3D ROI Image Reconstruction from Truncated Computed Tomography

This paper introduces a novel method for accurate region-of-interest (ROI) reconstruction from 3D computed tomography (CT), consisting of a wavelet-based regularized iterative reconstruction procedure which is guaranteed to converge to an exact or highly accurate solution within the ROI. ROI tomography is motivated by the goal to reduce the overall radiation exposure when primarily the reconstruction of a specified region rather than the whole object is required. Our approach assumes that only the 3D truncated X-ray projections restricted to the ROI are known and does not assume any previous knowledge about the density function, except for standard assumptions about integrability and regularity needed to ensure that forward and backward transforms are well defined. The main original contributions of this paper are the novel regularized reconstruction algorithm for 3D ROI CT, the theoretical justification of its convergence and the detailed analysis of the stability of the reconstruction algorithm as a function of the size of the ROI. Another benefit of our approach is that it not limited to a specific mode of acquisition. The algorithm performance is validated on both phantoms and experimental data using various simulated acquisition geometries.