复旦大学数学学院2011年《数据科学》暑期学校

7月11日-7月22日

由高等学校数学研究与高等人才培养中心，复旦大学资助，上海市现代应用数学重点实验室承办的2011年《数据科学》暑期学校将于2011年7月11日-7月22日在复旦大学举行.邀请的演讲人及演讲题目、摘要如下。欢迎高年级大学生、研究生及青年教师参加。报名请与

summerschool@fudan.edu.cn

高卫国教授，在6月30日之前联系。

复旦大学数学学院2011年《数据科学》暑期学校学术委员会

李大潜（复旦）, 鄂维南（普林斯顿）,沈佐伟（新加坡）,吴宗敏

复旦大学数学学院2011年《数据科学》暑期学校组织委员会（复旦） 高卫国、陆立强

###################################################################### 题目：High-dimensional statistical learning and inference 演讲人：Jianqing Fan （Princeton University）

摘要：Technological innovations have revolutionized the process of scientific research and knowledge discovery. The availability of massive data and challenges from frontiers of research and development have reshaped statistical thinking, data analysis and theoretical studies. The challenges of dimensionality arise from diverse fields of sciences and the humanities, ranging from computational biology and health studies to economics and finance. A comprehensive overview will be given on statistical challenges with vast dimensionality. The impact of dimensionality and spurious correlation will be addressed. What makes the high-dimensional

problems feasible is the notion of sparisty. While the dimensionality can be much higher than the sample size, the intrinsic dimensionality is much smaller. A unified framework expoiting sparsity will be outlined. Other related problems with vast-dimensionality are also discussed. High-dimensional classifications and related echniques will be unveiled.

题目：MRA based wavelet frame and applications

演讲人：Zuowei Shen （National University of Singapore）

摘要：One of the major driving forces in the area of applied and computational harmonic analysis during the last two decades is the evelopment and the analysis of redundant systems that produce sparse approximations for classes of functions of interest. Such redundant systems include wavelet frames, ridgelets, curvelets and shearlets, to name a few. This talk focuses on tight wavelet frames that are derived from multiresolution analysis and their applications in imaging. The pillar of this theory is the unitary extension principle and its various generalizations, hence we will first give a brief survey on the development of extension principles. The extension principles allow for systematic constructions of wavelet frames that can be tailored to, and effectively used in, various problems

in imaging science. We will discuss some of these applications of wavelet frames. The discussion will include frame-based image analysis and restorations, image inpainting, image denosing, image deblurring and blind deblurring, image decomposition, segmentation and CT image reconstruction.

题目： Mathematics of Data: Geometric and Topological Methods 演讲人：Yao Yuan （Beijing University）

摘要： In the past decade, there emerges a new direction in applied mathematics and statistical machine learning, which tends to exploit some traditional mathematics to capture nonlinear variation of data distribution in high dimensional spaces. Such a perspective includes various geometric embedding techniques, such as the locally linear embedding (LLE), ISOMAP, and diffusion maps etc. Most recently, computational topology techniques also began to enter data science. In this lecture series, we will give a systematic treatment of these techniques, in a broad sense of mathematics of data with an emphasis on geometric and topological approaches. However, the topics discussed here are of highly dynamic, whence the active participation of graduate students are welcome in this direction of research.

题目：Selected Mathematics Topics in Visual Information Processing 演讲人：Ji Hui （National University of Singapore）

摘要：This course focuses on the introduction to various mathematical concepts and numerical methods with wide applications in imaging and vision. The goal is to expose students to several important mathematical topics with strong relevance to visual data processing, in particular image processing/analysis. The students will also learn how to apply these methods to solve real problems in imaging and vision. This course is an inter-disciplinary course that emphasizes both rigorous treatment in mathematics and motivations from real-world applications. The following topics will be covered in the course: 1. Continuous and discrete Fourier transform 2. Convolution and time-invariant linear system. 3. Discrete cosine transform, JPEG and Image Compression 4. Sampling theory and Anti-aliasing 5. Digital filter theory and image de-convolution 6. Filter bank, wavelet and image denoising 7. Gabor transforms; scale-space theory and Image/Texture Analysis. 8. Regularization methods for solving ill-posed problems in image restoration