应002全讯白菜网数学系邀请，美国佛罗里达大学陈韵梅教授、英国利物浦大学陈柯教授、香港浸会大学曾铁勇教授将于近期来访数学系并做学术报告。欢迎感兴趣的老师和同学参加。

报告题目一：Kernel Methods: From Image Analysis to Deep Learning

报告时间：2017年5月20日（周六），活动中心331，上午9:30—10:30

报告摘要：In this talk we first present our work on kernel methods for multi-modal image registration and non-parametric image segmentation. The main idea of these methods is using the theory of reproducing kernel Hilbert space (RKHS) to find the nonlinear maps, which can map the images of different modalities to the ones whose intensities are linearly related, by optimizing a finite number of parameters. Inspired by these results, we will further discuss if we could combine the flexibility of kernel methods with the structural and scalable properties of deep neural networks to improve the learning ability of both methods.

 报告人简介：

陈韵梅，复旦大学理学博士、美国佛罗里达大学终身教授，曾获中华人民共和国国家自然科学三等奖、中华人民共和国教育部科技进步一等奖、美国发明专利三项。最近五年来，陈韵梅教授主要致力于数学和图像科学这一交叉学科的研究。研究课题不仅包括图像分析中数学模型的建立与数值方法的发展，而且对其潜在的数学理论进行了进一步的探索。她在国际最顶尖数学期刊《Inventiones mathematicae》, 《Communications on Pure and Applied Mathematics》等上发表多篇具有重要影响的学术论文。陈韵梅教授被公认为偏微分方程与图像处理领域内的世界级科学家，在国际上具有崇高的学术地位。

报告题目二：On Optimization Based Multilevel Algorithms for Variational Image Segmentation Models

       报告时间：2017年5月21日（周日），活动中心331，下午13:30—14:10

     报告摘要：Variational active contour models have become very popular in recent years, especially global variational models which segment all objects in an image. Given a set of user-defined prior points, selective variational models aim to segment selectively one object only. We are concerned with fast solution of the latter models. Time marching methods with semi-implicit schemes and an additive operator splitting method are used frequently to solve the resulting Euler Lagrange equations derived from these models. For images of moderate size, such methods are effective. However, to process images of large size, urgent need exists in developing fast iterative solvers. Here we propose an optimization based multilevel algorithm for efficiently solving a class of selective segmentation models. It also applies to solution of global segmentation models. In level set function formulation, our first variant of the proposed multilevel algorithm has the expected optimal O(N logN) efficiency. However modified localized models are proposed to exploit the local nature of segmentation contours and consequently our second variant after further acceleration is up to practically super-optimal efficiency O(sqrt(N)logN). Numerical results show that good segmentation quality isobtained and as expected excellent efficiency observed in reducing computational time.

报告人简介：

陈柯，英国利物浦大学终身教授，辽宁省百人计划入选者，大连理工大学“海天学者”，英国IMA Fellow、御批数学家。陈柯教授作为CMIT和LCMH创新团队负责人，主要研究方向为计算数学、应用数学、图像处理、医疗应用等，在SIAM Journal on Imaging Sciences、IEEE Transactions on Image Processing、Journal of Computational Physics等国际权威期刊上发表超过120余篇学术论文，其中顶级期刊论文30多篇；出版5本专著，总撰写章节累计超过45章节；作为项目主持人或参与人完成或在研42项英国科研项目（总经费超过3百万英镑）；20多次在国际会议上作邀请报告或特邀报告，包括大会报告。近年来，陈柯教授受聘为多个国际SCI杂志编委，包括：Journal of Numerical Algorithms、Journal of Mathematical Research and Applications、International Journal of Computer Mathematics等。

      报告题目三：Convex a Non-Convex Optimization in Image Recovery and Segmentation

     报告时间：2017年5月21日（周日），活动中心331，上午10:20—11:00

     报告摘要：In this talk, we present some recent progress on variational approaches for image recovery and segmentation. First, a new convex variational model for restoring images degraded by blur and Rician noise is proposed. Based on the statistical property of the noise, a quadratic penalty function technique is utilized to obtain a strictly convex model under mild condition, which ensures the uniqueness of the solution and the stabilization  of the algorithm. Numerical results are presented to demonstrate the good performance of our approach. The idea of convex relaxation is then extended to other image recovery and segmentation tasks.  Finally, we also discuss the image recovery issue in the framework of dictionary learning if time permitted.

报告人简介：

曾铁勇，博士，香港浸会大学副教授，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 Transactions on Image Processing，Pattern Recognition，Journal of Mathematical Imaging and Vision等发表过多篇SCI论文。