Shape-preserving, multiscale fitting of univariate data by cubic L1 smoothing splines Original Research Article

A new class of C1 -smooth univariate cubic L1 smoothing splines is introduced. The coefficients of these smoothing splines are calculated by minimizing the weighted sum of the ℓ1 norm of the residuals of the data-fitting equations and the L1 norm of the second derivative of the spline. Cubic L1 smoothing splines preserve shape well for arbitrary data, including multiscale data with abrupt changes in magnitude and spacing. Extensions to higher-degree and higher-dimensional smoothing splines are outlined.