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

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 $\ell_1$ 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-{\L}ojasiewicz 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

Altered functional and structural brain network organization in autism.

Structural and functional underconnectivity have been reported for multiple brain regions, functional systems, and white matter tracts in individuals with autism spectrum disorders (ASD). Although recent developments in complex network analysis have established that the brain is a modular network exhibiting small-world properties, network level organization has not been carefully examined in ASD. Here we used resting-state functional MRI (n = 42 ASD, n = 37 typically developing; TD) to show that children and adolescents with ASD display reduced short and long-range connectivity within functional systems (i.e., reduced functional integration) and stronger connectivity between functional systems (i.e., reduced functional segregation), particularly in default and higher-order visual regions. Using graph theoretical methods, we show that pairwise group differences in functional connectivity are reflected in network level reductions in modularity and clustering (local efficiency), but shorter characteristic path lengths (higher global efficiency). Structural networks, generated from diffusion tensor MRI derived fiber tracts (n = 51 ASD, n = 43 TD), displayed lower levels of white matter integrity yet higher numbers of fibers. TD and ASD individuals exhibited similar levels of correlation between raw measures of structural and functional connectivity (n = 35 ASD, n = 35 TD). However, a principal component analysis combining structural and functional network properties revealed that the balance of local and global efficiency between structural and functional networks was reduced in ASD, positively correlated with age, and inversely correlated with ASD symptom severity. Overall, our findings suggest that modeling the brain as a complex network will be highly informative in unraveling the biological basis of ASD and other neuropsychiatric disorders