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

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 [1, 2], 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.

• Type: Journal
• Year: 2011
• Where: JMIV
• Authors: A. Woiselle, Jean-Luc Starck, Jalal Fadili
• Keywords: 3-D Multi-scale Transforms, Implementation, JMIV 2011, Massive Data Sets