4 research outputs found
Sparse signal reconstruction from polychromatic X-ray CT measurements via mass attenuation discretization
We propose a method for reconstructing sparse images from polychromatic x-ray computed tomography (ct) measurements via mass attenuation coefficient discretization. The material of the inspected object and the incident spectrum are assumed to be unknown. We rewrite the Lambert-Beer’s law in terms of integral expressions of mass attenuation and discretize the resulting integrals. We then present a penalized constrained least-squares optimization approach forreconstructing the underlying object from log-domain measurements, where an active set approach is employed to estimate incident energy density parameters and the nonnegativity and sparsity of the image density map are imposed using negative-energy and smooth ℓ1-norm penalty terms. We propose a two-step scheme for refining the mass attenuation discretization grid by using higher sampling rate over the range with higher photon energy, and eliminating the discretization points that have little effect on accuracy of the forward projection model. This refinement allows us to successfully handle the characteristic lines (Dirac impulses) in the incident energy density spectrum. We compare the proposed method with the standard filtered backprojection, which ignores the polychromatic nature of the measurements and sparsity of theimage density map. Numerical simulations using both realistic simulated and real x-ray ct data are presented
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 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
Sparse X-ray CT image reconstruction and blind beam hardening correction via mass attenuation discretization
We develop a nonlinear sparse X-ray computed tomography (CT) image reconstruction method that accounts for beam hardening effects due to polychromatic X-ray sources. We adopt the blind scenario where the material of the inspected object and the incident polychromatic source spectrum are unknown and apply mass attenuation discretization of the underlying integral expressions that model the noiseless measurements. Our reconstruction algorithm employs constrained minimization of a penalized least-squares cost function, where nonnegativity and maximum-energy constraints are imposed on incident spectrum parameters and negative-energy and smooth â„“1-norm penalty terms are introduced to ensure the nonnegativity and sparsity of the density map image. This minimization scheme alternates between a nonlinear conjugate-gradient step for estimating the density map image and an active set step for estimating incident spectrum parameters. We compare the proposed method with the existing approaches, which ignore the polychromatic nature of the measurements or sparsity of the density map image.This is a manuscript of an article from 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013, 4pp.</p
Sparse X-ray CT image reconstruction and blind beam hardening correction via mass attenuation discretization
We develop a nonlinear sparse X-ray computed tomography (CT) image reconstruction method that accounts for beam hardening effects due to polychromatic X-ray sources. We adopt the blind scenario where the material of the inspected object and the incident polychromatic source spectrum are unknown and apply mass attenuation discretization of the underlying integral expressions that model the noiseless measurements. Our reconstruction algorithm employs constrained minimization of a penalized least-squares cost function, where nonnegativity and maximum-energy constraints are imposed on incident spectrum parameters and negative-energy and smooth â„“1-norm penalty terms are introduced to ensure the nonnegativity and sparsity of the density map image. This minimization scheme alternates between a nonlinear conjugate-gradient step for estimating the density map image and an active set step for estimating incident spectrum parameters. We compare the proposed method with the existing approaches, which ignore the polychromatic nature of the measurements or sparsity of the density map image.This is a manuscript of an article from 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013, 4pp.</p