Evaluation of 2D ROI Image Reconstruction Using ML-EM Method from Truncated Projections

Recently new analytical sufficient conditions and inversion formulas have been found for exact reconstruction of a region of interest (ROI) from truncated projections. However, it remains unknown whether these results can be applied to iterative reconstruction methods which are based discrete-discrete imaging models. In this paper, we explore the behavior of iterative reconstruction methods for truncated data. We evaluate the maximum-likelihood (ML) expectation-maximization (EM) method under three data truncation cases, namely, the classical interior and exterior tomography problems, and a new type of peripheral ROIs which satisfy the data sufficiency condition for the two-step Hilbert transform method [Noo et al., 2004]. The simulation results show that the peripheral ROIs can be reconstructed by ML-EM method regardless of truncation, but the interior and exterior problem suffer from different degrees of artifacts. These results are consistent with existing analytical data sufficiency conditions. We also numerically calculate the singular value decomposition (SVD) of the truncated system matrix, which shows that when the analytical sufficient condition for an ROI is satisfied, the singular vectors associated with very small singular values have little intersection with the ROI.