On the performance of linear phase wavelet transforms in low bit-rate image coding

The behavior of linear phase wavelet transforms in low bit-rate image coding is investigated. The influence of certain characteristics of these transforms such as regularity, number of vanishing moments, filter length, coding gain, frequency selectivity, and the shape of the wavelets on coding performance is analyzed. This work is divided in two parts. In the first part, the wavelet transforms performance is assessed based on a first-order Markov source. In the second part, the assessment is based on image quality, using subjective tests. More than 20 wavelet transforms of a test image were coded with a product code lattice quantizer with the image quality rated by different viewers. The results show that, as long as the wavelet transforms perform reasonably well, features like regularity and number of vanishing moments do not have any important impact on final image quality. The influence of the coding gain by itself is also small. On the other hand, the shape of the synthesis wavelet, which determines the visibility of coding errors on reconstructed images, is very important. Analysis of the obtained data strongly suggests that design of good wavelet transforms for low bit-rate image coding should take into account chiefly the shape of the synthesis wavelet and, to a lesser extent, the coding.