This thesis addresses the problem of using wavelet packets and empirical mode decomposition (EMD) for image compression. The wavelet packet basis selection algorithm is studied through an extensive experimental survey of the generated decomposition trees. We formulate the "triplet problem" for image compression as follows: How is the decomposition tree related to the image content, filter set and cost function? Our aim is to find an optimal basis for compression of images. Results are presented using test images from the Brodatz texture set. We also present a method to analytically calculate the cost of splitting a node, for a given signal model and filter, without actually performing the split.

A totally different approach to signal decomposition is the EMD. This is an adaptive decomposition scheme with which any complicated signal is decomposed into its intrinsic mode functions (IMF). The concept of EMD is extended to two dimensions to make it useful for image processing. The EMD and the sifting process to generate the IMFs are described. Different known and newly found difficulties with implementation of the method in two dimensions are highlighted and solutions are proposed. The method of variable sampling of the EMO, using overlapping blocks, is presented and the concept of empiquency is introduced to describe spatial

frequency since the traditional Fourier-based frequency concept is not applicable.

Several ways to use EMD for image compression are examined and presented. The two-dimensional extension of the EMD is original as well as its application for image compression.