A perfect reconstruction property for PDE-constrained total-variation minimization with application in Quantitative Susceptibility Mapping

@article{Bredies2019APR,
  title={A perfect reconstruction property for PDE-constrained total-variation minimization with application in Quantitative Susceptibility Mapping},
  author={Kristian Bredies and David Vicente},
  journal={ESAIM: Control, Optimisation and Calculus of Variations},
  year={2019}
}
We study the recovery of piecewise constant functions of finite bounded variation (BV) from their image under a linear partial differential operator with unknown boundary conditions. It is shown that minimizing the total variation (TV) semi-norm subject to the associated PDE-constraints yields perfect reconstruction up to a global constant under a mild geometric assumption on the jump set of the function to reconstruct. The proof bases on establishing a structural result about the jump set… 

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