Finding the minimum rate of innovation in the presence of noise
Journal
ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Journal Volume
2016-May
ISBN
9781479999880
Date Issued
2016-05-18
Author(s)
Gilliam, Christopher
Abstract
Recently, sampling theory has been broadened to include a class of non-bandlimited signals that possess finite rate of innovation (FRI). In this paper, we consider the problem of determining the minimum rate of innovation (RI) in a noisy setting. First, we adapt a recent model-fitting algorithm for FRI recovery and demonstrate that it achieves the Cramer-Rao bounds. Using this algorithm, we then present a framework to estimate the minimum RI based on fitting the sparsest model to the noisy samples whilst satisfying a mean squared error (MSE) criterion - a signal is recovered if the output MSE is less than the input MSE. Specifically, given a RI, we use the MSE criterion to judge whether our model-fitting has been a success or a failure. Using this output, we present a Dichotomic algorithm that performs a binary search for the minimum RI and demonstrate that it obtains a sparser RI estimate than an existing information criterion approach.
Subjects
Finite rate of innovation | model order | model-fitting | recovery of Dirac pulses | sampling theory
SDGs
Type
conference paper