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3-D data denoising and inpainting with the low-redundancy fast curvelet transform. (English) Zbl 1255.68273
Summary: 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 by Ying et al. and Candès et al., 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.

MSC:
68U10 Computing methodologies for image processing
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
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