Mathematical Sciences: Wavelets and their Applications to Neural Network Theory, Vision, and Image Processing

数学科学：小波及其在神经网络理论、视觉和图像处理中的应用

• 批准号: 9410859
• 负责人: Mark Kon
• 金额: $ 6万
• 依托单位: Trustees of Boston University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9410859&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Wavelets; their; Applications

9410859 Kon The investigator and his colleagues study wavelets and their applications to neural network theory and processing of visual images. It has been shown recently that wavelets are useful as activation functions in neural networks, permitting faster adaptation to required tasks than do sigmoidal activation functions, in common use up to now. The success of wavelet methods has already been impressively demonstrated in important optimization problems using radial basis functions. The work of this project develops better theoretical underpinnings for the construction of neural nets that learn efficiently, and studies minimal complexities of neural nets that emulate "intelligent" tasks, e.g., recognition of visual images. The investigators also study the construction of wavelet-based algorithms for image compression. They examine the optimization of signal compression, aiming at an improved theoretical understanding of how such signal compression works from the standpoint of the mapping between functions and their wavelet transforms. Applications of the mathematics proposed here are closely related to the creation of "intelligent" systems using neural network technology. This technology in many ways emulates the operation of biological nervous systems. The present work is based on indications that the actions of biological neurons have in some cases been too well emulated in artificial neural systems. It has been shown in the work of Girosi and Poggio and others that attaining desired behavior in neural networks can be better achieved with networks that have "localized activation functions," i.e., ones for which output eventually decreases with very large inputs. An additional issue related to effecting proper input-output behavior using neural networks is knowledge of the basic complexity of certain desired tasks, and how neural networks can best achieve this level of complexity. Such tasks (e.g., the visual recognition of object s) can already be performed by biological neural networks, and have a complexity that can be defined and studied in a relatively precise way, to determine how complicated artificial neural networks need to be in order to emulate the behaviors of the biological networks. In addition, the work on signal compression using wavelets has a two-fold impact. The first involves the improvement of techniques for compression, e.g., storage of large quantities of video, audio or other data on compact media (such as compact discs, hard disks, or random access memory). The second is related to the fact that if such data are compressed to smaller sizes, certain kinds of information may be extracted from them more easily. For example, it is easier to find evidence of an irregular heartbeat (or precursors to arhythmia) using a computer if the cardiological data have been compressed in a way that allows them to be more easily manipulated. These and other applications have made the data compression issues that are studied here an area with high priority in mathematical signal processing.

9410859 Kon 研究人员和他的同事研究小波及其在神经网络理论和视觉图像处理中的应用。 最近已经表明，小波是有用的神经网络中的激活函数，允许更快地适应所需的任务比S形激活函数，在目前常用的。 小波方法的成功已经在使用径向基函数的重要优化问题中得到了令人印象深刻的证明。 该项目的工作为构建有效学习的神经网络开发了更好的理论基础，并研究了模拟“智能”任务的神经网络的最小复杂性，例如，视觉图像的识别。 研究人员还研究了基于小波的图像压缩算法的建设。 他们研究了信号压缩的优化，旨在从函数及其小波变换之间的映射的角度来提高对这种信号压缩如何工作的理论理解。 这里提出的数学应用与使用神经网络技术创建“智能”系统密切相关。 这项技术在许多方面模仿了生物神经系统的运作。 目前的工作是基于生物神经元的行动，在某些情况下，太好地模仿人工神经系统的迹象。 在Girosi和Poggio等人的工作中已经表明，在神经网络中获得期望的行为可以更好地通过具有“局部激活函数”的网络来实现，即，产出最终会随着投入的增加而减少的情况。 与使用神经网络实现适当的输入-输出行为相关的另一个问题是某些期望任务的基本复杂性的知识，以及神经网络如何才能最好地实现这种复杂性水平。 这些任务（例如，物体的视觉识别已经可以由生物神经网络执行，并且具有可以以相对精确的方式定义和研究的复杂性，以确定人工神经网络需要有多复杂，以便模拟生物网络的行为。 此外，使用小波进行信号压缩的工作具有双重影响。 第一个涉及压缩技术的改进，例如，将大量视频、音频或其他数据存储在压缩介质（如光盘、硬盘或随机存取存储器）上。 第二个问题是，如果将这些数据压缩到较小的尺寸，则可以更容易地从其中提取某些种类的信息。 例如，如果心脏数据经过压缩，可以更容易地进行操作，那么使用计算机就更容易找到不规则心跳（或心律失常的前兆）的证据。 这些和其他应用程序的数据压缩问题，在这里研究的数学信号处理领域具有很高的优先级。