Performance bounds and design criteria for estimating finite rate of innovation signals
Venue
IEEE Transactions on Information Theory, vol. 58 (2012), pp. 4993-5015
Publication Year
2012
Authors
Zvika Ben-Haim, Tomer Michaeli, Yonina C. Eldar
BibTeX
Abstract
In this paper, we consider the problem of estimating finite rate of innovation (FRI)
signals from noisy measurements, and specifically analyze the interaction between
FRI techniques and the underlying sampling methods. We first obtain a fundamental
limit on the estimation accuracy attainable regardless of the sampling method.
Next, we provide a bound on the performance achievable using any specific sampling
approach. Essential differences between the noisy and noise-free cases arise from
this analysis. In particular, we identify settings in which noise-free recovery
techniques deteriorate substantially under slight noise levels, thus quantifying
the numerical instability inherent in such methods. This instability, which is only
present in some families of FRI signals, is shown to be related to a specific type
of structure, which can be characterized by viewing the signal model as a union of
subspaces. Finally, we develop a methodology for choosing the optimal sampling
kernels for linear reconstruction, based on a generalization of the Karhunen–Loeve
transform. The results are illustrated for several types of time-delay estimation
problems.
