Convex Super-Resolution Detection of Lines in Images

Kévin Polisano (1) , Laurent Condat (2) , Marianne Clausel (3) , Valérie Perrier (1)

1 CVGI - Calcul des Variations, Géométrie, Image
2 GIPSA-AGPIG - GIPSA - Architecture, Géométrie, Perception, Images, Gestes
3 DAO - Données, Apprentissage et Optimisation

In this paper, we present a new convex formulation for the problem of recovering lines in degraded images. Following the recent paradigm of super-resolution, we formulate a dedicated atomic norm penalty and we solve this optimization problem by means of a primal–dual algorithm. This parsimonious model enables the reconstruction of lines from lowpass measurements, even in presence of a large amount of noise or blur. Furthermore, a Prony method performed on rows and columns of the restored image, provides a spectral estimation of the line parameters, with subpixel accuracy.

Mots clés: Primal-Dual Algorithm; Prony; Convex Optimization; Atomic norm; Super-resolution; Sparsity; Line Detection

Domaines: Traitement du signal et de l'image [eess.SP]

Kévin Polisano, Laurent Condat, Marianne Clausel, Valérie Perrier. Convex Super-Resolution Detection of Lines in Images. EUSIPCO 2016 - 24th European Signal Processing Conference, Aug 2016, Budapest, Hungary. pp.336-340, ⟨10.1109/EUSIPCO.2016.7760265⟩. ⟨hal-01281979v2⟩