19 research outputs found
Joint Reconstruction of Multi-channel, Spectral CT Data via Constrained Total Nuclear Variation Minimization
We explore the use of the recently proposed "total nuclear variation" (TNV)
as a regularizer for reconstructing multi-channel, spectral CT images. This
convex penalty is a natural extension of the total variation (TV) to
vector-valued images and has the advantage of encouraging common edge locations
and a shared gradient direction among image channels. We show how it can be
incorporated into a general, data-constrained reconstruction framework and
derive update equations based on the first-order, primal-dual algorithm of
Chambolle and Pock. Early simulation studies based on the numerical XCAT
phantom indicate that the inter-channel coupling introduced by the TNV leads to
better preservation of image features at high levels of regularization,
compared to independent, channel-by-channel TV reconstructions.Comment: Submitted to Physics in Medicine and Biolog
A Spectral CT Method to Directly Estimate Basis Material Maps From Experimental Photon-Counting Data
The proposed spectral CT method solves the constrained one-step spectral CT reconstruction (cOSSCIR) optimization problem to estimate basis material maps while modeling the nonlinear X-ray detection process and enforcing convex constraints on the basis map images. In order to apply the optimization-based reconstruction approach to experimental data, the presented method empirically estimates the effective energy-window spectra using a calibration procedure. The amplitudes of the estimated spectra were further optimized as part of the reconstruction process to reduce ring artifacts. A validation approach was developed to select constraint parameters. The proposed spectral CT method was evaluated through simulations and experiments with a photon-counting detector. Basis material map images were successfully reconstructed using the presented empirical spectral modeling and cOSSCIR optimization approach. In simulations, the cOSSCIR approach accurately reconstructed the basis map images
An algorithm for constrained one-step inversion of spectral CT data
We develop a primal-dual algorithm that allows for one-step inversion of
spectral CT transmission photon counts data to a basis map decomposition. The
algorithm allows for image constraints to be enforced on the basis maps during
the inversion. The derivation of the algorithm makes use of a local upper
bounding quadratic approximation to generate descent steps for non-convex
spectral CT data discrepancy terms, combined with a new convex-concave
optimization algorithm. Convergence of the algorithm is demonstrated on
simulated spectral CT data. Simulations with noise and anthropomorphic phantoms
show examples of how to employ the constrained one-step algorithm for spectral
CT data.Comment: Submitted to Physics in Medicine and Biolog