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Sparse Estimation Using Bayesian Hierarchical Prior Modeling for Real and Complex Linear Models

Pedersen, Niels Lovmand and Manchon, Carles Navarro and Badiu, Mihai-Alin and Shutin, Dmitriy and Fleury, Bernard Henry (2015) Sparse Estimation Using Bayesian Hierarchical Prior Modeling for Real and Complex Linear Models. Signal Processing, 115, pp. 94-109. Elsevier. DOI: 10.1016/j.sigpro.2015.03.013 ISSN 0165-1684

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Official URL: http://www.sciencedirect.com/science/article/pii/S0165168415001140


In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex-valued models, this paper proposes a GSM model - the Bessel K model - that induces concave penalty functions for the estimation of complex sparse signals. The properties of the Bessel K model are analyzed when it is applied to Type I and Type II estimation. This analysis reveals that, by tuning the parameters of the mixing pdf different penalty functions are invoked depending on the estimation type used, the value of the noise variance, and whether real or complex signals are estimated. Using the Bessel K model, we derive a sparse estimator based on a modification of the expectation–maximization algorithm formulated for Type II estimation. The estimator includes as a special instance in the algorithms proposed by Tipping and Faul [1] and Babacan et al. [2]. Numerical results show the superiority of the proposed estimator over these state-of-the-art estimators in terms of convergence speed, sparseness, reconstruction error, and robustness in low and medium signal-to-noise ratio regimes.

Item URL in elib:https://elib.dlr.de/95622/
Document Type:Article
Title:Sparse Estimation Using Bayesian Hierarchical Prior Modeling for Real and Complex Linear Models
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Pedersen, Niels Lovmandnlp (at) es.aau.dkUNSPECIFIED
Manchon, Carles Navarrocnm (at) es.aau.dkUNSPECIFIED
Badiu, Mihai-Alinin_mba (at) es.aau.dkUNSPECIFIED
Shutin, DmitriyDmitriy.Shutin (at) dlr.deUNSPECIFIED
Fleury, Bernard Henrybfl (at) es.aau.dkUNSPECIFIED
Date:20 March 2015
Journal or Publication Title:Signal Processing
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In ISI Web of Science:Yes
DOI :10.1016/j.sigpro.2015.03.013
Page Range:pp. 94-109
Keywords:Sparse Bayesian learning; Sparse signal representations; Underdetermined linear systems; Hierarchical Bayesian modeling; Sparsity-inducing priors
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Communication and Navigation
DLR - Research area:Raumfahrt
DLR - Program:R KN - Kommunikation und Navigation
DLR - Research theme (Project):R - Vorhaben GNSS2/Neue Dienste und Produkte
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Communication and Navigation > Communications Systems
Deposited By: Shutin, Dmitriy
Deposited On:05 Oct 2015 16:05
Last Modified:31 Jul 2019 19:52

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