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

  • Authors:

  • A. Woiselle;J. -L. Starck;J. Fadili

  • Affiliations:

  • CEA, IRFU, SEDI-SAP, Laboratoire Astrophysique des Interactions Multi-échelles (UMR 7158), CEA/DSM-CNRS-Universite Paris Diderot, Gif-Sur-Yvette, France 91191 and Sagem groupe SAFRAN, Argente ...;CEA, IRFU, SEDI-SAP, Laboratoire Astrophysique des Interactions Multi-échelles (UMR 7158), CEA/DSM-CNRS-Universite Paris Diderot, Gif-Sur-Yvette, France 91191;Image Processing Group, ENSICAEN, GREYC CNRS UMR 6072, Caen Cedex, France 14050

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 2011

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Abstract

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.