ℓ1-concave versus ℓ1 - TV energies. Questions and challenges

Mila Nikolova
École Normale Supérieure de Cachan

Recently a new family of cost functions for signal and image recovery was proposed: they are composed of l1 data fitting term combined with concave regularization. Their minimizers were shown to exhibit strong properties: each one of their entries is involved either in an exact data fitting component or in a null component of the regularization part. Numerical tests have shown the possibilities they offer for signal and image recovery. These l1-concave energies can be seen as an extension of the convex l1-TV energies. Indeed, the minimizers of these two kinds of energies share some properties like “contrast preservation”. Mathematically, they solve similar forms of linear systems. For the new family, all these features appear in an enhanced way. Here we compare analytically and experimentally these two kinds of energies.

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