  It is well-known that point sources with sufficient mutual distance can be
reconstructed exactly from finitely many Fourier measurements by solving a
convex optimization problem with Tikhonov-regularization (this property is
sometimes termed superresolution). In case of noisy measurements one can bound
the reconstruction error in unbalanced Wasserstein distances or weak
Sobolev-type norms. A natural question is to what other settings the phenomenon
of superresolution extends. We here keep the same measurement operator, but
replace the regularizer to anisotropic total variation, which is particularly
suitable for regularizing piecewise constant images with horizontal and
vertical edges. Under sufficient mutual distance between the horizontal and
vertical edges we prove exact reconstruction results and $L^1$ error bounds in
terms of the measurement noise.
