Wavelets and Wavelet Transform Approach in Image Compression
by
Anuj Bhardwaj
Department of Mathematics, Vishveshwarya Institute of Engineering and Technology, P.O. Dadri, G. B.Nagar - 203207. U. P. , India
Coauthors: Rashid Ali, Bani Singh

Wavelets are mathematical tool for hierarchically decomposing functions. They allow a functions to be described in terms of a coarse overall shape plus details that range from broad to narrow. Although wavelets have their roots in approximation theory and signal processing. The application of wavelet transform to image compression is fairly new. The important application of wavelets is separating the smooth variations and details of the image, which is done by wavelet decomposition of the image using a discrete wavelet transform (DWT). This paper introduces some principles of image compression. Further my main focus is to show the reader the application of wavelets to image compression using Haar, Daubechies and Bi-orthogonal wavelets. A comparative study of above stated wavelets is also done in terms of their compression ratio, mean square error (MSE) and energy conservation. Few examples of signals and images are used to design several case studies and illustrate concepts and results. I also included matlab code for Haar and Daubechies decomposition.

Key Words: Wavelets, Image compression, Wavelet Transform, Discrete Wavelet Transform, Matlab Code.

Date received: November 1, 2004