Performance bounds for the estimation of finite rate of innovation signals from noisy measurements

In this paper, we derive lower bounds on the estimation error of finite rate of innovation signals from noisy measurements. We first obtain a fundamental limit on the estimation accuracy attainable regardless of the sampling technique. Next, we provide a bound on the performance achievable using any specific sampling method. 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. The results are illustrated in a time-delay estimation scenario.