Backprojection‐filtration reconstruction without invoking a spatially varying weighting factor

Abstract

To develop a backprojection-filtration (BPF) algorithm with improved noise properties over the existing BPF algorithm through utilizing (approximate) redundant information in circular cone-beam or fan-beam scans. The backprojection steps in the existing filtered-backprojection (FBP) and BPF algorithms for fan-beam and cone-beam projections invoke spatially varying weighting factors, which may not only increase the computational load in image reconstruction but also, more importantly, result in reconstruction artifacts. Redundant information in fan-beam projections has been exploited for eliminating the weighting factor in the existing FBP algorithm. However, the new FBP algorithm cannot be applied to image reconstruction in a region of interest from transversely truncated data. In this work, the authors identify approximate data redundancy in circular cone-beam projections and propose a new BPF algorithm in which the approximate data redundancy is exploited for eliminating the spatially varying weighting factor in the existing BPF algorithm. The authors have implemented and evaluated the proposed BPF algorithm in numerical studies of reconstructing 3D images from both the nontruncated and truncated projection data in a circular cone-beam scan. The results of numerical studies demonstrate that the proposed BPF algorithm retains the resolution property of the existing BPF algorithm, and that it can also reconstruct accurately ROI images from truncated data. More importantly, the results also indicate that the proposed BPF algorithm not only is computationally more efficient but also yields generally lower image variances than the existing BPF algorithm. A BPF algorithm was proposed that not only retains the desirable properties of the existing BPF algorithm but also possesses improved computational and noise properties over the latter.