Convex Super-Resolution Detection of Lines in Images

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

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

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 the 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 line parameters, with subpixel accuracy.

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

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. 2016. ⟨hal-01281979v1⟩