Abstract
It is well known that the image compression task can be effectively accomplished by means of the wavelet transform. A new method has been recently proposed for the computation of this transform, i.e. the Lifting Scheme (LS). Besides being computationally more efficient than the classical filter bank scheme, the LS also enables the computation of a wavelet transform which maps integers to integers, so allowing for the design of joint lossless and lossy compression schemes. The performance of this Integer Wavelet Transform (IWT) has already been studied in the literature, and compared to that of the Discrete Wavelet Transform (DWT) in the lossy case; it has been found that in most cases the DWT achieves slightly better performance with respect to the DWT. In this paper we show that this result does not hold in the case of lossy compression of smooth images, as the IWT has a much larger loss of performance, making it ineffective for the compression of such images. We first select measures of image smoothness; then we study the IWT lossy compression performance in the presence of different degrees of smoothness, on an set containing various kinds of images. Finally, we relate the IWT compression performance to the degree of image smoothness.
