Adaptive Estimation in Wavelet Image Compression: Thresholding and Quantization

随着互联网应用和多媒体通信需求的爆炸性增长，图像压缩已经成为信号处理和通信中最重要的领域之一。压缩良好的图像接近原始图像，但存储空间要小得多，或者传输速度更快。事实上，网络计算趋势正在朝着用于网上冲浪的高质量图像和用于视频会议的实时视频的方向发展，而压缩对于它们的实时传输和合理的小内存存储是必要的。近年来，在图像压缩方面积累了大量的工程智慧和启发式算法，而自适应(针对图像的局部特征)被发现是有效图像压缩的关键。这项研究遵循的是统计学中许多(如果不是全部)重要发展的基础方法。也就是说，它的目的是从一个应用领域--(小波)图像压缩中找出问题，在统计框架中制定解决方案，并在这个框架中寻找与原始图像压缩问题相关的答案和见解。一方面，本研究使用和扩展了现代统计估计理论；另一方面，它总结或形式化了工程启发式。因此，它在图像压缩和统计估计文献之间架起了一座桥梁。研究人员正在从去噪和压缩的角度对小波图像编码的自适应阈值方法进行研究。他们还在研究基于量化数据的估计和自适应量化方法，用于一般数字信号压缩，包括基于小波的图像压缩。统计研究为图像的自适应小波阈值处理建立了一个框架，并为基于量化数据估计的一般统计问题提供了解决方案，这些数据在现代通信时代大量使用。一种努力程度声明。在建议的支持水平下，私人投资委员会将尽一切努力满足项目最初的范围和努力水平。

With the exploding demand in Internet applications and multimedia communications, image compression has become one of the most important areas in signal processing and communication. Well compressed images are close to the original images, but take much less space to store or are faster to transmit. Indeed, the network computing trend is moving towards high quality images for Web surfing and real- time video for video conferencing, and compression is necessary for their real-time transmission and reasonably small memory storage. Much engineering wisdom and heuristics have accumulated on image compression in recent years, and adaptivity (to the local characteristics of an image) is found to be the key to efficient image compression. This research follows an approach underlying many, if not all, important developments in statistics. That is, it aims at identifying problems from an applied field --(wavelet) image compression, developing their solutions in a statistical framework, and seeking answers and insights in this framework relevant to the original image compression problems. On one hand, this research uses and extends modern statistical estimation theory; on the other hand, it summarizes or formalizes engineering heuristics. Therefore it builds a bridge between image compression and statistical estimation literatures. The investigators are studying adaptive thresholding methods for wavelet image coding from the point of view of denoising and compression. They are also studying estimation and adaptive quantization methods based on quantized data for general digital signal compression including wavelet-based image compression. The statistical research establishes a framework for adaptive wavelet thresholding for images, and provides solutions to the general statistical problem of estimation based on quantized data, which are available in large quantities in the modern communications age. A level of effort statement. At the recommended level of support, the PI will make every attempt to meet the original scope and level of effort of the project.