Image compression with wavelet transforms and set partitioning in hierarchical trees method

Abstract

Digital images are claiming an increasingly larger portion of the information world. In this study, the wavelet transform is chosen for image compression. The image is decomposed into subbands of averages and details with the wavelet transform. The obtained detail subbands have small valued coefficients that also constitute a small percentage of image energy. If these small valued coefficients are quantized to zero with a chosen threshold, there will be no great loss in the image. This feature provided by wavelet transform is a basis for the set partitioning in hierarchical trees algorithm. With this algorithm discrete wavelet transform coefficients are organized in spatial orientation trees. The reason to have formed these trees is to gather all pixels that are highly correlated with each other. With this kind of set structure, the similarity among the coefficients in a set from one level to the next is increased. The main aim in this algorithm is to code the trees with highly correlated, zero valued coefficients with a single codeword.