Image Compression Using Critical Sampling and Mixed Orthogonal-Based Algorithms

Abstract

The task of digital image compression has been the subject of several studies over the past decades. Wavelet transform requires filters that combine a number of desirable properties, such as orthogonality and symmetry. Advances in such transform have produced algorithms capable of outperforming in several application of image processing. In addition, Multiwavelets transform has showed promise in removing some of limitations of wavelet. The features of Multiwavelet transform open the way for the application to image compression. These may provide much greater performance than these developed using discrete cosine transform (DCT). Also, there are several methods of computation for Multiwavelet transform, different from scalar wavelet systems in requiring two or more input streams to the Multiwavelet filter bank. Two methods (Mixed and matrix approximation) for computing the Multiwavelet transform are studied.
This research attempts to give a recipe for selecting two proposed image compression algorithms based on Multiwavelet approaches, as well as to make comparison of these approaches on color images (256 x 256).
After testing several methods of Multiwavelet transform computation for image compression, the mixed method was chosen. This is because the other method introduces more complexity of computation. In data compression applications, one is seeking to remove redundancy not to increase it. Such implementation shows that this transform method gives much better performance. In addition to that it (Multiwavelet) gives a better reconstructed image quality and data rate using the same quantization matrix and in terms of complexity. It was shown that the compressed color image using Multiwavelet transform possesses %80 of compressed image . Therefore the Multiwavelet transform can support a low loss of resolution of reconstructed images which is a desirable feature.