A Novel Algorithm for the Identification of Dirac Impulses from Filtered Noisy Measurements

Sylvain Meignen, Quentin Legros, Yoann Altmann, Stephen McLaughlin

Research output: Contribution to journalArticle

Abstract

In this paper we address the recovery of a finite stream of Dirac pulses from noisy lowpass-filtered samples in the discrete-time setting. While this problem has been successfully addressed for the noise-free case using the concept of signals with finite rate of innovation, such techniques are not efficient in the presence of noise. In the FRI framework, the determination of the location of Dirac pulses is based on the singular value decomposition of a matrix whose rank in the noise-free case equals the number of Dirac pulses and the signal can be related to the non zero singular values. However, in noisy situations this matrix becomes full rank and the singular value decomposition is subject to subspace swap, meaning some singular values associated with noise become larger than some values related to the signal. This phenomenon has been recognized as the reason for performance breakdown in the method. The goal of this paper is to propose a novel algorithm that limits the alteration of these singular values in the presence of noise, thus significantly improving the estimation of Dirac pulses.

LanguageEnglish
Pages268-281
Number of pages14
JournalSignal Processing
Volume162
Early online date13 Apr 2019
DOIs
Publication statusE-pub ahead of print - 13 Apr 2019

Fingerprint

Singular value decomposition
Innovation
Recovery

Keywords

  • Finite rate of innovation
  • Fourier analysis
  • Optimal sampling
  • Sparse deconvolution

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering

Cite this

@article{c6707792290d445dbddc55e5393d9bca,
title = "A Novel Algorithm for the Identification of Dirac Impulses from Filtered Noisy Measurements",
abstract = "In this paper we address the recovery of a finite stream of Dirac pulses from noisy lowpass-filtered samples in the discrete-time setting. While this problem has been successfully addressed for the noise-free case using the concept of signals with finite rate of innovation, such techniques are not efficient in the presence of noise. In the FRI framework, the determination of the location of Dirac pulses is based on the singular value decomposition of a matrix whose rank in the noise-free case equals the number of Dirac pulses and the signal can be related to the non zero singular values. However, in noisy situations this matrix becomes full rank and the singular value decomposition is subject to subspace swap, meaning some singular values associated with noise become larger than some values related to the signal. This phenomenon has been recognized as the reason for performance breakdown in the method. The goal of this paper is to propose a novel algorithm that limits the alteration of these singular values in the presence of noise, thus significantly improving the estimation of Dirac pulses.",
keywords = "Finite rate of innovation, Fourier analysis, Optimal sampling, Sparse deconvolution",
author = "Sylvain Meignen and Quentin Legros and Yoann Altmann and Stephen McLaughlin",
year = "2019",
month = "4",
day = "13",
doi = "10.1016/j.sigpro.2019.04.016",
language = "English",
volume = "162",
pages = "268--281",
journal = "Signal Processing",
issn = "0165-1684",
publisher = "Elsevier",

}

A Novel Algorithm for the Identification of Dirac Impulses from Filtered Noisy Measurements. / Meignen, Sylvain; Legros, Quentin; Altmann, Yoann; McLaughlin, Stephen.

In: Signal Processing, Vol. 162, 13.04.2019, p. 268-281.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A Novel Algorithm for the Identification of Dirac Impulses from Filtered Noisy Measurements

AU - Meignen, Sylvain

AU - Legros, Quentin

AU - Altmann, Yoann

AU - McLaughlin, Stephen

PY - 2019/4/13

Y1 - 2019/4/13

N2 - In this paper we address the recovery of a finite stream of Dirac pulses from noisy lowpass-filtered samples in the discrete-time setting. While this problem has been successfully addressed for the noise-free case using the concept of signals with finite rate of innovation, such techniques are not efficient in the presence of noise. In the FRI framework, the determination of the location of Dirac pulses is based on the singular value decomposition of a matrix whose rank in the noise-free case equals the number of Dirac pulses and the signal can be related to the non zero singular values. However, in noisy situations this matrix becomes full rank and the singular value decomposition is subject to subspace swap, meaning some singular values associated with noise become larger than some values related to the signal. This phenomenon has been recognized as the reason for performance breakdown in the method. The goal of this paper is to propose a novel algorithm that limits the alteration of these singular values in the presence of noise, thus significantly improving the estimation of Dirac pulses.

AB - In this paper we address the recovery of a finite stream of Dirac pulses from noisy lowpass-filtered samples in the discrete-time setting. While this problem has been successfully addressed for the noise-free case using the concept of signals with finite rate of innovation, such techniques are not efficient in the presence of noise. In the FRI framework, the determination of the location of Dirac pulses is based on the singular value decomposition of a matrix whose rank in the noise-free case equals the number of Dirac pulses and the signal can be related to the non zero singular values. However, in noisy situations this matrix becomes full rank and the singular value decomposition is subject to subspace swap, meaning some singular values associated with noise become larger than some values related to the signal. This phenomenon has been recognized as the reason for performance breakdown in the method. The goal of this paper is to propose a novel algorithm that limits the alteration of these singular values in the presence of noise, thus significantly improving the estimation of Dirac pulses.

KW - Finite rate of innovation

KW - Fourier analysis

KW - Optimal sampling

KW - Sparse deconvolution

UR - http://www.scopus.com/inward/record.url?scp=85065085451&partnerID=8YFLogxK

U2 - 10.1016/j.sigpro.2019.04.016

DO - 10.1016/j.sigpro.2019.04.016

M3 - Article

VL - 162

SP - 268

EP - 281

JO - Signal Processing

T2 - Signal Processing

JF - Signal Processing

SN - 0165-1684

ER -