框架理论在图像和信号处理中的应用综述
Review on the Application of Frame Theory in Image and Signal Processing
DOI: 10.12677/CSA.2019.92043, PDF,    国家自然科学基金支持
作者: 王莲子, 庄晓东*：青岛大学电子信息学院，山东 青岛
关键词: 框架理论；图像处理；紧框架；信号重构；Frame Theory； Image Processing； Tight Frame； Signal Reconstruction
摘要: 小波分析是傅里叶变换发展史上的突破性的发展，其基础理论涉及到数字信号处理、泛函分析、傅里叶变换等多个方面。框架理论是小波分析的一个重要内容，随着小波分析的快速发展，框架理论逐渐成为研究的热点。本文对近年来的框架理论在信号与图像处理中的应用的文献进行了分类与总结，对框架概念、基本性质、框架边界、偶框架的计算以及应用进行了概述，最后做出了总结。
Abstract: Wavelet analysis is a breakthrough in the history of Fourier development. Its basic theory involves digital signal processing, functional analysis, Fourier transform and other aspects. Frame theory is an important content of wavelet analysis. With the rapid development of wavelet analysis, frame theory has gradually become a heated topic. This paper classifies and summarizes the literature on the application of frame theory in signal and image processing in recent years, summarizes the concept of frame, basic properties, frame boundary, calculation and application of dual frame, and finally makes a summary.
文章引用：王莲子, 庄晓东. 框架理论在图像和信号处理中的应用综述[J]. 计算机科学与应用, 2019, 9(2): 384-392. https://doi.org/10.12677/CSA.2019.92043

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