Performance comparison of Bayesian iterative algorithms for three classes of sparsity enforcing priors with application in computed tomography

Dumitru, Mircea; Wang, Li; Gac, Nicolas; Mohammad-Djafari, Ali

doi:10.1109/icip.2017.8296949

Cited by 4 publications

(3 citation statements)

References 15 publications

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“…In this context, as future work, we are investigating the causes of the relatively weak influence of the hyper-parameters and the theoretical foundation of the corresponding robust interval, extending the discussion to the same approach using sparsity-enforcing priors expressed as normal variance mixtures, but for other mixing distributions (Gamma, generalized inverse Gaussian) [ 66 ].…”

Section: Discussionmentioning

confidence: 99%

Bayesian 3D X-Ray Computed Tomography with a Hierarchical Prior Model for Sparsity in Haar Transform Domain

Wang

Mohammad-Djafari

Gac

et al. 2018

Entropy

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In this paper, a hierarchical prior model based on the Haar transformation and an appropriate Bayesian computational method for X-ray CT reconstruction are presented. Given the piece-wise continuous property of the object, a multilevel Haar transformation is used to associate a sparse representation for the object. The sparse structure is enforced via a generalized Student-t distribution (S t g ), expressed as the marginal of a normal-inverse Gamma distribution. The proposed model and corresponding algorithm are designed to adapt to specific 3D data sizes and to be used in both medical and industrial Non-Destructive Testing (NDT) applications. In the proposed Bayesian method, a hierarchical structured prior model is proposed, and the parameters are iteratively estimated. The initialization of the iterative algorithm uses the parameters of the prior distributions. A novel strategy for the initialization is presented and proven experimentally. We compare the proposed method with two state-of-the-art approaches, showing that our method has better reconstruction performance when fewer projections are considered and when projections are acquired from limited angles.

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Section: Discussionmentioning

confidence: 99%

Bayesian 3D X-Ray Computed Tomography with a Hierarchical Prior Model for Sparsity in Haar Transform Domain

Wang

Mohammad-Djafari

Gac

et al. 2018

Entropy

Self Cite

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“…For the sake of keeping conjugacy between prior and posterior distributions of u , a Gamma distribution

scriptG false(u falsefalse| α_{k}, β_{k} false)

with shape and rate parameters

false(α_{k}, β_{k} false)

is chosen for

p_{k} false(u false) = p false(u falsefalse| z = k false) = scriptG false(u falsefalse| α_{k}, β_{k} false)

. Integrating (13) out u , the resulting marginal

p false(bold-italicx falsefalse| z, boldΘ, scriptK false)

is a heavy‐tailed distribution known as the Student‐ t distribution [38].…”

Section: Modelmentioning

confidence: 99%

Radar emitters classification and clustering with a scale mixture of normal distributions

Revillon

Mohammad-Djafari

Enderli

2019

IET Radar, Sonar & Navigation

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“…For the sake of keeping conjugacy between prior and posterior distributions of u, a Gamma distribution G(u|α k , β k ) with shape and rate parameters (α k , β k ) is chosen for p k (u). Integrating (7) out u, the resulting marginal p(x|z, Θ, K) is a heavy-tailed distribution known as the Student-t distribution [5].…”

Section: Latent Variable Model a Gmmmentioning

confidence: 99%

Variational Bayesian Inference For A Scale Mixture Of Normal Distributions Handling Missing Data

Revillon,

Djafari,

Enderli

2017

Preprint

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In this paper, a scale mixture of Normal distributions model is developed for classification and clustering of data having outliers and missing values. The classification method, based on a mixture model, focuses on the introduction of latent variables that gives us the possibility to handle sensitivity of model to outliers and to allow a less restrictive modelling of missing data. Inference is processed through a Variational Bayesian Approximation and a Bayesian treatment is adopted for model learning, supervised classification and clustering.

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Performance comparison of Bayesian iterative algorithms for three classes of sparsity enforcing priors with application in computed tomography

Cited by 4 publications

References 15 publications

Bayesian 3D X-Ray Computed Tomography with a Hierarchical Prior Model for Sparsity in Haar Transform Domain

Bayesian 3D X-Ray Computed Tomography with a Hierarchical Prior Model for Sparsity in Haar Transform Domain

Radar emitters classification and clustering with a scale mixture of normal distributions

Variational Bayesian Inference For A Scale Mixture Of Normal Distributions Handling Missing Data

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