Accurate image reconstruction from truncated offset CT data using TVL1 algorithm

In computed tomography (CT), transverse truncation occurs when the X-ray beam's transverse field-of-view (FOV) is smaller than the subject's size. While the FOV can be expanded by offsetting the detector, this adjustment may still be insufficient for large subjects or small detectors. Existing research primarily focuses on image reconstruction within the FOV. In contrast, our study aims to achieve accurate reconstructions both within the FOV and across a significantly larger region. We formulate the reconstruction problem from truncated CT data as a convex optimization problem, incorporating hybrid constraints on total variation (TV) and L1-norm within different image regions. We propose the TVL1 algorithm for accurate reconstructions within a region substantially larger than the FOV. Through simulations and real-data experiments involving various truncation levels using the offset detector setup, we demonstrate the algorithm's robustness and performance. Our findings reveal the TVL1 algorithm's effectiveness in reconstructing images within and beyond the FOV under different practical truncation scenarios.