Efficient Sampling of Bernoulli-Gaussian-Mixtures for Sparse Signal Restoration - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Efficient Sampling of Bernoulli-Gaussian-Mixtures for Sparse Signal Restoration

Résumé

This paper introduces a new family of prior models called Bernoulli-Gaussian-Mixtures (BGM), with a view to efficiently address sparse inverse problems in the Bayesian framework. The BGM family is based on continuous Location and Scale Mixtures of Gaussians (LSMG), which includes a wide range of symmetric and asymmetric heavy-tailed probability distributions. The decomposition of a distribution as a Gaussian mixture is a case of data augmentation from which we derive a Partially Collapsed Gibbs Sampler (PCGS) for the BGM, in a systematic way. the derived PCGS is shown to be more efficient than the standard Gibbs sampler, both in terms of number of iterations and CPU time. Moreover, special attention is paid to BGM involving a density defined over a real half-line. An asymptotically exact LSMG approximation is introduced, which allows us to expand the applicability of PCGS to cases such as BGM models with a non-negative support.
Fichier principal
Vignette du fichier
draft.pdf (850.14 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03573517 , version 1 (14-02-2022)
hal-03573517 , version 2 (24-02-2022)

Identifiants

  • HAL Id : hal-03573517 , version 1

Citer

Mehdi Amrouche, Hervé Carfantan, Jérôme Idier. Efficient Sampling of Bernoulli-Gaussian-Mixtures for Sparse Signal Restoration. 2022. ⟨hal-03573517v1⟩
168 Consultations
293 Téléchargements

Partager

Gmail Facebook X LinkedIn More