Variational approximation for a functional governing point-like singularities

Daniele Graziani (1) , Gilles Aubert (2)

1 ARIANA - Inverse problems in earth monitoring
2 JAD - Laboratoire Jean Alexandre Dieudonné

The aim of this report is to provide a variational formulation for the detection of points in $2$-d biological images. To this purpose we introduce a new functional of the calculus of variation whose minimizers gives the points we want to detect. Then we build an approximating sequence of functional, for which we prove the $\Gamma$-convergence to the initial one.

Domaines: Analyse classique [math.CA]

Daniele Graziani, Gilles Aubert. Variational approximation for a functional governing point-like singularities. [Research Report] RR-7095, INRIA. 2009, pp.35. ⟨inria-00403232v3⟩