Estimating SignalsWith Finite Rate of Innovation From Noisy Samples: A Stochastic Algorithm

Vincent Y.F. Tan (1) , Vivek K. Goyal (1)

1 EECS - Department of Electrical Engineering and Computer Science

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 variants of this problem has been approached previously, satisfactory 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 simulations that demonstrate the accuracy and robustness of our algorithm.

Domaines: Traitement du signal et de l'image [eess.SP]; Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Traitement du signal et de l'image [eess.SP]

Vincent Y.F. Tan, Vivek K. Goyal. Estimating SignalsWith Finite Rate of Innovation From Noisy Samples: A Stochastic Algorithm. SAMPTA'09, May 2009, Marseille, France. Special Session on sampling using finite rate of innovation principles. ⟨hal-00452215⟩