Separable versus Quincunx Wavelet Transforms for Image Compression

TRANSFORMS FOR IMAGE COMPRESSION R. Andrews D.T. Nguyen Department of Electrical Engineering and Computer Science University of Tasmania Churchill Ave. Sandy Bay 7005 AUSTRALIA Abstract { It has been demonstrated that wavelets compete well against DCT based image compression techniques [1]. However the advantages of nonseparable wavelet transforms for image and video coding have not yet been adequately explored. In this paper we discuss nonseparable wavelet transforms on the quincunx lattice and compare results under simple data reduction methods using separable and nonseparable symmetrical (linear-phase) biorthogonal lters, where the two-dimensional lters for use on the quincunx lattice are obtained from the one-dimensional lters [3]. We attempt to use the most general coding schemes possible which do not disadvantage either separable or nonseparable techniques. For a comparison of separable wavelets, quantizers and coders the reader is directed to [2]. We attempt to use separable and quincunx wavelet lters of similar size and with similar properties. Even so it is di cult to determine the most appropriate lters for comparison. We show that the performance of separable and nonseparable techniques is comparable under similar constraints. Finally we investigate methods for performance enhancement through the use of psychovisual coding with the nonseparable transform. Introduction Wavelets have become a eld of intense research in the image processing eld due to their close relationship with the well understood eld of subband coding. However the research to date has been almost exclusively concerned with separable wavelet transforms, the natural extension into two dimesnions of onedimensional wavelet transforms which are well understood and well documented. There are, however, restrictions which occur when applying separable one dimensional wavelet transforms to images which are two dimensional signals. Some of these restrictions can be lifted by moving from separable one dimensional wavelet transforms to truely twodimensional wavelet transforms. G H