  The recovery of structured signals from a few linear measurements is a
central point in both compressed sensing (CS) and discrete tomography. In CS
the signal structure is described by means of a low complexity model e.g.
co-/sparsity. The CS theory shows that any signal/image can be undersampled at
a rate dependent on its intrinsic complexity. Moreover, in such undersampling
regimes, the signal can be recovered by sparsity promoting convex
regularization like $\ell_1$- or total variation (TV-) minimization. Precise
relations between many low complexity measures and the sufficient number of
random measurements are known for many sparsity promoting norms. However, a
precise estimate of the undersampling rate for the TV seminorm is still
lacking. We address this issue by: a) providing dual certificates testing
uniqueness of a given cosparse signal with bounded signal values, b)
approximating the undersampling rates via the statistical dimension of the TV
descent cone and c) showing empirically that the provided rates also hold for
tomographic measurements.
