Some Results of Mathematical-Based Transformation Methods and their Application to Image Compression

The main purpose of this thesis is to study and investigate the most important properties of integral transforms ( the discrete fourier transform, the discrete sine transform, and the discrete wavelet transform) and their mathematical aspects both from the theoretical point of view and for the application to image compression. As well as, we study the singular value decomposition method and its application to image representation.Two mathematical models are developed. The first model consists of a new multi-transform method that takes advantage of each of the discrete wavelet transform and the singular value ecomposition method while the second model takes advantage of the discrete sine transform and the singular value decomposition method. These models are applied to compress images.Results show that this new approach yields better function representation and reconstruction in image compression application than is possible with the use of a single fixed transform. The proposed models improve the efficiency of
the compressing process in the discrete wavelet transform and the discrete sine transform domains.