  We introduce phase-diagram analysis, a standard tool in compressed sensing,
to the X-ray CT community as a systematic method for determining how few
projections suffice for accurate sparsity-regularized reconstruction. In
compressed sensing a phase diagram is a convenient way to study and express
certain theoretical relations between sparsity and sufficient sampling. We
adapt phase-diagram analysis for empirical use in X-ray CT for which the same
theoretical results do not hold. We demonstrate in three case studies the
potential of phase-diagram analysis for providing quantitative answers to
questions of undersampling: First we demonstrate that there are cases where
X-ray CT empirically performs comparable with an optimal compressed sensing
strategy, namely taking measurements with Gaussian sensing matrices. Second, we
show that, in contrast to what might have been anticipated, taking randomized
CT measurements does not lead to improved performance compared to standard
structured sampling patterns. Finally, we show preliminary results of how well
phase-diagram analysis can predict the sufficient number of projections for
accurately reconstructing a large-scale image of a given sparsity by means of
total-variation regularization.
