We describe several \wavelet transforms" which characterize smoothness spaces and for which the coe cients are obtained by sampling rather than integration. We use them to re-interpret the empirical wavelet transform, i.e. the common practice of applying pyramid lters to samples of a function.

We developed a general way to create integer wavelet transformations that can be used in lossless (reversible) compression of images with arbitrary size. The method, based on some updating techniques such as lifting and correction, allows us to generate a series of reversible integer transformations which have the similar features with the corresponding biorthogonal wavelet transforms and some ...