Wavelets for image compression.

Abstract

Wavelets are becoming increasingly important in image compression applications because of its flexibility in representing nonstationary signals. To achieve a high compression ratio, the wavelet has to be adapted to the image. Current techniques use exhaustive search procedures which are computationally intensive to find the optimal basis (type/order/tree) for the image to be coded. In this thesis, we have carried out extensive performance analysis of various wavelets on a wide variety of images. Based on the investigation, we propose some guidelines for searching for the optimal wavelet (type/order) based on the overall activity (measured by the spectral flatness) of the image to be coded. These guidelines will provide the degree of improvement that can be achieved by using the "optimal" over "standard" wavelets. The proposed guidelines can be used to find a good initial guess for faster convergence when searching for optimal wavelet is essential. We propose a wave packet decomposition algorithm based on the local transform gain of the wavelet decomposed bands. The proposed algorithm provides good coding performance at significantly reduced complexity. Most practical coders are designed to minimize the mean square error (MSE) between the original and reconstructed image. It is known that at high compression ratio, MSE does not correspond well to the subjective quality of the image. In this thesis, we propose an image adaptive coding algorithm which tries to minimize the MSE weighted by the visual importance of various wavelet bands. It has been observed that the proposed algorithm provides a better coding performance for a wide variety of images.