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It is well-known that point sources with sufficient mutual distance can bereconstructed exactly from finitely many Fourier measurements by solving aconvex optimization problem with Tikhonov-regularization (this property issometimes termed superresolution). In case of noisy measurements one can boundthe reconstruction error in unbalanced Wasserstein distances or weakSobolev-type norms. A natural question is to what other settings the phenomenonof superresolution extends. We here keep the same measurement operator, butreplace the regularizer to anisotropic total variation, which is particularlysuitable for regularizing piecewise constant images with horizontal andvertical edges. Under sufficient mutual distance between the horizontal andvertical edges we prove exact reconstruction results and $L^1$ error bounds interms of the measurement noise.

Exact reconstruction and reconstruction from noisy data with anisotropic total variation