  We study recoverability in fan-beam computed tomography (CT) with sparsity
and total variation priors: how many underdetermined linear measurements
suffice for recovering images of given sparsity? Results from compressed
sensing (CS) establish such conditions for, e.g., random measurements, but not
for CT. Recoverability is typically tested by checking whether a computed
solution recovers the original. This approach cannot guarantee solution
uniqueness and the recoverability decision therefore depends on the
optimization algorithm. We propose new computational methods to test
recoverability by verifying solution uniqueness conditions. Using both
reconstruction and uniqueness testing we empirically study the number of CT
measurements sufficient for recovery on new classes of sparse test images. We
demonstrate an average-case relation between sparsity and sufficient sampling
and observe a sharp phase transition as known from CS, but never established
for CT. In addition to assessing recoverability more reliably, we show that
uniqueness tests are often the faster option.
