A study on wavelets, QMF filter banks, and entropy for a digital image compression system

The purpose of this study was to investigate the use of wavelets for image and data compression and to determine what influence entropy had in that process. The wavelet compression system developed used QMF (Quadrature Mirror Filter) perfect reconstruction banks for subband decomposition. Several different wavelets were used namely the Haar, and the Daubechies D4, D6, D8 and D10. The results of this study indicated that perfect reconstruction for images from the wavelet subband decomposition are easily achieved. Also, high compression ratios (64:1 or more) are possible with little to no discernable difference in the reconstructed image without any entropy encoding, even though there is a statistical difference between the original image and the reconstructed image. Entropy did play an important part in the compression of images and that by properly selecting the wavelet and the image compression algorithm based on the entropy, a better quality image compression can be achieved. This is possible because the entropy of the data or image determines how ordered the pixels or picture elements are. If the entropy is high, then it indicates a high amount of disorder, so generally, it is harder to compress. However, entropy by itself was not enough to make a decision on how good the image compression would be. The type of image used was also a key component. Based on the small sample of test images used, it was clear that there was not a linear correlation between entropy and compression ratio quality.