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.
