Blind X-ray CT Image Reconstruction from Polychromatic Poisson Measurements Gu, Renliang Dogandžić, Aleksandar Dogandžić, Aleksandar
dc.contributor.department Electrical and Computer Engineering 2018-02-17T11:42:14.000 2020-06-30T02:03:39Z 2020-06-30T02:03:39Z Thu Jan 01 00:00:00 UTC 2015 2016-06-01
dc.description.abstract <p>We develop a framework for reconstructing images that are sparse in an appropriate transform domain from polychromatic computed tomography (CT) measurements under the blind scenario where the material of the inspected object and incident-energy spectrum are unknown. Assuming that the object that we wish to reconstruct consists of a single material, we obtain a parsimonious measurement-model parameterization by changing the integral variable from photon energy to mass attenuation, which allows us to combine the variations brought by the unknown incident spectrum and mass attenuation into a single unknown mass-attenuation spectrum function; the resulting measurement equation has the Laplaceintegral form. The mass-attenuation spectrum is then expanded into basis functions using B-splines of order one. We consider a Poisson noise model and establish conditions for biconvexity of the corresponding negative log-likelihood (NLL) function with respect to the density-map and mass-attenuation spectrum parameters. We derive a block-coordinate descent algorithm for constrained minimization of a penalized NLL objective function, where penalty terms ensure nonnegativity of the mass-attenuation spline coefficients and nonnegativity and gradient-map sparsity of the density-map image, imposed using a convex total-variation (TV) norm; the resulting objective function is biconvex. This algorithm alternates between a Nesterov’s proximal-gradient (NPG) step and a limited-memory Broyden-Fletcher-Goldfarb-Shanno with box constraints (L-BFGSB) iteration for updating the image and mass-attenuation spectrum parameters, respectively. We prove the Kurdyka-Łojasiewicz property of the objective function, which is important for establishing local convergence of block-coordinate descent schemes in biconvex optimization problems. Our framework applies to other NLLs and signal-sparsity penalties, such as lognormal NLL and `1 norm of 2D discrete wavelet transform (DWT) image coefficien- s. Numerical experiments with simulated and real X-ray CT data demonstrate the performance of the proposed scheme.</p>
dc.description.comments <p>This is a manuscript of an article from <em>IEEE Transactions </em><em>on Computational Imaging</em> 2 (2016): 150, <a href="" target="_blank">doi:10.1109/TCI.2016.2523431</a>. Posted with permission.</p>
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dc.identifier archive/
dc.identifier.articleid 1084
dc.identifier.contextkey 8071541
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath ece_pubs/85
dc.language.iso en
dc.source.bitstream archive/|||Sat Jan 15 02:12:26 UTC 2022
dc.source.uri 10.1109/TCI.2016.2523431
dc.subject.disciplines Biomedical
dc.subject.disciplines Electromagnetics and Photonics
dc.subject.disciplines Other Electrical and Computer Engineering
dc.subject.keywords x-ray CT
dc.subject.keywords statistical model-based iterative reconstruction (MBIR)
dc.subject.keywords beam-hardening correction
dc.title Blind X-ray CT Image Reconstruction from Polychromatic Poisson Measurements
dc.type article
dc.type.genre article
dspace.entity.type Publication
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relation.isOrgUnitOfPublication a75a044c-d11e-44cd-af4f-dab1d83339ff
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