT图像增强及临床验证

王冬

摘要：PET-CT是核医学中最常用的成像技术之一，在癌症精准诊疗中优势明显。但由于成像机理和临床实践等方面限制，现有PET-CT的数据采集时间很长，通常需要20-40分钟。面向PET-CT成像对于数据快速采集的需求，我们提出了一种基于多模态图像结构相似度深度神经网络的短时PET-CT增强算法，并在合作医院开展临床验证。通过构建多模态多分支带自注意力机制的深度卷积神经网络，在损失函数中引入多模态图像结构相似度来学习CT图像中的结构信息，该方发使得短时PET图像（每个窗位采集时间10s）的峰值信噪比提高9%，成功达到标准剂量PET图像（每个窗位采集时间60s）的效果，相比于其他前沿的方法也有一定的提高。

个人简介：王冬，南京应用数学中心助理研究员，博士毕业于南京理工大学。研究方向为医学图像处理中的数学理论，主要包括压缩感知理论、核磁共振成像、计算机断层扫描成像等医学成像的模型和快速算法、基于图形处理单元的并行计算程序设计、深度学习理论及其在医学图像处理方面的应用等。在Magnetic Resonance in Medicine、International Journal of Biomedical Imaging等期刊发表多篇论文。(邮箱：dongwang@seu.edu.cn)

Nonlocal Tensor Decomposition With Joint Low Rankness and Smoothness for Spectral CT Image Reconstruction

王建军

摘要：Spectral computed tomography (CT) is a medical imaging technology that utilizes the measurement of X-ray energy absorption in human tissue to obtain image information. It can provide more accurate and detailed image information, thereby improving the accuracy of diagnosis. However, the process of spectral CT imaging is usually accompanied by a large amount of radiation and noise, which makes it difficult to obtain high-quality spectral CT image. Therefore, this paper constructs a basic third-order tensor unit based on the self-similarity of patches in the spatial domain and spectral domain while proposing nonlocal spectral CT image reconstruction methods to obtain high-quality spectral CT image. Specifically, the algorithm decomposes the recombination tensor into a low-rank tensor and a sparse tensor, which are applied by weighted tensor nuclear norm (WTNN) and weighted tensor total variation (WTTV) norm to improve the reconstruction quality, respectively. In order to further improve algorithm performance, this paper also uses weighted tensor correlated total variation regularization(WTCTV) to simultaneously characterize the low rankness and smoothness of low-rank tensor, while the sparse tensor uses weighted tensor total variation regularization (WTTV) to represent the piecewise smooth structure of the spatial domain and the similarity between pixels and adjacent frames in the spectral domain. Hence, the proposed models can effectively provide faithful underlying information of spectral CT image while maintaining spatial structure. In addition, this paper uses the Alternating Direction Method of Multipliers(ADMM) to optimize the proposed spectral CT image reconstruction models. To verify the performance of the proposed algorithms, we conducted a large number of experiments on numerical phantom and clinic patient data. The experimental results indicate that incorporating weighted regularization

outperforms the results without weighted regularization, and nonlocal similarity can achieve better results than that without nonlocal similarity. Compared with existing popular algorithms, the proposed models significantly reduce running time and improve the quality of spectral CT image, thereby assisting doctors in more accurate diagnosis and treatment of diseases.

个人简介：王建军，西南大学数学与统计学院副院长，教授，博士生导师。重庆市英才计划，创新创业领军人才，巴渝学者特聘教授，重庆市学术技术带头人， 美国数学评论评论员，重庆数学会常务理事。2006年12月西安交通大学获理学博士学位，为西安交通大学优秀博士毕业生（导师：徐宗本院士，应用数学专业）。 2006年12月至今在西南大学任教，2008年1月至2009年12月在西安交通大学博士后力学流动站从事研究工作。2012年6月破格评聘为研究员，2012年8月至2013年8月受国家留学基金委资助在美国Texas A&M大学访问。主持国家自然科学基金 5项，教育部科研项目 1 项，部委级科研项目 2 项，校级科研项目 2 项等。在IEEE Trans、Signal Processing等国内外期刊和会议发表高质量论文 100 余篇。(邮箱：wjjmath@163.com)

医学影像人工智能基础模型研究与应用

王珊珊

摘要：近年来，泛化医学人工智能（AI）基础模型备受关注，并展示出对医疗保健的巨大变革潜力。不同于现有医学AI模型，基础模型能够在“仅有少量特定任务标签”甚至“无标签”的情况下，解决复杂多样的任务。然而，医学影像领域仍面临众多技术与临床挑战，目前的深度学习方法大多为特定任务设计，泛化能力不足且高度依赖大规模数据集和标注。本次报告将探讨医学影像基础模型的发展，重点介绍我们团队在快速MR成像及图像分析基础模型临床应用与转化的研究工作，研讨我们在提升AI模型泛化能力、高数据保真度及减少数据依赖性的解决方案。

个人简介：王珊珊，中国科学院深圳先进技术研究院研究员、博士生导师，国家优青、吴文俊人工智能优秀青年奖获得者，2014 年于悉尼大学和上海交通大学分别获信息技术与生物医学工程双博士学位，多次入选斯坦福 “全球前 2%顶尖科学家” 榜单。长期从事人工智能、快速医学成像、放射组学与多模态分析等研究，在Nature 子刊、IEEE Trans 等发表高质量论文 100 余篇；曾荣获 OCSMRM 杰出研究奖、省部级一等奖 3 项等；先后主持科技部 2030 新一代人工智能重大研发计划课题、NSFC 联合基金重点项目、优秀青年等国家级项目 6 项；担任多个高质量 SCI 学术期刊的副主编/编委（如 IEEE Transactions on Medical Imaging, Magnetic Resonance in Medicine, Pattern Recognition、IEEE Reviews in Biomedical Engineering 等)。曾受邀在第 31 届国际医学磁共振年会给大会主题冠名报告（入选率 1/6000，英国伦敦）及美国第 10 届 GRC 活体磁共振给大会主题报告。(邮箱：ss.wang@siat.ac.cn)

图像去模糊的优化展开神经网络建模

王卫卫

摘要：图像在获取过程中由于相机抖动、聚焦不准等因素造成模糊而质量下降，严重影响视觉效果和下游应用。图像去模糊研究如何设计模型和算法从模糊图像中恢复出清晰图像。正则化是解决图像去模糊的主要方法，传统优化模型主要用解析正则项例如总变差、稀疏表示等约束清晰图像，虽然取得了良好的效果，但解析正则项仅适用于某类图像，不具有数据自适应性；其次，求解优化模型需要大量迭代，计算量较大。近年来，深度神经网络已成为解决图像处理问题的最活跃的工具，报告介绍在图像去模糊应用中，如何基于优化算法展开构建神经网络模型，以及本课题组在这方面的几个工作。

个人简介：王卫卫，西安电子科技大学教授、博士生导师。于2001年在西安电子科技大学应用数学系获得应用数学专业博士学位。曾在澳大利亚悉尼大学、美国宾夕法尼亚大学、杜兰大学、新奥尔良大学、香港理工大学做访问研究。兼任陕西省计算数学学会副理事长（2014-2019）。主要研究方向：机器学习、图像处理的数学方法。主持完成国家自然科学基金面上项目2项。曾获陕西省科技奖1项。在科学出版社合作出版科研专著《图像处理的变分与偏微分方程方法》一部，在国内外重要学术期刊与会议上合作发表论文70余篇，SCI检索论文30余篇，发表期刊包括IEEE Trans. on Image Processing，IEEE Trans. On Circuits and Systems for Video Technology, SIAM J. on Multiscale Modeling and Simulation，Pattern Recognition，Signal Processing等。(邮箱：wwwang@mail.xidian.edu.cn)

Inhomogeneous Image Correction and Segmentation Based on Retinex Model

王媛

摘要：Images usually suffer from intensity inhomogeneity problem caused by many factors such as spatial variations in illumination, which affects the subsequent image processing. In order to address this problem, this paper proposes a Retinex-based variational model for image correction and segmentation. According to Retinex theory, the inhomogeneous image can be decoupled into illumination parts and reflectance parts. The existence of the minimizers to the variational model is established. Furthermore, we develop an efficient algorithm to solve the model numerically by using the alternating minimization method. Experimental experiments on the simulated and real images illustrate the effectiveness and the robustness of our proposed model both visually and quantitatively by compared with some related state-of-the-art variational models.

个人简介：王媛，2023年博士毕业于浙江大学数学科学学院，导师孔德兴教授，现为浙江理工大学数学系讲师。研究方向为医学图像处理、医学人工智能等多学科交叉。在Inverse Problems and Imaging、Ultrasound in Medicine and Biology等期刊发表多篇论文。(邮箱：wangyuan2028@163.com)

Dual-Domain Optimization Method for Solving Linear Inverse Problems via Latent Diffusion Model

王泽龙

摘要：Linear inverse problems (LIPs) play a crucial role in image and signal processing, with the main challenge lying in finding their unique solutions by exploring appropriate priors of the ground truth. Motivated by the remarkable generation capacity, diffusion models (DMs) have been employed to solve the ill-posedness of LIPs by deep generative priors (DGP). However, DMs typically operate in pixel domain, leading to high computation complexity. Fortunately, latent DMs (LDMs) have been proposed to accelerate generation process via diffusion in latent space, offering a novel approach for efficiently solving LIPs with DGP. In this talk, we will introduce a dual-domain optimization method for solving LIPs via LDMs, where the kernel is to enhance the measurement guidance that has been weakened by the autoencoding networks in LDMs. Experimental results on various image restoration tasks, including image deburring, image superresolution, and image inpainting, verify its feasibility and superiority.

个人简介：王泽龙，国防科技大学理学院应用数学研究中心副教授，英国华威大学访问学者。长期从事智能信息感知与处理、系统建模与优化等研究工作，主持国家自然科学基金、国防973专题、高分创新基金、自主科研基金等科研项目20余项，出版学术专著1部，在SIAM J Imaging Sciences、Pattern Recognition、IEEE GRSL等期刊发表学术论文30余篇，申请与授权国家发明专利与国防专利14项，获军队科技进步一等奖1项，获国防科技三等功1次，获军队优秀专业技术人才三类岗位津贴。(邮箱：zelong_wang@163.com)

Non-Negative Sparse Recovery via Momentum-Boosted Adaptive Thresholding algorithm

温金明

摘要：Recovering a non-negative sparse signal from an underdetermined linear system remains a challenging problem in signal processing. Despite the development of various approaches, such as non-negative least squares, as well as variants of greedy algorithms and iterative thresholding methods, their recovery performance and efficiency often fall short of practical expectations. Aiming to address this limitation, this paper first devises a momentum-boosted adaptive thresholding (MBAT) algorithm for non-negative sparse signal recovery. Then, we establish two sufficient conditions of stable recovery for the proposed algorithm by using the restricted isometry property and mutual coherence. Extensive tests based on synthetic and real-world data demonstrate the superiority of our approach over the state-of-the-art non-negative orthogonal greedy algorithms and iterative thresholding methods, in terms of the probability of successful recovery, phase transition, and computational attractiveness.

个人简介： 温金明，暨南大学三级教授、博士生导师、国家高层次青年人才、广东省青年珠江学者，中国数学会理事、人工智能学会离散智能计算专委会常务委员兼副秘书长、广东省运筹学会常务理事、广东省工业与应用数学学会理事、广东省计算数学学会理事，近5年主持国家自然科学基金3项、省级项目4项。2015年6月博士毕业于加拿大麦吉尔大学数学与统计学院，从2015年3月到2018年8月，先后在法国科学院里昂并行计算实验室、加拿大阿尔伯塔大学、多伦多大学从事博士后研究工作。 温教授的研究方向是整数信号和稀疏信号恢复的算法设计与理论分析，近年来以第一作者/通讯作者在Applied and Computational Harmonic Analysis、Inverse Problem、IEEE Transactions on Information Theory、IEEE Transactions on Signal Processing、Journal of Scientific Computing等权威期刊和会议发表70余篇学术论文。(邮箱：jinmingwen1@163.com)

$L_0$ Gradient Regularization and Scale Space Representation Model for Cartoon and Texture Decomposition

文有为

摘要：本报告考虑图像卡通与纹理分解问题。传统方法主要依赖图像梯度幅值来区分卡通与纹理成分，这种方法在处理小尺度、高对比度纹理模式与大尺度、低对比度结构组件时存在局限性，易忽视两者固有的尺度特征。为应对此挑战，我们提出一种新的变分模型，该模型采用基于$L_0$范数的总变分作为卡通图像的先验信息，同时采用尺度空间表示的$L_2$范数作为纹理图像的先验信息。我们证明了纹理图像在尺度空间表示中具有较小的$L_2$范数。在算法实现上，我们采用二次惩罚函数方法克服了不可分的$L_0$范数最小化问题所带来的数值计算困难。数值实验验证了我们方法的有效性和效率。

个人简介：文有为，湖南师范大学数学与统计学院教授，博导，湖南省计算数学与应用软件学会副理事长。获香港大学博士学位，曾在新加坡国立大学、香港中文大学从事访问研究员、博士后等工作。主要研究方向为科学计算、数字图像处理与计算机视觉，在SIAM J. Sci. Comput., SIAM J. Imaging Sciences, Multiscale Model. Simul.，SIAM J. Matrix Anal., IEEE Trans. Image Process.等期刊发表论文30余篇，主持国家自然科学基金4项。以第一完成人身份，获2019年湖南省自然科学奖二等奖。(邮箱：wenyouwei@gmail.com)

Medical image reconstruction：classical methods and deep Learning

武婷婷

摘要：In the field of medical image reconstruction, we present a novel model that integrates deep learning with variational techniques for image reconstruction. This model employs a multi-level wavelet convolutional neural network (MWCNN) and a tight-frame regularizer to achieve enhanced performance. Furthermore, for single-particle reconstruction (SPR) in cryo-EM, we propose a three-dimensional weighted nuclear norm minimization (3DWNNM) model paired with a solver based on the forward-backward splitting algorithm.

个人简介：武婷婷，南京邮电大学理学院教授、博士生导师。入选江苏省高校“青蓝工程”优秀青年骨干教师、南京邮电大学“1311 人才计划-鼎新学者”、江苏省科技副总，获得南京邮电大学“教学标兵奖” 称号。兼任江苏省运筹学会理事，中国商业统计学会理事，中国运筹学会科普委员会副秘书长。2011年取得湖南大学理学博士学位；2015 至 2018 年在南京师范大学从事博士后研究工作。近年来分别在香港中文大学、香港浸会大学、新加坡南洋理工大学、中科院数学与系统科学研究院等进行长期访问。主要针对大规模数值算法的理论分析，以及在图像恢复、图像分割、机器学习及人工智能等热点问题进行研究，在国内外高水平期刊发表论文近 40 篇，申请发明专利 8 项(授权 2 项)。近年来，担任 Frontiers in Applied Mathematics and Statistics 等杂志编委。主持国家自然科学基金 4 项，省级科研项目 1 项，市厅级科研项目 1 项，校级科研项目 2 项目，参与国家自然科学基金 3 项。(邮箱：wutt@njupt.edu.cn)

医学影像数据处理与医工结合：挑战与机遇

徐静

摘要：随着计算机存储和运算能力的快速提升，以及深度学习模型的日益强大，许多图像相关领域迎来了快速发展和实际应用。然而，医学影像处理因其专业性和知识壁垒，仍然是一个有待探索的广阔领域，需要跨学科的合作与交流。医工结合的需求也越来越迫切。在本次报告中，将介绍本人与医院间交流的几个科研议题，并分享医工结合心得。

个人简介：徐静，浙江工商大学统计与数学学院数据科学系主任，教授，硕士生导师。博士毕业于中国科学院数学与系统科学研究院，新加坡南洋理工大学博士后，美国加州洛杉矶分校访问。章乃器学院创新实验班学生专业导师。荣获2016-2018年校“ 三育人 ”先进个人荣誉称号。中国科学院大学附属肿瘤医院超声医学科客座教授。台州市肿瘤医院客座教授。浙江省数理医学学会超声介入与智能诊断分会青委会副主任委员。主要研究领域为大数据分析，统计学习方法，图像处理。特别注重与医学相交叉，对医疗影像处理。如利用计算机来自动分析进行肿瘤的精准标注研究，减轻医生的读图工作；通过图像，数据分析，辅助医生制定准确的医疗方案等。已在Journal of Computational and Applied Mathematics、Inverse Problems and Imaging等刊物发表论文十余篇。主持完成国家自然科学基金两项，主持完成教育部留学回国基金一项，主持教育部高教司产学研协同育人项目一项，主持虚拟仿真教学实验项目一项，主持线上线下混合教学改革项目一项。参与国家自然科学基金，省自然科学基金多项。(邮箱：jingxu@amss.ac.cn)

A Ginzburg-Landau-H⁻¹ Model and Its SAV Algorithm for Image Inpainting

姚文娟

摘要：Image inpainting models and the corresponding numerical algorithms play key roles in image processing. At present, the visual output of the oscillatory inpainting area is usually not natural. For this reason, we propose an image inpainting model based on the Ginzburg-Landau functional and H⁻¹-norm. In the model, the H ⁻¹-fidelity term performs well in preserving the edges of the oscillatory inpainting areas, and the Ginzburg-Landau functional can provide additional geometric content. Theoretically, we prove the existence of the minimizer for the proposed energy functional. Based on the scalar auxiliary variable approach, we develop an efficient numerical scheme to solve the proposed model. Further, we use a time step adaptive strategy to accelerate the convergence. 

个人简介：姚文娟，哈尔滨工业大学数学学院副教授，硕士生导师，于2019年哈尔滨工业大学获得博士学位。研究方向为分数阶偏微分方程数值解法、基于分数阶偏微分方程的纹理图像处理，在SIAM Journal on Imaging Sciences、Signal Processing、Inverse Problems and Imaging等国内外期刊和会议发表10余篇论文，主持和参与多项国家级、省部级项目。(邮箱：mathywj@hit.edu.cn)

Towards Decentralized Optimization over Digraphs: Effective metrics, lower bound, and optimal algorithms

袁坤

摘要: In this talk, we will investigate the influence of directed networks on the convergence of smooth non-convex stochastic decentralized optimization associated with column-stochastic mixing matrices. We find that the canonical spectral gap, a widely-used metric in undirected networks, alone fails to adequately characterize the impact of directed networks. Through a new analysis of the Push-Sum strategy, a fundamental building block for decentralized algorithms over directed graphs, we identify another novel metric called the equilibrium skewness. Next, we establish the first convergence lower bound for non-convex stochastic decentralized algorithms over directed networks, which explicitly manifests the impact of both the spectral gap and equilibrium skewness and justifies the imperative need for both metrics in analysis. Moreover, by jointly considering the spectral gap and equilibrium skewness, we present the state-of-the-art convergence rate for the Push-DIGing algorithm, which, however, is far worse than the established lower bound. We further integrate the technique of multi-round gossip to Push-DIGing to obtain MG-Push-DIGing, which nearly achieves the established lower bound, demonstrating its convergence optimality, best-possible resilience to directed networks, and the tightness of our lower bound. Experiments verify our theoretical findings.

个人简介: Dr. Kun Yuan is an Assistant Professor at Center for Machine Learning Research (CMLR) in Peking University. He completed his Ph.D. degree at UCLA in 2019, and was a staff algorithm engineer in Alibaba (US) Group between 2019 and 2022. His research focuses on the development of fast, scalable, reliable, and distributed algorithms with applications in large-scale optimization, deep neural network training, federated learning, and Internet of Things. He was the recipient of the 2017 IEEE Signal Processing Society Young Author Best Paper Award, and the 2017 ICCM Distinguished Paper Award.(邮箱：kunyuan@pku.edu.cn)

高光谱与多光谱图像融合的低秩正则化方法

张俊

摘要：最近的研究凸显了核范数在解决高光谱图像（Hyperspectral Image, HSI）与多光谱图像（Multispectral Image, MSI）融合问题时的有效性。然而，标准的核范数方法在处理过程中，未能对不同的奇异值进行差异化对待，这导致了其在实际应用中存在一定的局限性和不足。针对该问题，本报告从矩阵分解和张量分解两个角度开展HSI-MSI融合方法研究：（1）创新性地引入了图像去噪中的加权核范数概念，以确保在图像融合过程中关键数据成分的保留。确切地说，提出了一个整合了加权核范数、稀疏先验和全变分正则化的统一框架；（2）为了深度挖掘高光谱图像的低秩特性，本报告在张量环（Tensor Ring, TR）分解框架下，通过整合TR因子对数张量核范数与加权TV，介绍了一种新开发的HSI-MSI融合方法。

个人简介：张俊，南昌工程学院理学院副教授，硕士生导师，江西省优秀青年基金获得者。2013年6月毕业于湖南大学，获理学博士学位。2017.10-2018.10美国德克萨斯大学访问学者，并于2024年短期访问香港城市大学。现为“应用统计”硕士专业学位点数据科学方向的负责人，“智慧水利江西省重点实验室”骨干成员，江西省电子学会理事。研究兴趣：高光谱遥感图像处理，数值最优化，图像复原与分割。主持在研国自科地区科学基金项目、江西省自然科学基金优秀青年基金项目和面上项目各1项；主持完成国自科数学天元基金、中国博士后科学基金面上资助项目、江西省自然科学基金青年项目和江西省教育厅科技项目各1项。在IEEE TGRS、IEEE JSTARS、SP、AMC、AMM等著名学术期刊上发表学术论文30余篇。(邮箱：junzhang0805@126.com)

Registration-Based Image Segmentation Models

张道平

摘要：Image segmentation is to extract meaningful objects from a given image. For degraded images due to occlusions, obscurities or noises, the accuracy of the segmentation result can be severely affected. To alleviate this problem, prior information about the target object is usually introduced. In Chan et al. (J Math Imaging Vis 60(3):401–421, 2018), a topology-preserving registration-based segmentation model was proposed, which is restricted to segment 2D images only. In this talk, we will talk about the registration-based 3D segmentation, convexity segmentation, and star-shape segmentation.

个人简介：张道平, 南开大学数学科学学院讲师, 分别于2012年和2019年在大连理工大学和英国利物浦大学获得学士和博士学位。曾在香港中文大学从事博士后研究工作。2021年加入南开大学数学科学学院。研究兴趣包括图像处理及其优化算法。近年来在国际图像科学及计算数学知名杂志比如Siam Journal on Imaging Sciences, Journal of Mathematical Imaging and Vision, Numerical Algorithms, Journal of Scientific Computing, Applied Mathematical Modelling等上发表多篇学术论文。(邮箱：daopingzhang@nankai.edu.cn)

Registration-Based Image Segmentation Models

张建峰

摘要： 基于医学影像的人体生物脉管系统分析是医学图像计算领域的热点与难点。结合脉管生长扩展所遵循的物理规律，报告人提出生物机理与数据融合的脉管系统分析方法，旨在更好地解决连续性、精准性等难题。该研究首先可以解决智能精准辅助诊疗中的实际需求，同时也可为融合生物机理的医学图像处理方法体系提供借鉴。除计算方法的研究进展，本报告也会围绕医学图像处理和人工智能的框架研究进行探讨。

个人简介：张建峰，浙师大数理医学院讲师，硕导，浙师大数理医学院人工智能专业副主任。博士毕业于浙江大学应用数学系。中国工业与应用数学学会专委会委员、浙江省数理医学学会专委会委员，中国生物医学工程学会、中国运筹学会及CCF等会员。主要从事生物医学图像处理、数值计算与优化、数理医学、医学人工智能等方面的多学科交叉研究。主持国家自然科学基金、省自然科学基金、揭榜挂帅在内的科研项目6项，参与国家级、省部级重点课题多项，参编中文专著2部（科学出版社出版），作为主要成员获批浙江省“十四五”重点教材建设项目1项，担任国际期刊/会议审稿人、国际国内学术会议作报告多次，在IJCM、PMB、EABE、ICCM、DICTA等发表SCI论文多篇（其中一作/通讯9篇），公开/授权国家发明专利7项。(邮箱：jfzhang@zjnu.edu.cn)

A Dual-Domain Unified CT Reconstruction with Multi-sparse-view and Multi-scale Refinement-correction

张建平

摘要：X-ray Computed Tomography (CT) is one of the most important diagnostic imaging techniques in clinical applications. Sparse-view CT imaging reduces the number of projection views to a lower radiation dose and alleviates the potential risk of radiation exposure. Most existing deep learning (DL) and deep unfolding sparse-view CT reconstruction methods: 1) do not fully use the projection data; 2) do not always link their architecture designs to a mathematical theory; 3) do not flexibly deal with multi-sparse-view reconstruction assignments. This paper aims to use mathematical ideas and design optimal DL imaging algorithms for sparse-view tomography reconstructions. We propose a novel dual-domain unified framework that offers a great deal of flexibility for multi-sparse-view CT reconstruction through a single model. This framework combines the theoretical advantages of model-based methods with the superior reconstruction performance of DL-based methods, resulting in the expected generalizability of DL. We propose a refinement module that utilizes unfolding projection domain to refine full-sparse-view projection errors, as well as an image domain correction module that distills multi-scale geometric error corrections to reconstruct sparse-view CT. This provides us with a new way to explore the potential of projection information and a new perspective on designing network architectures. The multi-scale geometric correction module is learnable end to end, and our method could function as a plug-and-play reconstruction technique, adaptable to various applications. Extensive experiments demonstrate that our framework is superior to other existing state-of-the-art methods.

个人简介：张建平，湘潭大学教授，博士生导师。先后获得湘潭大学“数学与应用数学”专业学士学位、大连理工大学“计算数学”专业博士学位；在香港城市大学、利物浦大学做过 Reserch Assistant 和 Research Associate 博士后工作。长期致力于计算机视觉及图像处理中的数学问题、机器学习、深度学习及其应用方面的研究，相应成果以第一作者或通讯作者发表在 SIAM J.Imaging Sci.、SIAM J.Numer.Anal.、IEEE JBHI、IEEE TCI、IEEE TGRS、J Comput.Phys.、AMM、Inverse Probl.Imag.、BSPC 等国际重要刊物上；主持完成国家自然科学基金青年、面上项目共 2 项、湖南省科技厅及教育厅省部级项目 3 项；作为主要骨干成员或子课题负责人参与科技部遥感重大项目、湖南省科技厅重大应用基础研究与成果转化及产业化医学项目、湖南省科技厅高新技术发展及产业重点研发项目、湖南省科技厅"社会发展领域重点研发项目"、国家自然科学基金与省部级项目近 10 项。(邮箱：jpzhang@xtu.edu.cn)

Gromov-Wasserstein Barycenter Methods for Spectral Clustering

张婕

摘要：In this talk, we propose to do spectral embeddings learning via optimal transport, which is rarely studied in the literature. Based on the theory of Gromov-Wasserstein discrepancy, we connect samples with clusters and formulate the similarity information involving in them as a Gromov-Wasserstein barycenter.  Due to the advantage of Gromov-Wasserstein barycenter, we can avoid direct transport between samples and clusters that have a large distribution map and improve the accuracy of sample-cluster correspondence. Moreover, we further present the relationship between our proposed method and traditional spectral clustering methods, which raises possibilities for applying optimal transport to address spectral clustering. Numerical results on benchmark datasets also show the effectiveness of the proposed methods.

个人简介：张婕，2024年9月博士毕业于香港大学数学系，研究方向为数据科学、图像处理。目前已在图像处理领域发表SCI论文4篇，在数据科学及相关应用领域发表SCI论文2篇、国际顶级机器学习会议论文1篇。(邮箱：zj199607@connect.hku.hk)

参会人员

(按姓氏首字母排序)