Sparse sampling of structured information and its application to compression

It has been shown recently that it is possible to sample classes of non-bandlimited signals which we call signals with Finite Rate of Innovation (FRI). Perfect reconstruction is possible based on a set of suitable measurements and this provides a sharp result on the sampling and reconstruction of sparse continuous-time signals. In this paper, we first review the basic theory and results on sampling signals with finite rate of innovation. We then discuss variations of the above framework to handle noise and model mismatch. Finally, we present some results on compression of piecewise smooth signals based on the FRI framework.