Image compression using cosine transform, vector quantisation and Gabor transform

Abstract

Image transmission and storage are required in many areas. However, a digital image needs to be represented by a very large number of bits. In order to take the advantages offered by digital communication systems, image compression technique must be used to reduce the number of bits for representing an image.

Performance of discrete cosine transform (DCT) approaches to that of Karhunen-Loéve transform, which is the optimal transform in the sense of decorrelation and energy packing abilities. DCT has been widely used for image compression. A number of fast algorithms as well as intergrated circuits for implementing DCT are available. In this thesis, magnetic resonance imaging (MRI) data compression and reconstruction using DCT is presented. In MRI, data sampled in the spatial frequency domain are equivalent to a set of discrete Fourier transform (DFT) coefficients. An effective algorithm is derived to convert the DFT coefficients to the DCT or block DCT coefficients, so that full power of existing DCT coding system can be used for MRI data.

A substantial data compression ratio can be achieved with vector quantisation (VQ). However, this method presents two problems, one is the high complexity of implementation, and other is no algorithm available to generate a universal code book. A new coding method is proposed to combine the DCT and the VQ. In this method, an image is classified in terms of its activity. The DCT is used for lower active parts of the image and the VQ for higher active parts. A small size code book is generated empirically. Thus, the complexity of implementation for this coding method is low, and this code book tends to be suitable for all kind of images.

Recent development on image coding is to find an accurate model of biological visual processing, for which the human visual system properties can be incorporated, so that a high image compression ratio can be achieved. Gabor transform is a very popular candidate because the profile of the human visual receptive fields can be very well represented with Gabor elementary functions. However, computation of the Gabor transform is very complicated because Gabor elementary functions are not mutually orthogonal. A neural network based method has been used to compute the Gabor transform. In this thesis, a new algorithm is presented to improve the computation efficiency of the neural network, where the lookup table technique and a successive over relaxation algorithm are used.

Both computation speed and data compression ratio are crucial issues in an image coding system. In the Gabor transform, however, the elementary functions as well as the transform coefficients are complex valued. Two real valued Gabor transforms are proposed to improve the computation speed and the data compression ratio. For images with high complexity, the energy distribution of their transform coefficients is more broader. A new adaptive Gabor transform coding method is proposed to improve the quality of reconstructed images.

It is expected that the techniques developed in this thesis would find practical applications in both medical picture archiving and communication systems (PACS) ans advanced video telecommunication systems.