期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 58, 期 8, 页码 4993-5015出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2012.2197719
关键词
Cramer-Rao bound (CRB); finite rate of innovation (FRI); sampling; time-delay estimation; union of subspaces
资金
- Israel Ministry of Industry and Trade
- Ollendorf Foundation
- Israel Science Foundation [170/10]
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 sub-spaces. Finally, we develop amethodology 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.
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