Reversible Wavelet Transforms and Their Application to Embedded Image Compression

The design and implementation of reversible wavelet/subband transforms and their application to reversible embedded image compression are studied. Reversible embedded image coding provides a natural way for building uni ed lossy/lossless image compression systems, and reversible transforms are a key component in such systems. A lifting-based method is examined as a means for constructing reversible versions of linear M -band subband transforms. The method is shown to produce reversible transforms that well approximate their parent linear transforms even when computed using xed-point arithmetic. Also, a simple and practical software algorithm for reversible transform construction is described. By combining ideas from both lifting and the S+P transform, a more general framework for the design of reversible transforms is proposed. This new framework generates a larger class of reversible transforms than lifting alone, and includes all lifted transforms as a subset. Several reversible transforms constructed using lifting are employed in a reversible embedded image compression system based on the so called Embedded Zerotree Wavelet (EZW) coding scheme. Both 2-band and M -band transforms are considered. Many practically useful observations as to which transforms are most e ective for various classes of images and what types of artifacts are associated with the various transforms are made. The merits of full versus partial embedding and periodic versus symmetric extension are also investigated. Based on some of the observations made, a multi-transform approach to image compression is proposed. With this scheme, the decorrelating transform employed by the image coder is selected on a per image basis using image-speci c information. Although the transform selection algorithm is extremely simple and has only modest computational requirements, results show that this new approach yields better compression performance than is possible with the use of a single xed transform such as the S+P transform.