3-D Data Denoising and Inpainting with the Low-Redundancy Fast Curvelet Transform

Arnaud Woiselle (1, 2) , Jean-Luc Starck (2) , Jalal M. Fadili (3)

1 SAGEM Défense Sécurité [Massy]
2 DEDIP - Département d'Electronique, des Détecteurs et d'Informatique pour la Physique (ex SEDI)
3 Equipe Image - Laboratoire GREYC - UMR6072

In this paper, we first present a new implementation of the 3-D fast curvelet transform, which is nearly 2.5 less redundant than the Curvelab (wrapping-based) implementation as originally proposed in Ying et al. (Proceedings of wavelets XI conference, San Diego, 2005) and Candès et al. (SIAM Multiscale Model. Simul. 5(3):861---899, 2006), which makes it more suitable to applications including massive data sets. We report an extensive comparison in denoising with the Curvelab implementation as well as other 3-D multi-scale transforms with and without directional selectivity. The proposed implementation proves to be a very good compromise between redundancy, rapidity and performance. Secondly, we exemplify its usefulness on a variety of applications including denoising, inpainting, video de-interlacing and sparse component separation. The obtained results are good with very simple algorithms and virtually no parameter to tune.

Mots clés: video deinterlacing; 3-D Curvelets; sparsity; denoising; inpainting; Morphological Component Analysis; video deinterlacing.

Domaines: Traitement des images [eess.IV]

Arnaud Woiselle, Jean-Luc Starck, Jalal M. Fadili. 3-D Data Denoising and Inpainting with the Low-Redundancy Fast Curvelet Transform. Journal of Mathematical Imaging and Vision, 2011, 39 (2), pp.121-139. ⟨10.1007/s10851-010-0231-5⟩. ⟨hal-00808579⟩