Monotonic iterative reconstruction algorithms for targeted reconstruction in emission and transmission computed tomography

Targeted reconstruction is reconstruction of a portion of an object, even when sufficient data are available to reconstruct the entire object. It is used in CT to zoom in on a region using smaller pixels without the burden of reconstructing a larger array. This is straightforward when using analytic algorithms. It is less apparent how to perform this kind of targeted reconstruction using iterative algorithms, since these algorithms involve reprojecting the entire object for comparison with the data. In this work, we consider two approaches to this problem. One is a simple extension of an approach previously proposed by Ziegler but which better preserves the statistical properties of the raw data. An initial analytic reconstruction is performed, the ROI of interest is removed, and what remains is reprojected to obtain an estimate of the contributions of the area outside the ROI to the projections. Then this estimate is added to the projections of the ROI at each iteration, allowing for comparison to be made with the original, unmodified data. The second approach treats the set of non-ROI projections as a second vector of unknowns, in addition to the pixel values within the ROI. We then seek to maximize a joint penalized likelihood objective function and we do so using an alternating update strategy that is guaranteed to monotonically increase the objective function.