In this paper, we propose a new method for support detection and estimation of sparse and approximately sparse signals from compressed measurements. Using a double Laplace mixture model as the parametric representation of the signal coefficients, the problem is formulated as a weighted l1 minimization. Then, we introduce a new family of iterative shrinkage-thresholding algorithms based on double Laplace mixture models. They preserve the computational simplicity of classical ones and improve iterative estimation by incorporating soft support detection. In particular, at each iteration, by learning the components that are likely to be nonzero from the current MAP signal estimate, the shrinkage-thresholding step is adaptively tuned and optimized. Unlike other adaptive methods, we are able to prove, under suitable conditions, the convergence of the proposed methods to a local minimum of the weighted l1 minimization. Moreover, we also provide an upper bound on the reconstruction error. Finally, we show through numerical experiments that the proposed methods outperform classical shrinkage-thresholding in terms of rate of convergence, accuracy, and of sparsity-undersampling trade-off.
Improved iterative shrinkage-thresholding for sparse signal recovery via Laplace mixtures models / Ravazzi, Chiara; Magli, Enrico. - In: EURASIP JOURNAL ON ADVANCES IN SIGNAL PROCESSING. - ISSN 1687-6172. - 2018:1(2018), pp. 1-26.
|Titolo:||Improved iterative shrinkage-thresholding for sparse signal recovery via Laplace mixtures models|
|Data di pubblicazione:||2018|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1186/s13634-018-0565-5|
|Appare nelle tipologie:||1.1 Articolo in rivista|