An algorithm for constrained one-step inversion of spectral CT data

Abstract

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.

Submitted to Physics in Medicine and Biology

References in corpus (3)

• Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT
• Joint Reconstruction of Multi-channel, Spectral CT Data via Constrained Total Nuclear Variation Minimization
• How little data is enough? Phase-diagram analysis of sparsity-regularized X-ray CT

Cited by in corpus (25)

• Image Domain Dual Material Decomposition for Dual-Energy CT using Butterfly Network
• Faster PET Reconstruction with Non-Smooth Priors by Randomization and Preconditioning
• A material decomposition method for dual-energy CT via dual interactive Wasserstein generative adversarial networks
• Dual-energy CT imaging with limited-angular-range data
• Systematic Review on Learning-based Spectral CT
• Estimating the spectrum in computed tomography via Kullback-Leibler divergence constrained optimization
• DLIMD: Dictionary Learning based Image-domain Material Decomposition for spectral CT
• Superiorized algorithm for reconstruction of CT images from sparse-view and limited-angle polyenergetic data
• Block Matching Frame based Material Reconstruction for Spectral CT
• Crystalline phase discriminating neutron tomography using advanced reconstruction methods
• Uniqueness criteria in multi-energy CT
• Regularization by Denoising Sub-sampled Newton Method for Spectral CT Multi-Material Decomposition
• One-step Method for Material Quantitation using In-line Tomography with Single Scanning
• ROI-Wise Material Decomposition in Spectral Photon-Counting CT
• Sparse-View Spectral CT Reconstruction Using Deep Learning
• Multi-modality imaging with structure-promoting regularisers
• Convergence for nonconvex ADMM, with applications to CT imaging
• Three material decomposition for spectral computed tomography enabled by block-diagonal step-preconditioning
• Invertibility of Multi-Energy X-ray Transform
• ADJUST: A Dictionary-Based Joint Reconstruction and Unmixing Method for Spectral Tomography
• Design of Spatial-Spectral Filters for CT Material Decomposition
• Solution existence, uniqueness, and stability of discrete basis sinograms in multispectral CT
• Improved Material Decomposition with a Two-step Regularization for spectral CT
• Non-convex primal-dual algorithm for image reconstruction in spectral CT
• Efficient Image Reconstruction and Practical Decomposition for Dual-energy Computed Tomography