Robust smoothing of gridded data in one and higher dimensions with missing values

A fully automated smoothing procedure for uniformly sampled datasets is described. The algorithm, based on a penalized least squares method, allows fast smoothing of data in one and higher dimensions by means of the discrete cosine transform. Automatic choice of the amount of smoothing is carried out by minimizing the generalized cross-validation score. An iteratively weighted robust version of the algorithm is proposed to deal with occurrences of missing and outlying values. Simplified Matlab codes with typical examples in one to three dimensions are provided. A complete user-friendly Matlab program is also supplied. The proposed algorithm, which is very fast, automatic, robust and requiring low storage, provides an efficient smoother for numerous applications in the area of data analysis.