Finding the minimum rate of innovation in the presence of noise

Christopher Gilliam; Thierry Blu

doi:10.1109/ICASSP.2016.7472432

Finding the minimum rate of innovation in the presence of noise

Christopher Gilliam, Thierry Blu

Electronic, Electrical and Systems Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

7 Citations (Scopus)

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.

Original language	English
Title of host publication	2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	4019-4023
Number of pages	5
ISBN (Electronic)	9781479999880
DOIs	https://doi.org/10.1109/ICASSP.2016.7472432
Publication status	Published - 18 May 2016
Event	41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Shanghai, China Duration: 20 Mar 2016 → 25 Mar 2016

Publication series

Name	ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume	2016-May
ISSN (Print)	1520-6149

Conference

Conference	41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016
Country/Territory	China
City	Shanghai
Period	20/03/16 → 25/03/16

Bibliographical note

Publisher Copyright:
© 2016 IEEE.

Keywords

Finite rate of innovation
model order
model-fitting
recovery of Dirac pulses
sampling theory

ASJC Scopus subject areas

Software
Signal Processing
Electrical and Electronic Engineering

Access to Document

10.1109/ICASSP.2016.7472432

Cite this

Gilliam, C., & Blu, T. (2016). Finding the minimum rate of innovation in the presence of noise. In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings (pp. 4019-4023). Article 7472432 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2016-May). Institute of Electrical and Electronics Engineers (IEEE). https://doi.org/10.1109/ICASSP.2016.7472432

Gilliam, Christopher ; Blu, Thierry. / Finding the minimum rate of innovation in the presence of noise. 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings. Institute of Electrical and Electronics Engineers (IEEE), 2016. pp. 4019-4023 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

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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.",

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Gilliam, C & Blu, T 2016, Finding the minimum rate of innovation in the presence of noise. in 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings., 7472432, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, vol. 2016-May, Institute of Electrical and Electronics Engineers (IEEE), pp. 4019-4023, 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016, Shanghai, China, 20/03/16. https://doi.org/10.1109/ICASSP.2016.7472432

Finding the minimum rate of innovation in the presence of noise. / Gilliam, Christopher; Blu, Thierry.
2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings. Institute of Electrical and Electronics Engineers (IEEE), 2016. p. 4019-4023 7472432 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2016-May).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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Gilliam C, Blu T. Finding the minimum rate of innovation in the presence of noise. In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings. Institute of Electrical and Electronics Engineers (IEEE). 2016. p. 4019-4023. 7472432. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). doi: 10.1109/ICASSP.2016.7472432

Finding the minimum rate of innovation in the presence of noise

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this