  Investigation of image reconstruction from data collected over a limited
angular range in X-ray CT remains a topic of active research because it may
yield insight into the development of imaging workflow of practical
significance. This reconstruction problem is well-known to be challenging,
however, because it is highly ill-conditioned. In the work, we investigate
optimization-based image reconstruction from data acquired over a
limited-angular range that is considerably smaller than the angular range in
short-scan CT. We first formulate the reconstruction problem as a convex
optimization program with directional total-variation (TV) constraints applied
to the image, and then develop an iterative algorithm, referred to as the
directional-TV (DTV) algorithm for image reconstruction through solving the
optimization program. We use the DTV algorithm to reconstruct images from data
collected over a variety of limited-angular ranges for breast and bar phantoms
of clinical- and industrial-application relevance. The study demonstrates that
the DTV algorithm accurately recovers the phantoms from data generated over a
significantly reduced angular range, and that it considerably diminishes
artifacts observed otherwise in reconstructions of existing algorithms. We have
also obtained empirical conditions on minimal angular ranges sufficient for
numerically accurate image reconstruction with the DTV algorithm.
