邢唷> BDA欹 餜 ,bjbj碫碫2.<<k cccccwww8$w42444444$; XicVVVXcc4Vcc2V2p羿痂 w$0]!]!]!cP"=UiXX"VVVV]! ):  Y鎒'Yf[pef[f[b2011t^ 0penc褃f[ 0慺gf[!h 7g11錯-7g22錯 1u貧I{f[!hpef[xvzN貧I{篘Mb鵚{Q-N胈 Y鎒'Yf[D崺R Nwm^皊鉔擽(upef[蛻筽瀃寶b濺剉2011t^ 0penc褃f[ 0慺gf[!h\嶯2011t^7g11錯-7g22錯(W Y鎒'Yf[>NL.愾媱vo矉篘蔛o矉槝顅0Xd亯俌 N0"k螐貧t^'Yf[u0xvzu蔛R梩^Ye^耂燫0 T鲖N summerschool@fudan.edu.cn 貧kS齎Ye坈 (W6g30錯KNMRT鹼0 Y鎒'Yf[pef[f[b2011t^ 0penc褃f[ 0慺gf[!hf[/g訷XTO Ng'Y\o Y鎒 , 戶~WSnf梘痚 ,坙POO癳燫aW ,4T梉Oe Y鎒'Yf[pef[f[b2011t^ 0penc褃f[ 0慺gf[!h膥莮訷XTO Y鎒 貧kS齎0F査z:_ ###################################################################### 槝顅High-dimensional statistical learning and inference o矉篘Jianqing Fan Princeton University Xd亯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.槝顅MRA based wavelet frame and applications o矉篘Zuowei Shen National University of Singapore Xd亯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.槝顅 Mathematics of Data: Geometric and Topological Methods o矉篘Yao Yuan Beijing University Xd亯 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. 槝顅Selected Mathematics Topics in Visual Information Processing o矉篘Ji Hui National University of Singapore Xd亯This course f.0HJl  " : B D v x ~ 镝镄僵晞vhWh処@;/hu'4hmCJaJo( h阧Io(hh0Jh蘟B*CJaJo(ph h阧IhmB*CJaJo(phhmB*CJaJo(phh阧IB*CJaJo(ph h阧Ih阧IB*CJaJo(ph'h阧Ih阧I0J5丅*CJaJo(ph'h阧IhY8+0J5丅*CJaJo(ph$h阧IhY8+0J5丅*CJaJph h阧IhB*CJaJo(phh阧IB*CJaJo(ph h阧Ih蘟B*CJaJo(ph0HD x   \ l h X:v $1$a$gd%gdmgd%$a$gd阧I~      H j l h p   ] ^  鲫鲫尥勘勘勘勘客縼蓖papapapapapapapah阧Ih%B*CJaJph h阧Ih%B*CJaJo(ph hmh阧IB*CJaJo(ph h阧IhmB*CJaJo(phh蘟B*CJaJo(phh阧IB*CJaJo(phhmB*CJaJo(ph h阧Ih阧IB*CJaJo(phhu'4h阧ICJaJo(hu'4hmCJaJo(h_p=CJaJo(&  X Y -.st9:X`vz:<$%FG  hjv   镟镟镟镟镟镟镟镟镟镟镟镟镟镟镟镟镟镟镟镟镟镟镟镟镟镟诛囡囡囡囡囡囡嗲镟h阧IhCJaJo(h阧Ih蘟B*CJaJphh阧Ih%aJo(h阧Ih%B*CJaJph h阧Ih%B*CJaJo(phG (++,,,,,, , , ,蹁靥亓劁舶拨灇灇灇灇h]0-jh]0-Uh阧IhU_aJo(Uh阧Ih%B*CJaJphh阧Ih%CJaJh阧Ih蘟CJaJo(h阧Ih%CJaJo( h阧Ih%B*CJaJo(phh阧IhCJaJM*|*** +?+k+++++,,,,,, , , , ,gdgd%gdocuses 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. 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