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报告人: 蔡剑锋 助理教授
University of Iowa
报告题目：Data-driven tight frame construction and image denoising
报告时间：2013年06月13日下午16:30开始
报告地点：行政楼703
报告摘要: Sparsity based
regularization methods for image restoration assume that the
underlying image
has a good sparse approximation under a certain system. Such a
system can be a
basis, a frame, or a general over-complete dictionary. One widely
used class of
such systems in image restoration are wavelet tight frames. There
have been
enduring efforts on seeking wavelet tight frames under which a
certain class of
functions or images can have a good sparse approximation. However,
the
structure of images varies greatly in practice and a system working
well for
one type of images may not work for another. I will present a
method that
derives a discrete tight frame system from the input image itself
to provide a
better sparse approximation to the input image. Such an adaptive
tight frame
construction scheme is applied to image denoising by constructing a
tight frame
tailored to the given noisy data. The experiments showed that the
proposed
approach performs better in image denoising than those wavelet
tight frames
designed for a class of images. Moreover, by ensuring the system
derived from
our approach is always a tight frame, our approach also runs much
faster than
some other adaptive over-complete dictionary based approaches with
comparable
PSNR performance.
报告人简介：蔡剑锋，2007年在香港中文大学获数学博士学位，获得香港最佳博士论文奖；2007-2009年在新加坡国立大学工作；2009-2011年在美国加州大学洛杉矶分校(UCLA)担任CAM
Assistant Adjunct Professor；2011年至今，在美国爱荷华大学(University of
Iowa)数学系任助理教授。蔡剑锋博士研究兴趣为计算与应用调和分析及其在成像科学中的应用，多次受邀在国际学术会议上做报告，目前担任多种重要数学期刊审稿人。蔡剑锋博士2012年以第一作者在数学顶级期刊J.
Amer. Math. Soc发表论文，目前已发表高水平SCI论文30多篇，其合作者包括Stanley Osher, Shen
zuowei, Raymond
Chan, Emmanuel Candes等，论文总被引用达一千多次。