Variational approximation for detecting points-like target problems

Daniele Graziani (1) , Gilles Aubert (2)

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

he aim of this report is to provide a rigourous 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 detecting points-like target problems. [Research Report] RR-6987., 2009, pp.35. ⟨inria-00403232v1⟩