The theory of compressed sensing has demonstrated that sparse signals can be reconstructed from few linear measurements. In this work, we propose a new class of iteratively reweighted least squares (IRLS) for sparse recovery. The proposed methods use a two state Gaussian scale mixture as a proxy for the signal model and can be interpreted as an Expectation Maximization algorithm that attempts to perform the constrained maximization of the log-likelihood function. Under some conditions, standard in the compressed sensing theory, the sequences generated by these algorithms converge to the fixed points of the maps that rule their dynamics. A condition for exact sparse recovery, that is verifible a posteriori, is derived and the convergence is proved to be quadratically fast in a neighborhood of the desired solution. Numerical experiments show that these new reconstructions schemes outperform classical IRLS for lp -minimization with p\in(0, 1] in terms of rate of convergence and accuracy

Fast IRLS for sparse reconstruction based on gaussian mixtures / Ravazzi, Chiara; Magli, Enrico. - ELETTRONICO. - (2015), pp. 24-24. (Intervento presentato al convegno International BASP Frontiers workshop 2015 tenutosi a Villars-sur-Ollon, Switzerland nel January 25 - 30, 2015).

Fast IRLS for sparse reconstruction based on gaussian mixtures

RAVAZZI, CHIARA;MAGLI, ENRICO
2015

Abstract

The theory of compressed sensing has demonstrated that sparse signals can be reconstructed from few linear measurements. In this work, we propose a new class of iteratively reweighted least squares (IRLS) for sparse recovery. The proposed methods use a two state Gaussian scale mixture as a proxy for the signal model and can be interpreted as an Expectation Maximization algorithm that attempts to perform the constrained maximization of the log-likelihood function. Under some conditions, standard in the compressed sensing theory, the sequences generated by these algorithms converge to the fixed points of the maps that rule their dynamics. A condition for exact sparse recovery, that is verifible a posteriori, is derived and the convergence is proved to be quadratically fast in a neighborhood of the desired solution. Numerical experiments show that these new reconstructions schemes outperform classical IRLS for lp -minimization with p\in(0, 1] in terms of rate of convergence and accuracy
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2623862
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