The Discrete Quincunx Wavelet Packet Transform

This chapter aims to present an efficient compression algorithm based on quincunx wavelet packet transform that can be applied on any image of size 128×128 or bigger. Therefore, a division process into sub-images of size 128×128 was applied on three gray-scale image databases, then pass each sub-image through the wavelet transform and a bit-level encoder, to finally compress the sub-image with respect to a fixed bit rate. The quality of the reconstructed image is evaluated using several parameters at a given bit rate. In order to improve the quality in sense of the evaluation quality, an exhaustive search has led to the best packet decomposition base. Two versions of the proposed compression scheme were performed; the optimal version is able to decrease the effect of block boundary artifacts (caused by the image division process) by 27.70% considering a natural image. This optimal version of the compression scheme was compared with JPEG standard using the quality evaluation parameters and visual observation. As a result, the proposed compression scheme presents a competitive performance to JPEG standard; where the proposed scheme performs a peak signal to noise ratio of 0.88dB over JPEG standard at a bit rate of 0.50bpp for a satellite image.