AbstractsMathematics

Still image compression by nonseparable wavelets on the quincunx lattice

by Richard Julian Andrews




Institution: University of Tasmania
Department:
Year: 2002
Keywords: Image processing; Image compression; Lattice theory; Wavelets (Mathematics)
Record ID: 1054504
Full text PDF: http://eprints.utas.edu.au/19137/1/whole_AndrewsRichardJulian2002_thesis.pdf


Abstract

The recent unification of wavelet and subband theories has allowed the creation of a new field of investigation for the efficient compression of digital images: wavelet compression. It has seen remarkable improvements in compression results over the previous generation of DCT-based image compression schemes. The focus of research in this field has, however, been almost exclusively in the separable domain, which uses one-dimensional transforms. The use of truly nonseparable wavelet transforms on two-dimensional image signals has been largely ignored. The purpose of this Thesis is to investigate more thoroughly this largely untouched field of wavelet-based image compression. In this Thesis we discuss in depth the techniques for using multidimensional wavelet transforms and subband coding for image compression and provide results for extending existing compression techniques to the quincunx domain. Various results covering a number of coding methodolgies are presented using the quincunx wavelet transform to demonstrate its advantages and disadvantages when compared to the separable decomposition method. Novel techniques are developed for the representation and storage of quincunx sampled images allowing in-place wavelet transforms to be performed in real-time. A novel extension to the Shapiro zero-tree compression method is developed which predicts and exploits, during coding, visually unimportant areas without the need for transmitting side-information. Results are presented which show that this process leads to significantly higher perceived image quality without increasing the bit-rate. Several advantageous psychovisual properties of the quincunx resampling lattice are exploited in the creation of various extensions to simple compression methods. Results isolating the effects of utilizing these properties are presented. We find that in general separable wavelet transforms perform better than their quincunx counterparts for bit-rate versus perceived quality of reconstruction, despite the quincunx resampling structure possessing inherent advantages over rectangular resampling. This is mainly attributed to the state of non-separable subband theory and filter design which has not progressed to a state where it is possible to achieve the same quality of filter design as exists in the one dimensional case.