Sampling and Wavelet Theory

Mathematical methods for signal processing like wavelets have played a pivotal role in signal processing applications recently. In recent years, wavelet based algorithms have been successful in different signal processing tasks. The wavelet transform is a powerful tool because it manages to represent both transient and stationary behaviours of a signal with few transform coefficients.  Discontinuities often carry relevant signal information  and so they represent a critical part to analyse. We have recently developed a new framework, known as wavelet footprints, to model the dependency accross scales of the wavelet coefficients. This scheme has been successfully used for compression, denoising and restoration. We are currently investigating new sampling schemes for non-bandlimited signals that still have a finite number of degrees of freedom per unit of time and exploring applications of such schemes to image super-resolution and distributed compression.

Main publications: 

• P. Shukla and P.L. Dragotti, Sampling Schemes for Multidimensional Signals with Finite Rate of Innovation,  IEEE Trans. on Signal Processing, vol. 55 (7),  pp. 3670-3686, July 2007.
• P.L. Dragotti, M. Vetterli and T. Blu, Sampling Moments and Reconstructing Signals of Finite Rate of Innovation: Shannon meets Strang-Fix, IEEE Trans. on Signal Processing, vol.55 (5), pp. 1741-1757, May 2007.
• J.Berent and P.L. Dragotti, Perfect Reconstruction Schemes for Sampling Piecewise Sinusoidal Signals, Proc. of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Toulouse, France, May 2006.
• P.L. Dragotti and M. Vetterli, Wavelet Footprints: Theory, Algorithms and Applications, IEEE Trans. on Signal Processing, vol. 51(5), pp. 1306-1323, May 2003