地点:双清综合楼C654
时间:2024年10月10日下午16:00-17:00
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TITLE: Low-rank optimization on matrix and tensor varieties
SPEAKER: Bin Gao (AMSS, Chinese Academy of Sciences)
ABSTRACT:
In the realm of tensor optimization, low-rank tensor decomposition, particularly Tucker decomposition, stands as a pivotal technique for reducing the number of parameters and for saving storage. We embark on an exploration of Tucker tensor varieties—the set of tensors with bounded Tucker rank—in which the geometry is notably more intricate than the well-explored geometry of matrix varieties. We give an explicit parametrization of the tangent cone of Tucker tensor varieties and leverage its geometry to develop provable gradient-related line-search methods for optimization on Tucker tensor varieties. The search directions are computed from approximate projections of antigradient onto the tangent cone, which circumvents the calculation of intractable metric projections. To the best of our knowledge, this is the first work concerning geometry and optimization on Tucker tensor varieties. In practice, low-rank tensor optimization suffers from the difficulty of choosing a reliable rank parameter. To this end, we incorporate the established geometry and propose a Tucker rank-adaptive method that is capable of identifying an appropriate rank during iterations while the convergence is also guaranteed. Numerical experiments on tensor completion with synthetic and real-world datasets reveal that the proposed methods are in favor of recovering performance over other state-of-the-art methods. Moreover, the rank-adaptive method performs the best across various rank parameter selections and is indeed able to find an appropriate rank.
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个人简介:高斌,中国科学院数学与系统科学研究院计算数学所副研究员。2019年毕业于中国科学院数学与系统科学研究院。曾先后赴比利时、德国从事博士后研究。其主要研究兴趣是矩阵和张量流形上的优化算法。曾获中国科学院院长特别奖、钟家庆数学奖。受到中国科协青托工程、中科院青年百人、基金委海外优青等项目资助。
地点:双清综合楼C654
时间:2024年10月23日下午3:00-4:00
Title: CUQI – Computational Uncertainty Quantification for Inverse Problems
Speaker:Per Christian Hansen, Technical University of Denmark
Abstract: Since 2019 we have worked on developing a practical framework for applying uncertainty quantification to inverse problems.
Our work contributes to the basis for UQ studies of a range of linear and nonlinear inverse problems with different priors and noise models. Specifically, building on the Bayesian framework we develop a modeling and computational platform, including an abstraction layer aimed at non-experts, which is implemented in the python software package CUQIpy.
In this talk I highlight some of our results and methods, with examples from X-ray computed tomography (CT). I describe how we handle uncertain projection angles, how we include structural priors tailored to the geometry of the scanned object, and how we use a goal-oriented approach to compute inclusion boundaries and their roughness. I also briefly describe our software package.
This is joint work with all the members of the CUQI project:https://sites.dtu.dk/cuqi The work is supported by a grant from the Villum Foundation.
Short bio: Per Christian Hansen is professor of scientific computing at the Technical University of Denmark (DTU). He received his PhD in 1985 and his Dr. Techn. (“habilitation”) in 1996, both from DTU. He is a SIAM Fellow, and he is currently heading the CUQI research project at DTU, which aims to create a modeling and computational platform to perform uncertainty quantification for inverse problems.
Before starting his professorship in 1996, Prof. Hansen was with Copenhagen University (1985–1988) and the Danish University Computing Center UNI•C (1988–1996). In 1986 he was at Stanford University, supported by a Fulbright grant, and I 1989 he was at UCLA. More recently, in 2020 he was at the National Institute of Informatics in Tokyo, supported by the JSPS.
His specialization is numerical analysis, numerical linear algebra, iterative reconstruction, uncertainty quantification, and computational methods for inverse problems – with applications in computed tomography, image deblurring, and signal analysis.
He is the author/coauthor of 5 books, and he has published 120+ scientific papers and 7 software packages.
时间:2024年10月23日下午4:00-5:00
Speaker: Yiqiu Dong
Title: Sampling Strategies in Sparse Bayesian Inference
Abstract: Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization. Although the solutions to many such regularized inverse problems can be considered as points of maximum probability of well-chosen posterior distributions, samples from these distributions are generally not sparse. In this talk, we present a sampling strategy for an implicitly defined probability distribution that combines the effects of sparsity imposing regularization with Gaussian distributions. It extends the randomize-then-optimize (RTO) method to sampling from implicitly described continuous probability distributions. We study the properties of these regularized distributions, and compare the proposed method with Langevin-based methods, which are often used for sampling high-dimensional densities.
Short bio: Yiqiu Dong was born in 1980 in Shandong, China. She received the B.Sc. degree in mathematics from Yantai University, Yantai, China, in 2002 and the Ph.D. degree in mathematics from Peking University under the supervision by Prof. Shufang Xu and Prof. Raymond Chan (Lingnan University, Hong Kong), Beijing, China, in 2007. She is currently associate professor in the Technical University of Denmark. Her research areas include inverse problem and variational methods, uncertianty quantification, mathematical imaging and optimization methods.
时间:7月11日下午4-5
地点:双清8楼B06
题目:在原子尺度上看生命:给蛋白和细胞做个CT
报告人:李雪明,副教授,生命科学学院
摘要:
冷冻电子显微学技术,简称冷冻电镜技术,在最近十年取得了一系列的技术突破,被称为“分辨率革命”,实现了对生物大分子复合物的原子或近原子分辨率结构解析。冷冻电镜技术为生物学家提供了在近生理状态下观察生物大分子原子组成结构的最直接方法,促进了对蛋白质大分子机器功能机制的理解,推动了基于结构的药物设计等领域的快速发展。随着AI技术的兴起,冷冻电镜技术为基于AI的蛋白质结构预测和药物设计提供了最直接最精准的实验数据基础。未来的冷冻电镜技术将目标定位于细胞结构及其中原位生物大分子的高分辨率结构,推动从原子分辨率水平上来理解生命的结构基础。冷冻电镜技术是一个多学科交叉的技术,涉及物理、数学、计算机和生物学等多个领域的技术整合。在本次讲座中,我将沿着冷冻电镜技术发展的时间线介绍多学科技术的融合,以及对相关技术的思考和展望。
个人简介:
李雪明,清华大学生命科学学院副教授,博士生导师,曾入选中组部“青年千人”,获香港求是科技基金会“求是杰出青年学者”奖和国家自然科学基金委优秀青年基金资助,中组部“万人计划”青年领军人才。2009年在中科院物理研究所获博士学位,之后赴美国加州大学旧金山分校从事博士后研究。2013年,李雪明在电子计数探测技术和电镜图像漂移修正算法方面的研究工作取得突破,为冷冻电镜技术的“分辨率革命”做出了重大贡献。李雪明也曾是最早的将通用图形处理器GPU引入冷冻电镜领域的研究者。2014年回国后,李雪明引入多项其他领域的先进技术,包括人工智能中的深度学习和电子工程中的粒子滤波算法,还发展了一系列针对蛋白微晶电子衍射结构解析的新技术,为实现自动化和更高分辨率的冷冻电镜结构解析系统奠定了基础。近年来,李雪明实验室的研究逐渐转向细胞的冷冻电子断层三维重构技术及其应用上来,希望能够实现对从组织到完整细胞或细胞器的纳米甚至亚纳米分辨率结构的三维重构,并能够在细胞中直接测定生物大分子的原子分辨率结构以及生物大分子之间的相互作用关系,也有望推动冷冻电镜技术在药物设计及医疗诊断领域中的应用。
时间:7月12日上午10-11
地点:双清8楼B06
报告人:Bin Han (University of Alberta)
Title: Directional (Quasi)-tight Wavelet Framelets for Image Processing
Abstract: Directional representation systems can effectively capture edge singularities for many high-dimensional problems such as image processing. In this talk, we first discuss directional complex tight framelets and their applications to image/video processing. However, constructing compactly supported multivariate tight framelets is known to be a challenging problem because it is linked to sum of squares and factorization of multivariate Laurent polynomials in algebraic geometry. To circumvent this difficulty, next we introduce the notion of quasi-tight framelets, which behaves almost identical to a tight framelet. From an arbitrary compactly supported multivariate refinable function (such as refinable box splines) with a general dilation matrix, we constructively prove that we can always derive a directional compactly supported quasi-tight framelet with vanishing moments. Moreover, any 1D wavelets or framelets can be adapted into bounded intervals. Consequently, their tensor products can avoid the boundary effects and can be applied to many problems such as manifold data processing and spherical data processing
Short bio: Bin Han is a professor in the Department of Mathematical and Statistical Sciences at the University of Alberta. He got his bachelor's degree from Fudan University in 1991, a master's degree from the Institute of Mathematics, Academia Sinica in 1994, and his Ph.D. from the University of Alberta in 1998. His research interests include computational mathematics, applied and computational harmonic analysis, and signal and image processing. He has published over 100 papers in various top journals in applied mathematics and serves on the editorial boards of several journals, such as Applied and Computational Harmonic Analysis and the Journal of Approximation Theory.
Title: Amnesia Effects in Complex Light Scattering
Speaker:Qihang Zhang (Tsinghua University)
Time:7月4日(周四)下午4-5
Venue:双清综合楼627
Abstract: Disordered media, such as fog, powder, emulsion, and biological tissue, induce complex distortion of light, resulting in intricate speckle patterns. The memory effect, a key speckle correlation, reveals the translational invariance of the scattered field for thin-layer media. The memory effect aids in understanding, manipulating, and reconstructing the field, forming the basis of applications such as imaging through turbid materials, complex beam shaping, and surface characterization. However, neglecting decorrelation in the memory effect becomes a bottleneck in these applications, particularly in the multi-scattering regime. In this work, we report an "amnesia effect" in complex scattering systems, which provides an analytical formula for speckle decorrelation under general conditions. The amnesia effect predicts that the decorrelation of back-scattered light is a linear combination of decorrelations from thin-layer scattering and volumetric scattering. This model achieves state-of-the-art accuracy even for strong and multi-scattering cases, potentially providing an advanced forward model for various inverse problems. As a proof-of-concept, we present two examples, model-based particle size estimation and reconstruction of the incident beam profile, to validate this improvement. Our conclusions incorporate a wide range of systems—however thin-layer, multi-layer or bulk materials—and apply to all complex wave scattering problems.
Bio: Qihang Zhang is currently a postdoc at Tsinghua University. He got his bachelor’s degree from the physics department of Tsinghua University in 2018 and got his Ph.D. from MIT electrical engineering and computer science department in 2023. He works on computational optics and develops novel approaches to combine machine learning and physical systems in different scenarios. His works were published in Nature Communications, Optics Letters. Some related work was also reported by MIT News.
时间:6月20日 下午 16:00-17:00
地点:双清综合楼654
题目:深度学习超分辨显微镜技术开发与应用
主讲人:李栋 清华大学生命科学学院
摘要:成像技术一直是推动生物医学领域发展的重要驱动力。在众多成像技术中,光学显微镜是唯一能够在活体条件下对任意蛋白分子进行连续追踪的技术方法。近年来,以超分辨显微镜为代表的技术进步,开启了在更高时空精度研究生命活动的大门。但需要注意的是,在对活体生物样品进行连续成像时,许多超分辨成像技术依然面临严重的局限和挑战。这是因为得到超分辨图像往往需要较高的激发光功率和较长的图像采集时间。这些因素都会造成超分辨活细胞成像性能的显著下降。本报告将介绍李栋课题组针对上述问题开展的高时空分辨成像技术研制工作。在显微镜硬件方面:开发了多模态结构光超分辨显微镜,以及晶格光片超分辨显微镜系统,集成了TIRF-SIM、GI-SIM、Nonlinear-SIM、3D-SIM等在内的多种成像模式,实现了在活细胞条件下对多种生物过程进行高速、多色、长时程超分辨成像;在超分辨图像重建软件方面:提出了傅立叶域注意力机制的特征图提取方法,以此开发了傅立叶域注意力卷积神经网络,以及合理化深度学习超分辨成像等技术方法,能够在低信噪比条件下获得与传统超分辨显微镜技术媲美的成像效果,从而显著扩展了传统超分辨显微镜的适用范围。
李栋,清华大学生命科学学院教授;2006年毕业于浙江大学光电信息工程学系,获工学学士学位;2011年毕业于香港科技大学获电子与计算机工程学系,获博士学位;2011-2015年在美国霍华德休斯医学研究所从事超分辨显微镜技术开发的博士后研究。目前,李栋研究员从事光学显微成像技术的开发与生命科学应用研究,特别是开发适于活体、高速、长时程、低损伤的超分辨荧光显微镜成像技术。首创了条纹激活非线性结构光显微镜、掠入射结构光超分辨显微镜,以及合理化深度学习超分辨成像等技术方法。代表性工作发表在Cell、Science、Nature Biotechnology、Nature Methods、Molecular Cell、Developmental Cell等期刊。