{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T20:01:26Z","timestamp":1760385686736,"version":"build-2065373602"},"reference-count":66,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2018,12,16]],"date-time":"2018-12-16T00:00:00Z","timestamp":1544918400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/e20120977","type":"journal-article","created":{"date-parts":[[2018,12,18]],"date-time":"2018-12-18T02:15:59Z","timestamp":1545099359000},"page":"977","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Bayesian 3D X-ray Computed Tomography with a Hierarchical Prior Model for Sparsity in Haar Transform Domain"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2727-6181","authenticated-orcid":false,"given":"Li","family":"Wang","sequence":"first","affiliation":[{"name":"Laboratoire des signaux et syst\u00e8me, Centralesupelec, CNRS, 3 Rue Joliot Curie, 91192 Gif sur Yvette, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0678-7759","authenticated-orcid":false,"given":"Ali","family":"Mohammad-Djafari","sequence":"additional","affiliation":[{"name":"Laboratoire des signaux et syst\u00e8me, Centralesupelec, CNRS, 3 Rue Joliot Curie, 91192 Gif sur Yvette, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6981-0368","authenticated-orcid":false,"given":"Nicolas","family":"Gac","sequence":"additional","affiliation":[{"name":"Laboratoire des signaux et syst\u00e8me, Centralesupelec, CNRS, 3 Rue Joliot Curie, 91192 Gif sur Yvette, France"}]},{"given":"Mircea","family":"Dumitru","sequence":"additional","affiliation":[{"name":"Laboratoire des signaux et syst\u00e8me, Centralesupelec, CNRS, 3 Rue Joliot Curie, 91192 Gif sur Yvette, France"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"R41","DOI":"10.1088\/0266-5611\/15\/2\/022","article-title":"Optical tomography in medical imaging","volume":"15","author":"Arridge","year":"1999","journal-title":"Inverse Probl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.nima.2008.03.016","article-title":"X-ray based methods for non-destructive testing and material characterization","volume":"591","author":"Hanke","year":"2008","journal-title":"Nucl. 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