Image compression with optimal wavelet

Wavelets have been successfully used in image compression. However, for the given image, the choice of the wavelet to use is an important issue. In this paper, we propose to use the optimal wavelet for image compression, given the number of most significant wavelet coefficients to be kept. Simulated annealing is used to find the optimal wavelet for the given image to be compressed. In simulated annealing, we need a cost function to minimize. This cost function is defined as the mean square error between the decompressed image and the original image. We conduct some experiments in Matlab by using the test images Lena, MRIScan and Fingerprint. These images are available in WaveLab, developed by Donoho et al., at Stanford University. Experimental results show that this approach is better than the Daubechies-8 wavelet (D8) for image compression. In some cases, we get nearly 0.6 dB improvement over D8 by using the optimal wavelet. This indicates that the choice of the wavelet indeed makes a significant difference in image compression.