Sparse approximation of multivariate functions from small datasets via weighted orthogonal matching pursuit

10/25/2018

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by   Ben Adcock, et al.

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We show the potential of greedy recovery strategies for the sparse approximation of multivariate functions from a small dataset of pointwise evaluations by considering an extension of the orthogonal matching pursuit to the setting of weighted sparsity. The proposed recovery strategy is based on a formal derivation of the greedy index selection rule. Numerical experiments show that the proposed weighted orthogonal matching pursuit algorithm is able to reach accuracy levels similar to those of weighted l1 minimization programs while considerably improving the computational efficiency.