Polychromatic Xray CT Image Reconstruction and MassAttenuation Spectrum Estimation
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 incidentenergy spectrum are unknown. We obtain a parsimonious measurementmodel 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 massattenuation spectrum function; the resulting measurement equation has the Laplace integral form. The massattenuation spectrum is then expanded into first order Bspline basis functions. We derive a block coordinatedescent algorithm for constrained minimization of a penalized negative loglikelihood (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 totalvariation (TV) and $\ell_1$ norms, applied to the densitymap image and its discrete wavelet transform (DWT) coefficients, respectively. This algorithm alternates between Nesterov's proximalgradient (NPG) and limitedmemory BroydenFletcherGoldfarbShanno with box constraints (LBFGSB) steps for updating the image and massattenuation spectrum parameters. To accelerate convergence of the densitymap NPG step, we apply a stepsize 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 KurdykaŁojasiewicz property of the objective function, which is important for establishing local convergence of the algorithm. Numerical experiments with simulated and real Xray CT data demonstrate the performance of the proposed scheme.
 Publication:

arXiv eprints
 Pub Date:
 September 2015
 DOI:
 10.48550/arXiv.1509.02193
 arXiv:
 arXiv:1509.02193
 Bibcode:
 2015arXiv150902193G
 Keywords:

 Statistics  Methodology
 EPrint:
 IEEE Trans. Comput. Imag., vol, 2, no. 2, (2016) 150165