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

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