Hierarchical Bayesian formulation of Sparse Signal Recovery algorithms using scale mixture priors

In the recent past, the Sparse Signal Recovery (SSR) problem has been very well studied using penalized regression approaches with different choice of penalty functions. In this work we revisit these penalized regression formulations in a Bayesian framework with suitable choice of supergaussian prio...

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Bibliographic Details
Published in:Conference record - Asilomar Conference on Signals, Systems, & Computers pp. 67 - 71
Main Authors: Giri, Ritwik, Rao, Bhaskar D.
Format: Conference Proceeding Journal Article
Language:English
Published: IEEE 01.11.2015
Subjects:
Algorithms
Bayes methods
Bayesian analysis
Conferences
Expectation-Maximization
Formulations
GSM
Laplace equations
Minimization
Noise measurement
Norms
Optimization
Recovery
Regression
Scale Mixtures
Shape
Sparse Bayesian Learning
ISSN:1058-6393
Online Access:Get full text
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Summary:In the recent past, the Sparse Signal Recovery (SSR) problem has been very well studied using penalized regression approaches with different choice of penalty functions. In this work we revisit these penalized regression formulations in a Bayesian framework with suitable choice of supergaussian prior distributions. We introduce a generalized scale mixture framework, and provide connections with well known norm minimization based SSR algorithms. Of particular interest is the re-weighted ℓ 1 approach. The scale mixture representation allows us to formulate the corresponding Type II version of these algorithms, following the hierarchical bayesian framework of Sparse Bayesian Learning (SBL) and enable a comparison of Type I versus Type II approaches.
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ISSN:1058-6393
DOI:10.1109/ACSSC.2015.7421083