Wavelet image compression rate distortion optimizations and complexity reductions

Compression of digital images has been a topic of research for many years and a number of image compression standards have been created for different applications. The role of compression is to reduce bandwidth requirements for transmission and memory requirements for storage of all forms of data. While today more than ever before new technologies provide high speed digital communications and large memories, image compression is still of major importance, because along with the advances in technologies there is increasing demand for image communications, as well as demand for higher quality image printing and display.; In this work we focus on some key new technologies for image compression, namely wavelet based image coders. Wavelet coders apart from offering superior compression ratios have also very useful features such as resolution scalability, i.e. they allow decoding a given image at a number of different resolutions depending on the application. We start by presenting in a simple manner a collection of tools and techniques to apply wavelet filtering in images, ranging from boundary extension to fast implementations. We continue by exploiting the use of rate distortion theory in trying to achieve very high compression ratios for a wavelet coder. The results we report are among the best in the literature. We apply rate distortion theory on a per coefficient basis combining a theoretical analysis with online probability estimation.; After presenting the rate distortion algorithm we focus on techniques to reduce the complexity of generic wavelet coders. One of the main contributions of this work is the ability to compress an image with a wavelet coder without the need to buffer the complete image. The memory requirements of the proposed approach are orders of magnitude lower than other algorithms proposed up to date, which would require buffering of the entire image. This limited low memory implementation is key in enabling widespread commercial use of wavelet image coding and has been incorporated in the informative part of the upcoming JPEG2000 standard.