Polychromatic X-ray CT Image Reconstruction and Mass-Attenuation Spectrum Estimation

dc.contributor.author Gu, Renliang
dc.contributor.author Dogandžić, Aleksandar
dc.contributor.department Electrical and Computer Engineering
dc.date.accessioned 2023-02-14T16:39:18Z
dc.date.available 2023-02-14T16:39:18Z
dc.date.issued 2015-09-07
dc.description.abstract We develop a method for sparse image reconstruction from polychromatic computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident-energy spectrum are unknown. 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 Laplace integral form. The mass-attenuation spectrum is then expanded into first order B-spline basis functions. We derive a block coordinate-descent algorithm for constrained minimization of a penalized negative log-likelihood (NLL) cost function, where penalty terms ensure nonnegativity of the spline coefficients and nonnegativity and sparsity of the density map. The image sparsity is imposed using total-variation (TV) and ℓ1 norms, applied to the density-map image and its discrete wavelet transform (DWT) coefficients, respectively. This algorithm alternates between Nesterov's proximal-gradient (NPG) and limited-memory Broyden-Fletcher-Goldfarb-Shanno with box constraints (L-BFGS-B) steps for updating the image and mass-attenuation spectrum parameters. To accelerate convergence of the density-map NPG step, we apply a step-size selection scheme that accounts for varying local Lipschitz constant of the NLL. We consider lognormal and Poisson noise models and establish conditions for biconvexity of the corresponding NLLs. We also prove the Kurdyka-Łojasiewicz property of the objective function, which is important for establishing local convergence of the algorithm. Numerical experiments with simulated and real X-ray CT data demonstrate the performance of the proposed scheme.
dc.description.comments This is a pre-print of the article Gu, Renliang, and Aleksandar Dogandžić. "Polychromatic X-ray CT image reconstruction and mass-attenuation spectrum estimation." arXiv preprint arXiv:1509.02193 (2015). DOI: 10.48550/arXiv.1509.02193. Copyright 2015 The Authors. Posted with permission.
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/qzoDMpmw
dc.language.iso en
dc.publisher arXiv
dc.source.uri https://doi.org/10.48550/arXiv.1509.02193 *
dc.subject.disciplines DegreeDisciplines::Engineering::Electrical and Computer Engineering
dc.title Polychromatic X-ray CT Image Reconstruction and Mass-Attenuation Spectrum Estimation
dc.type Preprint
dspace.entity.type Publication
relation.isAuthorOfPublication c910f7d3-c386-4c37-8143-4e653a539aa9
relation.isOrgUnitOfPublication a75a044c-d11e-44cd-af4f-dab1d83339ff
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