Wavelet and footprint sampling of signals with a finite rate of innovation

We consider classes of not bandlimited signals, namely streams of Diracs and piecewise polynomial signals, and show that these signals can be sampled and perfectly reconstructed using wavelets as sampling kernel. Due to the multiresolution structure of the wavelet transform, these new sampling theorems naturally lead to the development of a new resolution enhancement algorithm based on wavelet footprints (Dragotti, P.L. and Vetterli, M., IEEE Trans. Sig. Process., vol.51, no.5, p.1306-23, 2003). Preliminary results show the potentiality of this algorithm.