  In x-ray computed tomography (CT) it is generally acknowledged that
reconstruction methods exploiting image sparsity allow reconstruction from a
significantly reduced number of projections. The use of such reconstruction
methods is motivated by recent progress in compressed sensing (CS). However,
the CS framework provides neither guarantees of accurate CT reconstruction, nor
any relation between sparsity and a sufficient number of measurements for
recovery, i.e., perfect reconstruction from noise-free data. We consider
reconstruction through 1-norm minimization, as proposed in CS, from data
obtained using a standard CT fan-beam sampling pattern. In empirical simulation
studies we establish quantitatively a relation between the image sparsity and
the sufficient number of measurements for recovery within image classes
motivated by tomographic applications. We show empirically that the specific
relation depends on the image class and in many cases exhibits a sharp phase
transition as seen in CS, i.e. same-sparsity image require the same number of
projections for recovery. Finally we demonstrate that the relation holds
independently of image size and is robust to small amounts of additive Gaussian
noise.
