<title>Integer wavelet decomposition for lossy image compression</title>

Abstract

Using the lifting step approach for wavelet decomposition, Sweldens has recently introduced a fully integer based filtering method. There are several advantages to such an approach, one of the most interesting is the possibility to use wavelets for efficient lossless coding. However, this scheme is also interesting in case of lossy compression, especially for 'real-time' or 'low-cost' applications. In the PC based world, integer operations are more efficient than their floating-point counterparts, allowing much faster processing. In case of hardware implementations, integer based arithmetic units are much cheaper than those capable of handling floating points. In terms of memory usage, integer decomposition reduces the demands on the system by at least a factor two. For these reasons, we are interested in considering integer based filtering for lossy image compression as well. This raises an important question: what additional losses, if any, occur when using integer based wavelet decompositions in place of the usual floating point approach? First we compare the compressed images using standard SNR and other simple metrics. Next we evaluate our results using visually weighted objective metrics. This allows us to fully evaluate integer wavelet decomposition when applied to lossy image compression across a range of bit rates, filter characteristics and image types.