One-step inversion algorithms for spectral CT, with application to dynamic Cone Beam CT

Abstract

Dual energy Cone Beam Comptuted Tomography (DE-CBCT) is a promising technique for several medical applications, including dynamic angiography. Recently, a dynamical two-step method has been proposed : first, the water and iodine projections are computed from the multi-energy sinograms, then, a dynamic image of the iodine contrast is reconstructed using 4D Total-Variation (TV) constrained reconstruction from the iodine projections. In contrast to the 2-step methods, one-step methods use a model relating directly the multi-material images to the multi-energy sinograms. This kind of methods are well-known to reduce the noise correlation between the material images by avoiding the intermediate decomposition step, but request to solve an non-convex large scale optimization problem which can be challenging. In this work we use the Non-Linear Primal-Dual Hybrid Gradient Method (NL-PDHGM) optimization framework to propose two versions of a one-step method which is based on an empirical model : the first one is a version which considers the multi-material images as static object whereas the second version is developped for a spectific application with a static water image and a dynamic iodine image consisting of a series of 3D iodine images associated to different time points. This last version is developped to obtain the evolution of the iodine concentration in the blood vessels during a single CBCT scan. To evaluate the proposed one-step methods we used simulations which consider a CBCT system with dual layer spectral detector and a brain phantom with a static and a dynamic vascular tree. The proposed one-step methods are compared with 2-step methods.

Dual- and multi-energy CT for particle stopping-power estimation: current state, challenges and potential

“…Two-step methods (Faby et al 2015, Simard et al 2020b are analogous to the approach of Alvarez and Macovski (1976) as they resolve the image in 2 steps: (1) resolving the image parameters in the sinogram space based on the crosssection model, and (2) reconstructing each resolved sinogram independently. But two-step methods are limited by the presence of noise when applied to data with more than 2 energies (Schmidt et al 2017, Jolivet et al 2021. One-step methods resolve the image by formulating the problem as a large-scale optimization to extract image properties directly from spectral sinogram data.…”

“…One-step methods resolve the image by formulating the problem as a large-scale optimization to extract image properties directly from spectral sinogram data. A few of those methods were proposed over the last decade, first for DECT (Cai et al 2013, Long and Fessler 2014, Jolivet et al 2021, later for spectral PCCT focused on K-edge imaging (Foygel Barber et al 2016, Weidinger et al 2016, and recently for spectral PCCT in the context of radiotherapy (Simard and Bouchard 2022). Such approaches are currently the most promising for simultaneously correcting major reconstruction artefacts (e.g.…”