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

该研究项目的主要主题是（多）小波框架和谐波分析。主管Arai的首席研究人员研究了视力科学的小波框架和应用。特别是Arai构建了适合研究视觉科学（与S. arai）的新小波框架。这些小波框架将提供构建人类视觉系统的计算模型的基础。此外，Arai还研究了图像处理的实际应用。此外，他还构建了色彩知觉的计算模型，并给出了与幻觉相关的彩色视觉模拟。 Arai还研究了视觉错觉的出现机制。特别是，他提出了一种新的通用计划，以进行视觉分析。人们普遍认为，视觉错觉将为我们提供一个关键，以了解我们的视觉系统如何进行视觉信息处理。源自这个原因，在过去的100年中，许多视觉幻觉的研究已经……更加努力。但是，至于几种幻想，它们的机制尚未得到充分理解。在该研究计划中，Arai通过使用小波框架获得了早期视力的非线性模型，并研究了某种幻觉的数学机理。更具体地说，Arai构建了以人类大脑中策略皮质功能建模的过滤库，并使用这些系统进行了几个计算机模拟，这表明我们的视觉系统如何产生视觉错觉。通过他的研究，可以通过数学统一的方式来解释几种视觉错觉的机制。如果将图像输入到Arai的系统中，并且它以幻想输出图像，则可以包含它是由V1中的处理引起的（它们是）。 Kanjin研究了系统正交函数的谐波分析。例如，他在LP和HP上提供了Cesaro运营商的界限。 Nakamura Studio研究了分析波前组的局部平滑效果。 Yoshida研究了随机微分方程的抽样问题。 Tachizawa从小波理论的角度研究了一些加权功能空间。较少的