召集人：许志强（中科院数学与系统科学研究院）、郑国安（美国康涅狄格大学）、常慧宾（天津师范大学）

时间：2024.04.28—2024.05.04

计算调和分析及其超分辨率成像应用研讨会

计算调和分析是活跃的数学分支，其主要目的就是针对工程领域中信号和图像等信息进行分析和计算，特别是基于调和分析发展相应的数学理论及算法。该分支涉及到多个不同的数学领域及工程领域，来自这些不同领域的专家交流，对于促进该数学分支的发展无疑是十分重要的。

本研讨会主要针对计算调和分析中几个活跃的研究课题进行，包括但不限于：相位恢复、压缩感知、稀疏信号重建算法、框架理论、超分辨率成像等。特别是，近年来相位恢复问题受到了众多应用数学家和物理学家的关注，新的数学理论和算法也不断涌现，成为了计算和成像科学中的研究热点问题。在光学和x射线晶体学研究中，新的基于相位恢复的成像技术不断突破时空分辨率。因此本研讨会将聚焦相位恢复和超分辨成像的模型、理论和算法，主要围绕如下内容开展讨论：相位恢复基础理论进展，包括相位恢复基础数学理论，相位恢复算法以及稀疏表示理论等在相位恢复中的应用；基于深度学习的端到端相位恢复新方法、传统优化算法与机器学习相结合的新方向、基于深度生成模型获取图像先验以及训练数据生成；面向相位恢复问题的机器学习理论，包括可解释性、可靠性理论框架。此外，压缩感知是近年来发展迅速的研究领域，其与随机矩阵、解析数论等基础数学领域也密切相关。研讨会也将针对压缩感知中的理论基础和快速算法开展研讨，并研讨其中框架理论的数学基础。

会议日程

报告人简介及报告摘要

（按报告人姓氏拼音排序）

The Moments of Orientation Estimations Considering Molecular Symmetry in cryo-EM

包承龙

清华大学

摘要：CryoEM an invaluable technique for determining high-resolution three-dimensional structures of biological macromolecules using transmission particle images. In this talk, we introduce a novel method for estimating the mean and variance of orientations with molecular symmetry. Utilizing tools from non-unique games, we show that our proposed non-convex formulation can be simplified as a semi-definite programming problem. Moreover, we propose a novel rounding procedure to determine the representative values. Experimental results demonstrate that the proposed approach can find the global minima and the appropriate representatives with a high degree of probability.

报告人简介：包承龙，清华大学丘成桐数学科学中心助理教授。2014年博士毕业于新加坡国立大学数学系，2015年至2018年在新加坡国立大学数学系进行博士后研究。研究兴趣主要在图像处理的建模与大规模优化算法方面，担任SIAM Journal on Imaging Sciences 编委，已在顶级期刊和会议上发表学术论文 40余篇。 

Convergence Analysis of Nonlinear Kaczmarz Method for Systems of Nonlinear Equations with Component-wise Convex Mapping

陈冲

中国科学院数学与系统科学研究院

摘要：Motivated by a class of nonlinear imaging inverse problems, for instance, multispectral computed tomography (MSCT), we study the convergence theory of the nonlinear Kaczmarz method (NKM) for solving the system of nonlinear equations with component-wise convex mapping, namely, the function corresponding to each equation being convex. However, such kind of nonlinear mapping may not satisfy the commonly used component-wise tangential cone condition (TCC). For this purpose, we propose a novel condition named relative gradient discrepancy condition (RGDC), and make use of it to prove the convergence and even the convergence rate of the NKM with several general index selection strategies, where these strategies include cyclic strategy and maximum residual strategy. Particularly, we investigate the application of the NKM for solving nonlinear systems in MSCT image reconstruction. We prove that the nonlinear mapping in this context fulfills the proposed RGDC rather than the component-wise TCC, and provide a global convergence of the NKM based on the previously obtained results. Numerical experiments further illustrate the numerical convergence of the NKM for MSCT image reconstruction.

报告人简介：陈冲，中科院数学与系统科学研究院副研究员、博士生导师。2012 年于中科院数学院获计算数学博士学位，2015-2017 年在瑞典皇家理工学院数学系从事博士后研究。其研究兴趣包括医学成像反问题，图像处理，计算几何等，共发表学术论文二十多篇，研究成果主要发表在 SIAM J. Imaging Sci.、Inverse Problems、J. Comput. Phys.、Comput. Methods Appl. Mech. Engrg.等专业主流刊物，在科学出版社合著《图像重构的数值方法》专著一部。现任《计算数学》杂志编委。研究工作获国家自然科学基金委优秀青年科学基金资助。 

Signal and image restoration by non-convex methods

谌稳固

北京应用物理与计算数学研究所

摘要：Some new non-convex minimization models are introduced to investigate signal and image recovery from a certain number of noisy measurements by the proposed minimization models. Error bounds of robust image recovery from compressed measurements via the proposed minimization models are established, and the RIP based condition is improved compared with total variation (TV) minimization. Numerical results of image reconstruction demonstrate our theoretical results and illustrate the efficiency of the proposed TV type minimization models among state of-the-art methods.

报告人简介：谌稳固, 北京应用物理与计算数学研究所研究员, 博士生导师, 主要从事调和分析、非线性色散方程、大数据分析的理论及应用研究, 在Applied and Computational Harmonic Analysis, IEEE Transactions on Information Theory, Inverse Problems, Signal Processing, Journal of Computational and Applied Mathematics, IEEE Signal Processing Letter, Inverse Problems and Imaging, CPDE, JDE, Nonlinear Analysis: Real World Applications等学术刊物发表科研论文60余篇。

SVD-based graph Fourier transform on directed graphs

成诚

中山大学

摘要：Graph signal processing provides an innovative framework to process data on graphs. The widely used graph Fourier transform on the undirected graph is based on the eigen-decomposition of the Laplacian. In many engineering applications, the data is time-varying and pairwise interactions among agents of a network are not always mutual and equitable, such as the interaction data on a social network. Then the graph Fourier transform on directed graph is in demand and it should be designed to reflect the spectral characteristic for different directions, decompose graph signals into different frequency components, and to efficiently represent the graph signal by different modes of variation. In this talk, I will present our recent work on the graph Fourier transforms on directed graphs which are based on the singular value decompositions of the Laplacians.

报告人简介：成诚，2017年博士毕业于University of Central Florida(美国)，师从Xin Li 教授和 Qiyu Sun 教授，随后在 Duke University (joint appointment with SAMSI) 进行博士后研究，合作导师是 I. Daubechies  院士，现为中山大学数学学院副教授。成诚的研究方向是应用调和分析，其在相位恢复和图信号的分布式处理以及采样理论等方面展开了系统的研究，截至目前共发表论文 17 篇，其中包括期刊论文 14 篇，包括 Appl. Comput. Harmon. Anal.，J. Funct. Anal., J. Fourier Anal. Appl.，IEEE Trans. Signal Process.，Signal Process. ，IEEE Signal Process. Lett. 等。目前主持国自然基金面上项目一项，广东省自然基金面上项目一项。

Curvature regularization：models, algorithms and applications

段玉萍

北京师范大学

摘要：The geometric high-order regularization methods such as Euler’selatica, mean curvature, and Gaussian curvature, have been intensively studied during the last decades due to their abilities in preserving geometric properties including image edges, corners, and image contrast. However, the dilemma between restoration quality and computational efficiency is an essential roadblock for high-order methods. We propose novel curvature regularization models and develop fast multi-grid algorithms without sacrificing the accuracy for efficiency. Besides, we also extend the application of curvature energies for non-line-of-sight (NLOS) imaging. Both traditional and learnable curvature regularization model are developed for NLOS with under-scanning measurements.

报告人简介：段玉萍，2012 年在新加坡南洋理工大学大学取得计算数学博士学位，之后在新加坡科技研究局资讯通信研究院担任研究科学家。2016 年任天津大学应用数学中心教授，博士生导师，2023 年加入北京师范大学数学科学学院。主要研究方向包括变分图像处理方法、区域分解算法、模型驱动的深度学习和软组织形变仿真，已在 IEEE Transactions on Image Processing，IEEE Transactions on Medical Imaging，SIAM Journal on Imaging Sciences，Journal of Scientific Computing 等重要学术期刊和 CVPR，MICCAI，ISBI 等国际会议上发表研究论文五十多篇，已授权国际/国内专利 4 项，先后承担国家自然科学基金项目 2 项和天津市重大科技专项 1 项。

函数的稀疏多项式逼近

冯仁忠

北京航空航天大学

摘要：稀疏多项式以其计算量少和存储量少而受到人们的重视，在不确定性

量化、参数 PDEs 解和 PDE 解的逼近等方面得到了很好的应用。目前人们主要利用采样数据通过−最小化问题或贪婪算法获得函数的稀疏多项式逼近。对这些方法来说首先要解决的问题是稀疏多项式的精确恢复问题，然后扩展到一般连续函数或光滑函数的稀疏多项式逼近问题。 −最小化问题中的测量矩阵有多种生成方法，本报告从由 Gauss 积分点和权生成的离散正交系统中等概率地随机抽取m行生成测量矩阵，分析了此类测量矩阵的RIP性质，并利用其RIP性质给出了其对稀疏多项式的精确恢复保证；在 −最小化问题的约束条件中，误差的取值严重影响生成的稀疏多项式对函数f(x)的逼近误差，本报告将取成 N次多项式空间对函数f(x)的不同类型的最佳逼近误差，并给出了相应的稀疏多项式对函数的逼近误差。

报告人简介：冯仁忠，北京航空航天大学数学科学学院教授，博导。研究方向：数值逼近及其应用。

Divergence/curl-free quasi-interpolation

高文武

安徽大学

摘要：Divergence/curl-free interpolation has been extensively studied and widely used in approximating vector-valued functions that are divergence-free. However, so far the literature contains no treatment of divergence/curl-free quasi-interpolation. The aims of this talk are two-fold: to construct an analytically divergence-free quasi-interpolation scheme and to derive its simultaneous approximation orders to both the approximated function and its derivatives. To this end, we first explicitly construct a divergence-free matrix kernel based on polyharmonic splines and study its properties both in the spatial domain and Fourier domain. Then, with thisdivergence/curl-free matrix kernel, we construct a divergence/curl-free quasi-interpolation scheme defined in the whole space Rd for some positive integerd. We also derive corresponding approximation orders of quasi-interpolation to both the approximated divergence/curl-free function and its derivatives. Finally, by couplingdivergence/curl-free interpolation together with our divergence-free quasi-interpolation, we extend our construction to a divergence/curl-free quasi-interpolation scheme defined over a bounded domain.

报告人简介：高文武，2000年考入阜阳师范学院接受数学及应用数学本科教育，2004年考入大连理工大学计算数学专业硕士研究生，2009年考入复旦大学应用数学专业博士研究生，2012-2014年在上海宝钢研究院与复旦大学管理学院联合工作站从事士后工作，2018年-2019年在美国科罗拉多矿业大学应用数学与统计学做访问副教授。现为安徽大学大数据与统计学院统计学系教授、博士生导师、统计学博士点负责人、应用统计专硕硕士点负责人、“双带头人”教师党支部书记。研究工作主要聚焦在统计学与数据科学领域交叉方向的核心基础算法的构造理论及其应用如概率数值逼近、不确定量化、统计学习、无网格微分方程数值解等。先后获得国家自然科学基金青年项目、面上项目的资助，在SIAM Journal on Numerical Analysis(SINUM),SIAM Journal on Scientific Computing (SISC), Advances in Computational Mathematics, Numerical Algorithms, Applied Mathematical Modelling, Journal of Computational and Applied Mathematics 国际知名期刊上发表多篇学术论文。目前是：Foundations of Computational Mathematics, SIAM Journal on Numerical Analysis(SINUM),SIAM Journal on Scientific Computing (SISC), Advances in Computational Mathematics, Numerical Algorithms, Applied Mathematical Modelling, Journal of Computational and Applied Mathematics 等杂志的匿名审稿人。

对抗迁移视角下的图像深度模型鲁棒性研究

郭志昌

哈尔滨工业大学

摘要：对抗迁移的可转移性为黑盒攻击提供了一种有效的捷径，然而其成因尚不明确。尤其是目标对抗扰动的迁移更加困难。研究从样本密度的角度研究了图像分类网络中的对抗迁移性，理论和实验证明不同深度模型在每个类别的高样本密度区域（HSDR）具有更一致的性能，并进一步证明简单样本更倾向位于HSDR，从而给出了高效寻找HSDR样本的快速途径，据此通过目标类HSDR样本引导目标攻击，提出生成式目标攻击Easy Sample Matching Attack (ESMA)。

另一方面，深度神经网络 (DNNs) 在图像去噪领域相较于传统算法表现出了更优异的性能。然而，通过对大量主流深度去噪模型的对抗鲁棒性评估表明，去噪DNN在面对对抗攻击依旧会显示出普遍的脆弱性，并且它们在灰度和彩色图像上几乎共享相同的对抗样本集，这意味着对抗迁移在图像去噪DNN中依旧存在。为了进一步探究这样的可迁移集合的共性，提出衡量模型局部相似性的指标，称为鲁棒性相似度，我们发现非盲去噪模型之间具有较高的鲁棒性相似度，混合驱动模型也与纯数据驱动的非盲去噪模型具有较高的鲁棒性相似度，而数据驱动的非盲去噪模型是最具鲁棒性的。基于这样的观察，我们使用对抗训练来补充对对抗攻击的脆弱性，实验结果表明这有效地提升了去噪DNN的对抗鲁棒性。

报告人简介：郭志昌，男，理学博士，准聘教授，博士生导师。现任哈尔滨工业大学数学学院计算数学系副主任、中国工业与应用数学学会数学与医学交叉学科专业委员会委员、中国生物医学工程学会人工智能分会青年委员。主要从事偏微分方程及图像处理、人工智能（计算机视觉，大数据分析，股票趋势量化）研究工作。主持国家自然科学基金面上项目、黑龙江省自然科学基金、广东省基础与应用基础研究基金、国家自然科学基金青年基金、教育部新教师基金，哈尔滨工业大学校创新基金等项目；作为主要参与人参与国自然联合基金重点项目、黑龙江省基金重点项目、相关研究成果发表在SIAM、IEEE TIP、JMIV、JSC等高水平期刊上，累计发表论文40余篇，出版专著/教材3部，授权发明专利2项。

Semi-Supervised Deep Sobolev Regression: Estimation, Variable Selection and Beyond

焦雨领

武汉大学

摘要：We propose SDORE, a semi-supervised deep Sobolev regressor, for the nonparametric estimation of the underlying regression function and its gradient. SDORE employs deep neural networks to minimize empirical risk with gradient norm regularization, allowing computation of the gradient norm on unlabeled data. We conduct a comprehensive analysis of the convergence rates of SDORE and establish a minimax optimal rate for the regression function. Crucially, we also derive a convergence rate for the associated plug-in gradient estimator, even in the presence of significant domain shift. These theoretical findings offer valuable prior guidance for selecting regularization parameters and determining the size of the neural network, while showcasing the provable advantage of leveraging unlabeled data in semi-supervised learning. To the best of our knowledge, SDORE is the first provable neural network-based approach that simultaneously estimates the regression function and its gradient, with diverse applications including nonparametric variable selection and inverse problems. The effectiveness of SDORE is validated through an extensive range of numerical simulations and real data analysis.

报告人简介：焦雨领，武汉大学数学与统计学院副教授、博导。主要从事机器学习、科学计算的研究。相关工作发表在包括 SIAM J. Math. Anal.、SIAM J. Control Optim.、 SIAM J. Numer. Anal.、SIAM J. Sci. Comput.、SIAM J. Math. Data. Sci.、Appl. Comput. Harmon. Anal.、J. Mach. Learn. Res.、IEEE Trans. Inf. Theory、Ann. Stat.、J. Amer. Statist. Assoc.、Statist. Sci.、Inverse Probl.、IEEE Trans. Signal Process.、ICML、NeurIPS 等期刊和会议上。

Alternating Projection for Sparse Phase Retrieval with Outliers

李朋

兰州大学

摘要：In this talk, we focus on the nonlinear observations b=|Ax|+ f with orignal signal length n and number of measurements m, which is called (sparse) phase retrieval with outliers. Let the original signal has sparsity s and the outliers has the ratio t=pm with p<1. we consider the least square model with two variables x and f and solve it via an alternating projection algorithm.  We show that the measurements number m=O(max{ s/p, (s^2 log n)/(1-p) ) is sufficient for guaranteeing the exact recovery of both original sparse signal and outliers.

报告人简介：李朋，博士，兰州大学副教授，男, 1988年12月出生于湖北襄阳。李朋博士当前研究兴趣集中在使用数值逼近、数值代数、优化、统计等方法研究数据科学与机器学习的理论与算法，包括低秩矩阵恢复、非参数的统计估计等。他取得了一系列成果，在Inverse Problems, Signal Process, Comput. Math. Appl., J. Comput. Appl. Math.，等著名杂志发表学术成果近20篇。

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

李雨桐

天津师范大学

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.

报告人简介：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。

An Fast Numerical Approach for Over-parameterized Sparse Regularization

梁经纬  

上海交通大学

摘要：One difficulty in sparse regularized optimization problem is the non-smoothness of the objective function value, which brings obstacles to the adoption or theoretical analysis of high-order numerical schemes. In this talk, I’ll introduce an over-parameterization approach which transform the non-smooth problem into a smooth bi-level optimization problem. By combining with complexity-reduction technique (e.g. dimension reduction), we obtain an efficient numerical scheme which demonstrates impressive performance on several sparse regularization problems.

报告人简介：梁经纬，副教授，上海交通大学自然科学研究院，主要研究兴趣为非光滑优化，数学图像处理和数据科学等领域。在一阶算子分裂算法、随机优化算法和图像反问题等研究方向取得一定研究成果，发表在相关领域的高水平期刊会议。

On the reconstruction of medium conductivity by integral equation method based on the Levi function

刘继军

东南大学/南京应用数学中心

摘要：Consider an inverse problem of recovering the medium conductivity governed by an elliptic system, with partial information of the solution specified in some internal domain as inversion input. We firstly establish the uniqueness of this inverse problem and the conditional stability of H$\ddot{\text{o}}$lder type in internal domain in terms of the analytic extension of the solution. Then by representing the solution of  the direct problem with variable coefficient under the Levi function framework, this nonlinear inverse problem is reformulated as solving a linear integral system provided that the boundary value of the conductivity be known. Then this linear system is regularized to deal with the ill-posedness of the function extension, with an efficient numerical realization scheme for seeking the regularizing solution firstly for the density pair and then for the conductivity to be recovered. Numerical implementations are presented to show the validity of the proposed scheme.

报告人简介：刘继军，东南大学二级教授，博士生导师，享受国务院政府特殊津贴专家。现任东南大学丘成桐中心副主任，南京应用数学中心常务副主任，全国大学生数学建模竞赛组委会委员，中国工业与应用数学学会数学建模竞赛专业委员会委员，江苏省计算数学学会副理事长。国家精品资源共享课《数学建模与数学实验》主持人。历任日本东京大学访问教授，韩国延世大学访问教授，韩国庆熙大学IIRC访问研究员，西交利物浦大学外部考官，中国工业与应用数学学会常务理事，中国计算数学学会常务理事，江苏省工业与应用数学学会第五届、第六届理事会理事长。入选江苏省青蓝工程青年骨干教师，青蓝工程中青年学术带头人，江苏省333工程第三层次培养人选。获宝钢教育基金会全国优秀教师一等奖，作为主持人获江苏省教学成果一等奖、江苏省自然科学三等奖、教育部自然科学二等奖。

计算成像技术的变革性应用

刘金鹏

西安电子科技大学

摘要：光电成像技术是在工业时代发展起来的，在民用和军用中都发挥着重要作用。然而，传统的成像难以实现实际应用中系统更简化、探测距离更远、分辨率更高和成像信息更丰富等要求。计算光学成像技术集成了光学、数学和信息技术，通过信息编解码的方式突破了传统光学上的限制。报告深入分析了计算光学成像的发展现状，总结了计算光学成像的内涵。以偏振成像、三维成像、简化光学系统成像、合成孔径成像等几种典型的计算成像方法为例，以展示与传统成像方法相比的重大性能突破和应用边界拓展。此外，本报告中也提出了未来计算成像技术与实际应用结合的发展思路。

报告人简介：刘金鹏，副研究员，华山准聘副教授，硕士生导师，现工作于西安电子科技大学光电工程学院计算成像研究所。主要研究方向为强对抗环境下计算成像。近年来主持国家自然科学基金青年、国家重点项目子课题等多项国家及省部级项目，参与面上项目、863项目等课题。在散射成像、光场调控与分析等方面开展研究，并发表多篇OPTICS EXPRESS、OPTICS LETTERS等SCI期刊论文，任Scientific Report、OPTICS EXPRESS、Applied Optics等期刊审稿人。

Self-supervised Deep Learning Methods for Imaging

庞彤瑶

清华大学

摘要：Image restoration refers to recovering high-quality images from degraded or limited measurements, which has applications in many fields, such as science and medicine. Recently, deep learning has emerged as a prominent tool for many problems including image restoration. Most of the deep learning methods are supervised which requires large amount of paired training data including truth images. In this talk, I will introduce several self-supervised methods which only use the on-hand measurements for training while still showing comparable performance to supervised learning. These proposed self-supervised methods have great potential for real-world image restoration tasks, where it can be difficult to collect clean images and build high-quality training datasets.

报告人简介：庞彤瑶，现为清华大学丘成桐数学中心助理教授，2014年本科毕业于北京大学元培学院，2019年博士毕业于新加坡国立大学数学系，导师为沈佐伟和纪辉教授。其主要研究方向包括无监督深度学习算法，图像处理，深度生成模型等。

Weakly Supervised Medical Image Segmentation Based on Deep Threshold Geodesic Distance

庞志峰

河南大学

摘要：Interactive segmentation methods leveraging deep learning have recently garnered significant attention. One such technique is the U-net framework based on the U-shaped convolutional neural networks (UCNN) and their variants. However, these methods are limited in their ability to simultaneously capture both global and remote semantic information due to the restricted receptive domain caused by the intrinsic features of the convolution operation and the low quality images degraded by low contrast, inhomogeneous intensity, and high-level noise. To tackle these challenges, we present a novel coding method called Deep Threshold Geodesic Distance (DTGD) along with the U-net architecture. Specifically, our approach uses the DTGD in conjunction with the original image as input to construct a parallel network architecture so that the network contains information from both the image domain and the geodesic domain. We further employ Conditional Random Field Refinement (CRFR) to refine and improve the segmentation output. Our experimental results on various standard medical image dataset demonstrate that our proposed method outperforms several state-of-the-art segmentation methods in terms of segmentation accuracy and robustness.

报告人简介：庞志峰，河南大学教授，博导。南洋理工大学/香港城市大学博士后, 利物浦大学/香港中文大学/香港理工大学访问学者。目前兼任河南省数理医学学会副理事长，《CT 理论与应用研究》与《中国体视学与图像分析》编委。主持和参与省部级科研项目 11 项，发表学术论文近 50 篇，完成校企合作项目 2 项，授权专利 2 项。

域适应算法研究进展

彭亚新

上海大学

摘要：跨域数据分析一直是图像处理和人工智能中的难点问题，在图像分割、推荐系统和机器人决策等领域被广泛研究。跨域分析中的统计分布差异、遗忘灾难等问题亟待解决。我们将从特征提取和学习策略等方面介绍一些新的研究进展。

报告人简介：彭亚新，上海大学理学院数学系教授，博导，从事几何变分模型、统计学习的研究工作；并将统计学习、几何结构与优化算法相结合进行建模和求解；建立一系列度量学习检索、数据集匹配、语义分割的新算法，最终应用于医学、工业制造、交通等人工智能领域的数据挖掘和图像分析中。

借助于LLM有限推理能力的快慢思考的网络及其在机械臂操控中的应用

沈超敏

华东师范大学

摘要：The language-conditioned robotic manipulation aims to transfer natural language instructions into executable actions, from simple “pick-and-place” to tasks requiring intent recognition and visual reasoning. Inspired by the dual-process theory in cognitive science—which suggests two parallel systems of fast and slow thinking in human decision-making—we introduce Robotics with Fast and Slow Thinking (RFST), a framework that mimics human cognitive architecture to classify tasks and makes decisions on two systems based on instruction types. Our RFST consists of two key components: 1) an instruction discriminator to determine which system should be activated based on the current user’s instruction, and 2) a slow-thinking system that is comprised of a fine-tuned vision-language model aligned with the policy networks, which allow the robot to recognize user’s intention or perform reasoning tasks. To assess our methodology, we built a dataset featuring real-world trajectories, capturing actions ranging from spontaneous impulses to tasks requiring deliberate contemplation. Our results, both in simulation and real-world scenarios, confirm that our approach adeptly manages intricate tasks that demand intent recognition and reasoning.

报告人简介：沈超敏，华东师范大学计算机科学与技术学院副教授。长期从事机器学习的数学方法及其应用研究。主持国家自然基金面上项目，作为学术骨干承担973、国家自然基金重点项目等，发表学术论文40余篇; 是数学图像联盟 (Union of Mathematical Imaging, UMI) 秘书长、中国工业与应用数学学会数学与医学交叉学科专委会委员等。

Lower Estimations of Greedy Algorithms

沈益

浙江理工大学

摘要：Greedy Algorithms are often adopted to achieve sparse term elements from a dictionary to approximate the target function. A lot of previous work has studied the upper and lower bound of the convergence of greedy algorithms such as orthonormal matching pursuit, matching pursuit. In this talk, we provide some convergence analysis with explicit counter examples.

报告人简介：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。

人工智能生成与泛化的最优传输理论与方法

孙剑

西安交通大学

摘要：最优传输主要关注以最小代价实现两个概率测度之间的迁移或对齐。作为一种应用数学工具，其理论、算法与高效计算一直以来是数学与机器学习所关注的重要研究方向。本报告将从人工智能生成模型与泛化能力角度，介绍最优传输的基本模型，计算方法与神经网络高效实现。进一步介绍我们所提出的保持关键点关系的最优传输模型、算法及其所引导的人工智能生成模型，并介绍用于提升人工智能跨域泛化能力的最优传输分布对齐模型与算法。最后总结与思考最优传输对大模型的基础作用与可能的未来研究方向。

报告人简介：孙剑，西安交通大学数学与统计学院教授，获得国家杰出青年科学基金。长期从事人工智能（尤其是图像和医学影像分析）中的数学模型与算法研究，主要包括成像反问题与医学辅助诊断、解决人工智能泛化性瓶颈问题的基础模型与算法研究等，相关成果发表于 IEEE TPAMI, IJCV, MIA, NeurIPS, CVPR, ICCV,MICCAI 等；曾在微软亚洲研究院、法国巴黎高师、法国国家信息与自动化研究院等从事博士后或访问学者工作；获陕西省自然科学奖一等奖；担任教育部科技委委员、计算机视觉领域顶级国际期刊 IJCV 编委、ICCV/ECCV/MICCAI 等领域主席。

A Meshless Solver for Blood Flow Simulations in Elastic Vessels Using Physics-Informed Neural Network

台雪成

Norwegian Research Centre 

摘要：Investigating blood flow in the cardiovascular system is crucial for assessing cardiovascular health. Computational approaches offer some non-invasive alternatives to measure blood flow dynamics. Numerical simulations based on traditional methods such as finite-element and other numerical discretizations have been extensively studied and have yielded excellent results. However, adapting these methods to real-life simulations remains a complex task. In this paper, we propose a method that offers flexibility and can efficiently handle real-life simulations. We suggest utilizing the physics-informed neural network (PINN) to solve the Navier-Stokes equation in a deformable domain, specifically addressing the simulation of blood flow in elastic vessels. Our approach models blood flow using an incompressible, viscous Navier-Stokes equation in an Arbitrary Lagrangian-Eulerian form. The mechanical model for the vessel wall structure is formulated by an equation of Newton’s second law of momentum and linear elasticity to the force exerted by the fluid flow. Our method is a mesh-free approach that eliminates the need for discretization and meshing of the computational domain. This makes it highly efficient in solving simulations involving complex geometries. Additionally, with the availability of well-developed open-source machine learning framework packages and parallel modules, our method can easily be accelerated through GPU computing and parallel computing. To evaluate our approach, we conducted experiments on regular cylinder vessels as well as vessels with plaque on their walls. We compared our results to a solution calculated by Finite Element Methods using a dense grid and small time steps, which we considered as the ground truth solution. We report the relative error and the time consumed to solve the problem, highlighting the advantages of our method

This talk is based on a joint work with Raymond Chan and Han Zhang.

报告人简介：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。台老师的研究领域主要 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。

Multistability of Small Reaction Networks

唐晓弦

北京航空航天大学

摘要：The multistability problem of biochemical reaction systems is crucial for understanding basic phenomena such as decision-making process in cellular signaling. Mathematically, it is a challenging real quantifier elimination problem. We present some recent progress on multistability of small reaction networks. 1) For reaction networks with two reactions (possibly reversible), we find the multistable networks those have the minimum numbers of reactants and species. 2) For reaction networks with one-dimensional stoichiometric subspaces, we give the relation between the maximum numbers of stable steady states and steady states.

报告人简介：唐晓弦，2014年毕业于北京大学数学科学学院并取得博士学位。其后，她先后在韩国国家数学研究所，德国不来梅大学以及美国德州农工大学从事博士后研究， 现为北京航空航天大学副教授。主要研究方向是符号计算，研究兴趣为计算代数几何在生物与统计中的应用。在Journal of Symbolic Computation, Biometrika, SIAM Journal on Discrete Mathematics,  Journal of Mathematical Biology, 及Bulletin of Mathematical Biology等国际高水平期刊上发表论文。

Towards arbitrary resolution in hyperspectral and multispectral image fusion via self-supervised representations

王超

南方科技大学

摘要：The fusion of a low-resolution hyperspectral image (HSI) with a high-resolution (HR) multispectral image has emerged as an effective technique for achieving HSI super-resolution (SR). Previous studies have mainly concentrated on estimating the posterior distribution of the latent HR HSI, leveraging an appropriate image prior and likelihood computed from the discrepancy between the latent HSI and observed images. Low rankness stands out for preserving latent HSI characteristics through matrix decomposition among the various priors. However, this method only enhances resolution within the dimensions of the two modalities. To overcome this limitation, we propose a novel continuous matrix function representation by integrating two neural representations into the decomposition, capturing spatial and spectral information, respectively. This approach enables us to harness both the low-rankness from the decomposition and the continuity from neural representation in a self-supervised manner. Theoretically, we prove the low-rank property and Lipschitz continuity in the proposed matrix function decomposition. Experimentally, our method significantly surpasses existing techniques and achieves user-desired resolutions without the need for neural network retraining.

报告人简介：王超，南方科技大学统计与数据科学系助理教授，博士生导师。2018年毕业于香港中文大学数学系，在美国德州大学和加州大学共积累近三年海外博士后工作经验。其研究方向主要为图像处理、科学计算与交叉学科的数据科学，并在理论和算法上取得了一些创新性的研究成果。近年来以第一作者或通讯作者在 TIP, SISC, SIIMS, ICML, IP等国际期刊及学术会议上发表了十几篇论文。在2022年全球计算机视觉（CVPR）的研讨会获得最佳论文，在2017年获得第十五届中国工业与应用数学学会（CSIAM）年会最佳论文，并在2018与2020年分别获得全球SIAM学生/青年学者会议基金奖。

Untrained neural network embedded Fourier phase retrieval from few measurements

王红霞

国防科技大学

摘要：Fourier phase retrieval (FPR) is a challenging task used in various applications to recover an unknown signal from its Fourier phaseless measurements. FPR with few measurements helps reduce time and hardware costs but suffers from severe ill-posedness. Recently, untrained neural networks have offered new approaches by introducing learned priors to alleviate ill-posedness without requiring external data. However, they are computationally expensive and not ideal for reconstructing high-frequency structures in images. In this talk we propose an untrained neural network (NN) embedded FPR algorithm, based on the alternating direction method of multipliers. Specifically, we use a generative network to represent the image to be recovered, which confines the image to the space defined by the network structure. Additionally, total variation regularization is imposed to facilitate the preservation of image edges and local structures. Furthermore, to reduce the computational cost mainly caused by the updates of NN’s parameters, we develop an accelerated algorithm that adaptively trades off between explicit and implicit regularization. We theoretically analyze that the proposed algorithm can converge to a stationary point of the objective function under mild conditions. Experimental results indicate that the proposed algorithm outperforms existing untrained-NN-based algorithms with fewer computational resources and even performs competitively against trained-NN-based algorithms.

报告人简介：王红霞，博士，国防科技大学理学院数学系教授，计算数学方向博士生导师，湖南省计算数学与应用软件学会副理事长。长期从事信息处理中的新型算法研究。主持国家自然科学基金项目4项、科技部重点研发项目课题、军队173重点项目课题等10项。指导研究生获部委级优秀学位论文奖2篇，获军队科技进步二等奖、湖南省教学成果一等奖和国家教学成果二等奖。

Nonconvex Robust High-Order Tensor Completion Using Randomized Low-Rank Approximation

王建军

西南大学

摘要：Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD based low-rank approximation, which suffers from high computational costs when dealing with large-scale tensor data. Moreover, most of them are only applicable to third-order tensors. Against these issues, in this article, two efficient low rank tensor approximation approaches fusing random projection techniques are first devised under the order-d (d >= 3) T-SVD framework. Theoretical results on error bounds for the proposed randomized algorithms are provided. On this basis, we then further investigate the robust high-order tensor completion problem, in which a double nonconvex model along with its corresponding fast optimization algorithms with convergence guarantees are developed. Experimental results on large-scale synthetic and real tensor data illustrate that the proposed method outperforms other state-of-the-art approaches in terms of both computational efficiency and estimated precision.

报告人简介：王建军，博士，教授（研究员）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。

格理论、算法及应用简介

温金明

暨南大学

摘要：格的研究源于1611年开普勒提出的猜想，格在通信、信号处理、全球定位系统、数论、优化等领域具有重要应用。本报告首先介绍几类格重要常数界的优化、LLL等格规约算法的应用，然后介绍求解最近向量问题、最短向量问题、逐次极小问题等格困难问题的高效算法，最后介绍格困难问题求解中的一些挑战和瓶颈。

报告人简介：温金明，暨南大学三级教授、博导、国家高层次青年人才、广东省青年珠江学者，主持国家自然科学基金面上项目2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9月，温教授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，以第一作者/通讯作者在Applied and Computational Harmonic Analysis、IEEE Transactions on Information Theory、 IEEE Transactions on Signal Processing等期刊和会议发表50余篇学术论文。

Selecting Regularization Parameters for Nuclear Norm Type Minimization Problems

文有为

湖南师范大学

摘要：In this talk, we consider the regularization parameter selection in nuclear norm type minimization problems.  It can be reformulated into a constrained nuclear norm minimization problem, where the bound $\eta$ of the constraint is explicitly given or can be estimated by the probability distribution of the noise. We show that the F-norm of the discrepancy between the minimizer and the observed matrix is a strictly increasing function of the regularization parameter $\lambda$. From that we derive a closed-form solution for $\lambda$ in terms of $\eta$. The result can be used to solve the constrained nuclear-norm-type minimization problem when $\eta$ is given. For the unconstrained nuclear-norm-type regularized problems, our result allows us to automatically choose a suitable regularization parameter by using the discrepancy principle. Numerical experiments with both synthetic data and real MRI data are performed to validate the proposed approach.

报告人简介：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。

Sparse Phase Retrieval with Partial Convolutional Measurements

夏羽

杭州师范大学

摘要：We consider the sparse phase retrieval problem, that is, recovering an unknown s-sparse signal from the intensity-only measurements. Specifically, we focus on the problem of recovering x from the observations that are cyclically convoluted with some specific kernel. This model is motivated by real-world applications in optics and communications. We provide that if the convolutional kernel is generated by a random Gaussian vector and the number of subsampled measurements is on the order of spolylog(n), one can recover x up to a global phase provided that the initialization estimator is around x. Here we discuss the behavior of sparse convolutional phase retrieval under more realistic measurements, as opposed to independent Gaussian measurements.

报告人简介：夏羽, 杭州师范大学数学学院副教授。主要从事信号图像处理中的数学理论和算法研究。现阶段在应用数学及数学与信息交叉领域发表一系列学术论文，包括Applied and Computational Harmonic Analysis, Inverse Problems, IEEE Transactions on Information Theory, IEEE Transactions on Signal Processing等，主持国家自然科学基金项目两项。

Random star discrepancy based on stratified sampling

冼军

中山大学

摘要：In this talk, we consider the estimation of the expected star discrepancy. First, the expected star discrepancy upper bound is obtained for the jittered sampling. This improves the upper bound derived in B. Doerr(Math. Comp. \textbf{91}(2022) 1871-1892). Second, the strong partition principle of the star discrepancy version is obtained, which proves that the expected star discrepancy of stratified sampling is smaller than that of simple random sampling for any equal-measure partition. This partially solves open question 2 in M. Kiderlen and F. Pausinger(J. Complexity \textbf{70}(2022) 101616). In the end, we consider the estimation of the weighted star discrepancy. A better weighted probabilistic star discrepancy bound than the use of plain Monte Carlo point sets is provided in terms of convergence order, i.e., the convergence order of the weighted probabilistic bound is improved from $O(N^{-\frac{1}{2}})$ to $O(N^{-\frac{1}{2}-\frac{1}{2d}}\cdot \ln^{\frac{1}{2}} {N})$.

报告人简介：冼军, 男, 博士, 教授, 博士生导师, 现为中山大学数学学院教授、中国数学会理事、广东省数学会理事、广东省工业与应用数学学会副理事长。2004年毕业于中山大学获理学博士学位, 同年进入浙江大学数学博士后流动站, 2006年博士后出站至今在中山大学数学学院工作。主要研究方向为小波分析与应用调和分析、采样理论及其在信号处理中的应用。在Appl. Comput. Harmon. Anal., Inverse Probl., J. Fourier Anal. Appl., Proc. Amer. Math. Soc., J. Approx. Theory等国内外主流专业期刊发表多篇关于信号的采样与重构的理论及其应用的论文, 部分结果获得同行们的关注。曾作为项目负责人主持多项国家级和省部级基金项目。

人工智能算法在医学图像处理中的应用

许艳

中国海洋大学

摘要：弱人工智能时代，研究依赖于数据、算力与算法。因此数据科学领域的算法研发也会随着数据的可获得以及硬件的更迭升级，而产生质的蜕变。深度学习算法发展，能够有效的针对对高维数据降维。然而，在降维过程中，如何有效的特征提取, 如何获得有效的表征，成为深度学习能否广泛应用的核心问题。我们将介绍本团队在深度学习可解释性、自监督学习框架等领域的理论与应用研究成果，结合智慧医疗影像数据、函数型数据、介绍人工智能算法在医学影像领域的最新进展与应用。

报告人简介：许艳，中国海洋大学数学科学学院教授。中国海洋大学名师工程讲席教授。中国海洋大学工业互联网研究院首席教授、高智能家电国家创新中心特聘顾问、青岛金融研究院首席研究员、东北财经大学国民经济工程实验室（北京智库）首席研究员。入选富布赖特学者、辽宁省百千万人才工程、辽宁省教学名师、辽宁省优秀人才。美国Hofstra 大学商学院兼职助理教授；华盛顿大学经济学、西安大略大学经济学院、密歇根州立大学、清华大学统计研究中心、香港科技大学理学院与大数据研究中心访问学者。Mathematics Letter 编委、《理论数学前沿》副主编、教育部学位与研究生教育发展中心通讯评议专家、中国现场统计研究会多元分析分会常务理事、大连市科协八大代表、大连市女科技工作者代表。主持完成3项国家自然科学基金、主持教育部社科规划项目、辽宁省高等学校优秀人才支持计划、辽宁省教育厅科学研究项目、中央财政支持地方高校建设项目、博士后面上项目、博士后特别资助、大连市重点项目等多项国家以及省部级课题。作为主要参与人参与国家社科重大项目和国家自然科学基金重点项目各一项。作为任务负责人参与国家重点研发项目一项。荣获“大连市青年科技奖”（辽宁省政府以及科协组织部联合颁发，副省级科技奖）、辽宁省自然科学学术成果二等奖，大连市自然科学学术成果三等奖等多个奖项。主持2项国家级课程和3项省级一流课程。

Signal Recovery on an Algebraic Variety from Linear Samples

许志强

中国科学院数学与系统科学研究院

摘要：Signal recovery on an algebraic variety is an essential problem in many applications. Many well-known problems, such as compressed sensing, phase retrieval and low-rank matrix recovery, can be viewed as a signal recovery problem on an algebraic variety. A fundamental question is: How many measurements are needed to recover (almost) all the signals lying on an algebraic variety? In this talk, we focus on the problems of phase retrieval and low-rank matrix recovery. We use the tools from algebraic geometry to study the question and present many results to address it in many different settings. We also introduce the performance of several numerical models for solving these problems.

报告人简介：许志强，中国科学院数学与系统科学研究院研究员。研究领域包括逼近论、计算调和分析、数值分析，尤其对采样理论，压缩感知，框架理论以及相位恢复等领域感兴趣。一方面，他将纯粹数学中的研究方法引入到计算调和分析，系统发展了相位复原的代数簇方法，从而在信号量化、压缩感知和相位复原等一些困难问题得到实质性进展；另一方面，将逼近论中样条函数和代数多面体理论相结，从而解决了多个猜想和公开问题。其研究成果发表在多个领域的顶尖期刊上，如JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY（基础数学），APPLIED AND COMPUTATIONAL HARMONIC ANALYSI（计算数学），IEEE Transcations on Information Theory（信息论）。他主持多项国家自然科学基金，包括2020年获得国家杰出青年科学基金，2014年获得国家优秀青年科学基金。

Interlacing Polynomial Method for Matrix Approximation via Generalized Column and Row Selection

徐孜立

香港科技大学

摘要：In this talk I will introduce our recent work on the spectral norm version of the Generalized Column and Row Subset Selection (GCRSS) problem. Given a target matrix A, the objective of GCRSS is to select a column submatrix from the source matrix B and a row submatrix from the source matrix C, with the aim of minimizing the spectral norm of the residual matrix. By employing the interlacing polynomials method, we show that the largest root of the expected characteristic polynomial of the residual matrix serves as an upper bound on the smallest spectral norm of the residual matrix. We estimate this root for two specific GCRSS case: the Generalized Column Subset Selection (GCSS) problem and the submatrix selection problem. In the GCSS scenario, we connect the expected characteristic polynomials to the convolution of multi-affine polynomials, leading to the derivation of the first provable reconstruction bound on the spectral norm of the residual matrix for the GCSS problem. In the submatrix selection scenario, we show that any square matrix A contains a submatrix with a small spectral norm. Unlike previous studies that have produced comparable results for very special cases where the matrix is either a zero-diagonal or a positive semidefinite matrix, our results apply universally to any matrix A.

报告人简介：徐孜立，博士毕业于中科院数学与系统科学研究院，导师许志强研究员。目前在香港科技大学做博士后，合作导师蔡剑锋教授。研究方向为框架理论、势能极小化问题、球面设计、矩阵子集选择问题等。目前在国际著名期刊如Appl. Comput. Hamon. Anal. 等发表论文多篇。

Extrapolated Plug-and-Play Three-Operator Splitting Methods for Nonconvex Optimization with Applications to Image Restoration

曾铁勇

香港中文大学

摘要：This talk investigates the convergence properties and applications of the three-operator splitting method, also known as Davis-Yin splitting (DYS) method, integrated with extrapolation and Plugand-Play (PnP) denoiser within a nonconvex framework. We first propose an extrapolated DYS method to effectively solve a class of structural nonconvex optimization problems that involve minimizing the sum of three possible nonconvex functions. Our approach provides an algorithmic framework that encompasses both extrapolated forward-backward splitting and extrapolated DouglasRachford splitting methods. To establish the convergence of the proposed method, we rigorously analyze its behavior based on the Kurdyka- Lojasiewicz property, subject to some tight parameter conditions. Moreover, we introduce two extrapolated PnP-DYS methods with convergence guarantee, where the traditional regularization prior is replaced by a gradient step-based denoiser. This denoiser is designed using a differentiable neural network and can be reformulated as the proximal operator of a specific nonconvex functional. We conduct extensive experiments on image deblurring and image super-resolution problems, where our results showcase the advantage of the extrapolation strategy and the superior performance of the learning-based model that incorporates the PnP denoiser in terms of achieving high-quality recovery images.

报告人简介：曾铁勇，香港中文大学教授、数学人工智能中心主任，于2000年本科毕业于北京大学，2007年巴黎第十三大学获得博士学位。主要研究领域包括数据科学，优化理论，图像处理，反问题等。在优化、图像处理、反问题的国际一流杂志SIAM Journal on Imaging Sciences, SIAM Journal on Scientific Computing, International Journal of Computer Vision, Journal of Scientific Computing，IEEE PAMI, IEEE TNNLS, IEEE Transactions on Image Processing，Pattern Recognition，Journal of Mathematical Imaging and Vision等发表过近八十篇SCI论文。

相干调制成像方法和其性能提升的数学思考

张福才

南方科技大学

摘要：相干调制成像通过在样品后引入波前调制，极大地提升了对一般复透过率样品的相位恢复的性能。大量的实验和模拟表明，投影关系为非傅里叶变换的相位恢复问题更适合用投影迭代算法求解。目前其数学基础还没有完全建立。包括优化的调制器需要具有的特性。本报告将介绍该方法的算法和实验进展，提出对数学机理的需求。

报告人简介：张福才，南方科技大学副教授。早期从事分布式光纤传感器和数字全息方面的研究。目前的主要研究方向是无透镜相干成像技术，特别是针对X射线和相干电子源等缺乏高质量光学成像的相干辐射源的显微技术的开发。较早参与了扫描相干成像术（Ptychography) 的研究。独立提出利用波前调制解决相位问题中解不唯一问题的新思路，改进了传统相干衍射成像方法的性能及拓展了其应用领域。目前正尝试在电子显微镜和自由电子X射线激光器上实现该方案，及将其应用到生物学和材料科学上。在Nature Communications, Physical Review Letters 等主流期刊发表论文多篇。

Deep Unrolled Reconstructions for CT imaging and Remote Sensing Blind Deblurring

张建平

湘潭大学

摘要：Proximal gradient-based optimization is a widely used approach for addressing the inverse problem in CT imaging and remote sensing blind deblurring, known for its simplicity in implementation. However, this method often results in significant artifacts during image reconstruction and restoration. A common approach to alleviate these artifacts is the fine-tuning of the regularization parameter, though this can lead to higher computational demands and may not always be effective. In this talk, we introduce a novel unrolled blind deblurring learning framework that employs alternating iterations of shrinkage thresholds. This framework updates blurring kernels and images, with a theoretical foundation in network design, emphasizing the learning of deep geometric prior features to improve image restoration. Furthermore, we introduce a deep geometric incremental learning framework that utilizes the second Nesterov proximal gradient optimization for CT reconstruction. Our comprehensive end-to-end network is capable of effectively learning both high- and low-frequency image features and theoretically ensures the reconstruction of geometric texture details from initial linear reconstructions. We compare the reconstruction performance of the proposed methods with existing state-of-the-art methods to demonstrate their superiority.

报告人简介：张建平，男，理学博士，教授，博士生导师，于 2013 年 2 月加入湘潭大学数学与计算科学学院教师团队。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。

同步辐射扫描成像全栈式数据处理管道研究

张一

中科院高能所

摘要：断层扫描是一种揭示物质内部结构和功能特性的三维表征技术。新一代同步辐射光源等大科学装置的投入使用，进一步拓展了断层成像的技术边界，也导致了数据量和数据维度的爆炸式增长和数据处理流程复杂度的急剧增加。如今，在应对断层扫描成像的大数据挑战、数据处理管线全流程优化中，深度学习技术展现出巨大的潜力。

报告人简介：张一 ，男 ，博导，中国科学院高能物理研究所。研究领域：同步辐射实验控制与数据采集软件开发、多维度衍射/散射成像方法学研究、分级生物材料结构与力学性能研究。

Single-pixel optical fire

张子邦

暨南大学

摘要：We report a single-pixel computational optical imaging technique that can see through flames. Through structured illumination and the associated image recovery algorithm, flames can be computationally muted in the images recovered. Consequently, an optical fire “distinguisher” is achieved. The reported technique operates at the visible waveband and can see a dynamic scene through flames at the video frame rate in real-time.

报告人简介：张子邦，男，1988年生，广东省广州人，暨南大学光电工程系副教授。2014年和2017年在暨南大学分别获光学硕士和生物医学物理与生物医学信息技术博士学位，毕业后在暨南大学光电工程系任职，主要从事突破传统成像模式的新型光学成像技术研究。代表性工作为傅里叶单像素成像技术，该工作被评获2015中国光学重要成果奖，相关的一系列工作先后在Nature Communications、Optica、Optics Letters等期刊上发表。承担国家自然科学基金，广州市自然科学基金。目前担任学术期刊Photonics的客席编辑。

Stability of the Frank-Wolfe algorithm for Compressible Signals

钟轶君

浙江理工大学

摘要：The Frank-Wolfe algorithm and its variations are very practical for large-scale optimization problems appearing in signal processing, machine learning, and image restoration. We are concerned with the performance of the Frank-Wolfe algorithm in the framework of sparse representations. We provide a unified stability analysis of the Frank-Wolfe algorithm applied to l1 constrained least squares. Moreover, we show a sharp restricted isometry property condition for the support recovery of sparse vectors in relatively noise-free environments. Several numerical examples are shown to verify the accuracy and stability of the Frank-Wolfe algorithm for sparse recovery problems. The idea in this paper can also be applied to other l1 constrained problems such as phase retrieval.

报告人简介：钟轶君，浙江理工大学理学院数学科学系讲师，2013年毕业于大连理工大学数学科学学院，获运筹学与控制论专业理学硕士学位，2018年毕业于大连理工大学数学科学学院，获计算数学专业理学博士学位，师从李崇君教授。主要研究方向为稀疏逼近、稀疏恢复算法、计算几何等。主持国家自然科学基金青年基金项目，已在J. Comput. Appl. Math、J. Comput. Math等期刊发表学术论文多篇。

光学合成孔径成像：从干涉到非干涉

左超

南京理工大学

摘要：本报告将介绍傅里叶叠层成像（Fourier ptychography）这一新兴的合成孔径计算成像技术在非干涉定量相位成像、光强衍射层析成像以及远场超分辨成像方面的最新研究进展，并简要讨论合成孔径成像技术未来的发展方向。

报告人简介：左超，教授、博士生导师，南京理工大学智能计算成像实验室（SCILab: www.scilaboratory.com）学术带头人、南京理工大学智智能计算成像研究院首席科学家。研究方向为计算光学成像与光信息处理技术。发表SCI论文200余篇，其中40余篇论文被选作Light、Optica、AP等期刊封面论文，20篇论文入选ESI高被引/热点论文，论文被引超过15000次。国际光学工程学会/美国光学学会/英国物理学会会士（SPIE/Optica/IOP Fellow），科睿唯安全球高被引科学家。