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L1 Splines for Robust, Simple, and Fast Smoothing of Grid Data

Publication ,  Journal Article
Tepper, M; Sapiro, G
August 10, 2012

Splines are a popular and attractive way of smoothing noisy data. Computing splines involves minimizing a functional which is a linear combination of a fitting term and a regularization term. The former is classically computed using a (weighted) L2 norm while the latter ensures smoothness. Thus, when dealing with grid data, the optimization can be solved very efficiently using the DCT. In this work we propose to replace the L2 norm in the fitting term with an L1 norm, leading to automatic robustness to outliers. To solve the resulting minimization problem we propose an extremely simple and efficient numerical scheme based on split-Bregman iteration combined with DCT. Experimental validation shows the high-quality results obtained in short processing times.

Duke Scholars

Publication Date

August 10, 2012
 

Citation

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Tepper, Mariano, and Guillermo Sapiro. “L1 Splines for Robust, Simple, and Fast Smoothing of Grid Data,” August 10, 2012.
Tepper, Mariano, and Guillermo Sapiro. L1 Splines for Robust, Simple, and Fast Smoothing of Grid Data. Aug. 2012.

Publication Date

August 10, 2012