Estimating Signals with Finite Rate of Innovation from Noisy Samples: A Stochastic Algorithm

摘要

As an example of the recently-introduced concept of rate of innovation,signals that are linear combinations of a finite number of Diracs per unit timecan be acquired by linear filtering followed by uniform sampling. However, inreality, samples are rarely noiseless. In this paper, we introduce a novelstochastic algorithm to reconstruct a signal with finite rate of innovationfrom its noisy samples. Even though variants of this problem has beenapproached previously, satisfactory solutions are only available for certainclasses of sampling kernels, for example kernels which satisfy the Strang-Fixcondition. In this paper, we consider the infinite-support Gaussian kernel,which does not satisfy the Strang-Fix condition. Other classes of kernels canbe employed. Our algorithm is based on Gibbs sampling, a Markov chain MonteCarlo (MCMC) method. Extensive numerical simulations demonstrate the accuracyand robustness of our algorithm.