Sparse approximation of fitting surface by elastic net

The goal of this paper is to develop a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the principal shift invariant space and the balanced $l_1,l_2$ norm minimization (named elastic net). The elastic net can be solved efficiently by an adapted split Bregman iteration algorithm. Numerical experiments indicate that by choosing appropriate regularization parameters, the model can efficiently provide an acceptable compromise between the minimization of the data mismatch term and the sparsity of the solution.