Sampling Signals with Finite Rate of Innovation and Recovery by Maximum Likelihood Estimation
Summary :
We propose a maximum likelihood estimation approach for the recovery of continuously-defined sparse signals from noisy measurements, in particular periodic sequences of Diracs, derivatives of Diracs and piecewise polynomials. The conventional approach for this problem is based on least-squares (a.k.a. annihilating filter method) and Cadzow denoising. It requires more measurements than the number of unknown parameters and mistakenly splits the derivatives of Diracs into several Diracs at different positions. Moreover, Cadzow denoising does not guarantee any optimality. The proposed approach based on maximum likelihood estimation solves all of these problems. Since the corresponding log-likelihood function is non-convex, we exploit the stochastic method called particle swarm optimization (PSO) to find the global solution. Simulation results confirm the effectiveness of the proposed approach, for a reasonable computational cost.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E96-A No.10 pp.1972-1979
- Publication Date
- 2013/10/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E96.A.1972
- Type of Manuscript
- Special Section PAPER (Special Section on Sparsity-aware Signal Processing)
- Category
Authors
Akira HIRABAYASHI
Ritsumeikan University
Yosuke HIRONAGA
Yamaguchi University
Laurent CONDAT
Grenoble Institute of Technology
Keyword
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Akira HIRABAYASHI, Yosuke HIRONAGA, Laurent CONDAT, "Sampling Signals with Finite Rate of Innovation and Recovery by Maximum Likelihood Estimation" in IEICE TRANSACTIONS on Fundamentals,
vol. E96-A, no. 10, pp. 1972-1979, October 2013, doi: 10.1587/transfun.E96.A.1972.
Abstract: We propose a maximum likelihood estimation approach for the recovery of continuously-defined sparse signals from noisy measurements, in particular periodic sequences of Diracs, derivatives of Diracs and piecewise polynomials. The conventional approach for this problem is based on least-squares (a.k.a. annihilating filter method) and Cadzow denoising. It requires more measurements than the number of unknown parameters and mistakenly splits the derivatives of Diracs into several Diracs at different positions. Moreover, Cadzow denoising does not guarantee any optimality. The proposed approach based on maximum likelihood estimation solves all of these problems. Since the corresponding log-likelihood function is non-convex, we exploit the stochastic method called particle swarm optimization (PSO) to find the global solution. Simulation results confirm the effectiveness of the proposed approach, for a reasonable computational cost.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E96.A.1972/_p
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@ARTICLE{e96-a_10_1972,
author={Akira HIRABAYASHI, Yosuke HIRONAGA, Laurent CONDAT, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Sampling Signals with Finite Rate of Innovation and Recovery by Maximum Likelihood Estimation},
year={2013},
volume={E96-A},
number={10},
pages={1972-1979},
abstract={We propose a maximum likelihood estimation approach for the recovery of continuously-defined sparse signals from noisy measurements, in particular periodic sequences of Diracs, derivatives of Diracs and piecewise polynomials. The conventional approach for this problem is based on least-squares (a.k.a. annihilating filter method) and Cadzow denoising. It requires more measurements than the number of unknown parameters and mistakenly splits the derivatives of Diracs into several Diracs at different positions. Moreover, Cadzow denoising does not guarantee any optimality. The proposed approach based on maximum likelihood estimation solves all of these problems. Since the corresponding log-likelihood function is non-convex, we exploit the stochastic method called particle swarm optimization (PSO) to find the global solution. Simulation results confirm the effectiveness of the proposed approach, for a reasonable computational cost.},
keywords={},
doi={10.1587/transfun.E96.A.1972},
ISSN={1745-1337},
month={October},}
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TY - JOUR
TI - Sampling Signals with Finite Rate of Innovation and Recovery by Maximum Likelihood Estimation
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1972
EP - 1979
AU - Akira HIRABAYASHI
AU - Yosuke HIRONAGA
AU - Laurent CONDAT
PY - 2013
DO - 10.1587/transfun.E96.A.1972
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E96-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2013
AB - We propose a maximum likelihood estimation approach for the recovery of continuously-defined sparse signals from noisy measurements, in particular periodic sequences of Diracs, derivatives of Diracs and piecewise polynomials. The conventional approach for this problem is based on least-squares (a.k.a. annihilating filter method) and Cadzow denoising. It requires more measurements than the number of unknown parameters and mistakenly splits the derivatives of Diracs into several Diracs at different positions. Moreover, Cadzow denoising does not guarantee any optimality. The proposed approach based on maximum likelihood estimation solves all of these problems. Since the corresponding log-likelihood function is non-convex, we exploit the stochastic method called particle swarm optimization (PSO) to find the global solution. Simulation results confirm the effectiveness of the proposed approach, for a reasonable computational cost.
ER -
English
