  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.
