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The goal of this paper is to achieve a computational model and correspondingefficient algorithm for obtaining a sparse representation of the fittingsurface to the given scattered data. The basic idea of the model is to utilizethe principal shift invariant (PSI) space and the l1 norm minimization. Inorder to obtain different sparsity of the approximation solution, the problemis represented as a multilevel LASSO (MLASSO) model with differentregularization parameters. The MLASSO model can be solved efficiently by thealternating direction method of multipliers. Numerical experiments indicatethat compared to the AGLASSO model and the basic MBA algorithm, the MLASSOmodel can provide an acceptable compromise between the minimization of the datamismatch term and the sparsity of the solution. Moreover, the solution by theMLASSO model can reflect the regions of the underlying surface where highgradients occur.

Sparse approximate solution of fitting surface to scattered points by MLASSO model