Frame Toolbox for Bioimaging, Biometrics and Robust Transmission

用于生物成像、生物识别和稳健传输的框架工具箱

• 批准号: 0515152
• 负责人: Jelena Kovacevic
• 金额: --
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-01 至 2008-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0515152&HistoricalAwards=false
• 关键词: Frame; Toolbox; Bioimaging; Biometrics; Robust

In the past couple of decades, multiresolution techniques in signal and image processing have revolutionized the field. Most of the multiresolution techniques in use are nonredundant, that is, the underlying mathematical structures used are bases. However, many of today's applications require some redundancy in the system.The requirement of redundancy requires a mathematical structure more general than bases, termed frames. Although the initial work on frames dates back to the 1950s, frames have become more popular only recently, mostly due to emerging applications requiring tools which provide redundancy. A fair amount of work has already been done on frames; however, their level of maturity is nowhere near that of wavelets. This is about to change as a host of applications requires redundancy offered by frames; the theory needs to follow fast.This research addresses gaps in the current knowledge and solves some of the open questions in frames. These are related to the characterization of certain classes as well as the construction of a frame toolbox motivated by problems in bioimaging, biometrics and robust transmission. Developing the frame theory to this extent brings frames to the level of maturity of wavelets and significantly expands the multiresolution toolbox.

在过去的几十年中，信号和图像处理中的多解决技术彻底改变了该领域。大多数使用的多分辨率技术都是非冗余的，也就是说，使用的基本数学结构是碱。但是，当今的许多应用程序都需要在系统中进行一些冗余。冗余的要求需要比基础更通用的数学结构，称为框架。尽管最初的框架工作可以追溯到1950年代，但直到最近才变得更加流行，这主要是由于需要提供冗余工具的新兴应用程序。在框架上已经完成了相当多的工作。但是，它们的成熟水平远不及小波。这将要改变，因为众多应用程序需要框架提供的冗余；该理论需要快速遵循。这项研究解决了当前知识中的差距，并解决了一些框架中的一些开放问题。这些与某些类别的表征以及由生物成像，生物识别和鲁棒传播中的问题促进的框架工具箱的构建有关。开发框架理论在此范围内将框架带到小波的成熟度水平，并显着扩展多分辨率工具箱。