Analysis of Singularity Lines by Transforms with Parabolic Scaling

Panuvuth Lakhonchai (1) , Jouni Sampo (2) , Songkiat Sumetkijakan (1)

1 Department of Mathematics
2 Department of Applied Mathematics

Using Hart Smith's, curvelet, and shearlet transforms, we investigate L2 functions with sufficiently smooth background and present here sufficient and necessary conditions, which include the special case with 1-dimensional singularity line. Specifically, we consider the situation where regularity on a line in a non-parallel direction is much lower than directional regularity along the line in a neighborhood and how this is reflected in the behavior of the three transforms.

Domaines: Analyse classique [math.CA]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Panuvuth Lakhonchai, Jouni Sampo, Songkiat Sumetkijakan. Analysis of Singularity Lines by Transforms with Parabolic Scaling. SAMPTA'09, May 2009, Marseille, France. Special session on geometric multiscale analysis. ⟨hal-00451838⟩