Name
Abstract | ||
|---|---|---|
This paper addresses the problem of sampling non-bandlimited signals within the Finite Rate of Innovation (FRI) setting. We had previously shown that, by using sampling kernels whose integer span contains specific exponentials (generalized Strang-Fix conditions), it is possible to devise non-iterative, fast reconstruction algorithms from very low-rate samples. Yet, the accuracy and sensitivity to noise of these algorithms is highly dependent on these exponential reproducing kernels — actually, on the exponentials that they reproduce. Hence, our first contribution here is to provide clear guidelines on how to choose the sampling kernels optimally, in such a way that the reconstruction quality is maximized in the presence of noise. The optimality of these kernels is validated by comparing with Cramér-Rao's lower bounds (CRB). Our second contribution is to relax the exact exponential reproduction requirement. Instead, we demonstrate that arbitrary sampling kernels can reproduce the “best” exponentials within quite a high accuracy in general, and that applying the exact FRI algorithms in this approximate context results in near-optimal reconstruction accuracy for practical noise levels. Essentially, we propose a universal extension of the FRI approach to arbitrary sampling kernels. Numerical results checked against the CRB validate the various contributions of the paper and in particular outline the ability of arbitrary sampling kernels to be used in FRI algorithms. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1109/TSP.2013.2278152 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
estimation theory,signal reconstruction,signal sampling,CRB lower bounds,Cramér-Rao lower bounds,FRI sampling,FRI setting,arbitrary sampling kernels,exact exponential reproduction requirement,fast reconstruction algorithm,finite rate of innovation setting,generalized Strang-Fix conditions,near-optimal reconstruction accuracy,nonbandlimited signal sampling,noniterative algorithm,signal reconstruction quality,DSP-SAMP,MOMS,finite rate of innovation,matrix Pencil,noise,sampling | Integer,Mathematical optimization,Exponential function,Sampling (statistics),Estimation theory,Mathematics,Signal reconstruction | Journal |
Volume | Issue | ISSN |
61 | 21 | 1053-587X |
Citations | PageRank | References |
32 | 1.17 | 19 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jose Antonio Uriguen | 1 | 32 | 1.17 |
| T Blu | 2 | 2574 | 259.70 |
| Dragotti, P.L. | 3 | 512 | 39.29 |