Estimating signals with finite rate of innovation from noisy samples: A stochastic algorithm

As an example of the concept of rate of innovation, signals that are linear combinations of a finite number of Diracs per unit time can be acquired by linear filtering followed by uniform sampling. However, in reality, samples are not noiseless. In a recent paper, we introduced a novel stochastic algorithm to reconstruct a signal with finite rate of innovation from its noisy samples. Even though vari-ants of this problem has been approached previously, sat-isfactory solutions are only available for certain classes of sampling kernels, for example kernels which satisfy the Strang–Fix condition. In our paper, we considered the infinite-support Gaussian kernel, which does not satisfy the Strang–Fix condition. Other classes of kernels can be employed. Our algorithm is based on Gibbs sampling, a Markov chain Monte Carlo (MCMC) method. This paper summarizes the algorithm and provides numerical simula-tions that demonstrate the accuracy and robustness of our algorithm. 1