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Multi-wavelet frames and applications to harmonic analysis

多小波框架及其在调和分析中的应用

基本信息

批准号：
16340035
负责人：
ARAI Hitoshi
金额：
$ 5.38万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2006
项目状态：
已结题

项目摘要

Main themes of this research project are (multi-) wavelet frames and harmonic analysis. The head investigator, Arai, studied wavelet frames and applications to vision science. In particular Arai constructed new wavelet frames which are appropriate to studying vision science (with S. Arai). These wavelet frames will give basis of constructing computational models of human's visual system. In addition, Arai studied also practical applications to image processing. Furthermore he has constructed a computational model of color perception, and gave computer simulation of illusions related color vision. Arai has studied also the mechanism of appearance of visual illusions. In particular, he proposed a new general scheme for discrete wavelet analysis of vision. It is widely believed that visual illusions will provide us a key in order to understand how our visual system carries out visual information processing. From this reason, over the past 100 years, many studies of visual illusion have be … More en made. However as for several illusions, their mechanisms are not yet well understood. In this research program Arai obtained nonlinear models of the early vision by using wavelet frames, and investigated mathematical mechanism of appearance of a certain illusion. More specifically, Arai constructed filter banks modeled after the function of the striate cortex in human's brain, and using these systems Arai made several computer simulations which indicate how our visual system produces visual illusions. By his research the mechanisms of several visual illusions can be explained by a mathematical unified way. If an image is inputted to Arai's system and if it outputs an image with illusion, then we can conclude that it is (they are) caused by processing in V1. Kanjin studied harmonic analysis of systems orthogonal functions. For example he proved boundedness of Cesaro operators on Lp and Hp. Nakamura studied local smoothing effect of analytic wave front sets. Yoshida studied sampling problem for stochastic differential equations. Tachizawa studied some weighted function spaces from viewpoint of wavelet theory. Less

本课题的主要研究内容是（多）小波框架与谐波分析.首席研究员Arai研究了小波框架及其在视觉科学中的应用。特别是Arai构造了新的小波框架，适合于研究视觉科学（与S。Arai）。这些小波框架将为建立人类视觉系统的计算模型奠定基础。此外，新井还研究了图像处理的实际应用。此外，他还建立了色觉的计算模型，并给出了色觉错觉的计算机模拟。Arai还研究了视觉错觉出现的机制。特别是，他提出了一个新的通用方案离散小波分析的视觉。人们普遍认为，视错觉将为我们理解视觉系统如何进行视觉信息处理提供一把钥匙。基于这个原因，在过去的100年里，许多关于视错觉的研究都是 ...更多信息恩做的。然而，对于一些错觉，其机制尚未得到很好的理解。在本研究计划中，新井利用小波框架获得了早期视觉的非线性模型，并研究了某种错觉出现的数学机制。更具体地说，新井构建了模仿人类大脑中纹状体皮层功能的滤波器组，并使用这些系统进行了几次计算机模拟，这些模拟表明我们的视觉系统如何产生视觉错觉。通过他的研究，几种视错觉的机制可以用数学的统一方法来解释。如果一个图像被输入到新井的系统中，如果它输出一个带有错觉的图像，那么我们可以得出结论，这是（它们是）由V1中的处理引起的。Kanjin研究了系统正交函数的调和分析。例如，他证明有界的塞萨罗运营商的Lp和Hp。中村研究了解析波前集的局部平滑效应。Yoshida研究了随机微分方程的抽样问题。立泽从小波理论的角度研究了一些加权函数空间。少