Two‐dimensional iterative region‐of‐interest (ROI) reconstruction from truncated projection data

Abstract

A small detector or limited gantry rotation angles may cause data truncation, in which case the entire object cannot be completely reconstructed. However, a small region of interest (ROI) may be recoverable in certain truncation situations. Two analytical methods have been proposed for exact ROI reconstruction. Here we evaluate the capability of ROI reconstruction using an maximum-likelihood expectation-maximization (ML-EM) method, which directly solves the inverse problem of the system equations. ROI reconstruction using the ML-EM method is compared with that using the two analytical methods. Comparisons are based on reconstructions of four specifically designed, computer-simulated truncation cases. In the simulation, each reconstructed ROI is coupled with its counterpart in the nontruncated case to evaluate the accuracy of the reconstructed ROI. We found that, (a) in two truncation situations the ROI can be reconstructed by both the analytical methods and the two-dimensional ML-EM method, but the ML-EM method may produce a larger ROI; (b) for a truncation case [Fig. 3(c)] that neither analytical algorithm is applicable, the ML-EM method provides a quantitative ROI reconstruction; and (c) for the well-known "interior" truncation problem, neither the analytical methods nor the ML-EM method can perform an exact ROI reconstruction, but the ML-EM method provides informative ROI images. We also propose an analysis using the truncated projection matrix and its Moore-Penrose inverse matrix which can help to determine the recoverable ROI using iterative methods for a given truncation situation.