Author:
Adcock Ben,Brugiapaglia Simone
Abstract
AbstractWe 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 for small values of the sparsity level.
Publisher
Springer International Publishing
Reference17 articles.
1. Adcock, B.: Infinite-dimensional compressed sensing and function interpolation. Found. Comput. Math. 18(3), 661–701 (2018)
2. Adcock, B., Bao, A., Brugiapaglia, S.: Correcting for unknown errors in sparse high-dimensional function approximation (2017). Preprint. arXiv:1711.07622
3. Adcock, B., Brugiapaglia, S., Webster, C.G.: Compressed sensing approaches for polynomial approximation of high-dimensional functions. In: Boche, H., Caire, G., Calderbank, R., März, M., Kutyniok, G., Mathar R. (eds.) Compressed Sensing and Its Applications: Second International MATHEON Conference 2015, pp. 93–124. Springer International Publishing, Cham (2017)
4. Bouchot, J.-L., Rauhut, H., Schwab C.: Multi-level compressed sensing Petrov-Galerkin discretization of high-dimensional parametric PDEs (2017). Preprint. arXiv:1701.01671
5. Chkifa, A., Dexter, N., Tran, H., Webster, C.G.: Polynomial approximation via compressed sensing of high-dimensional functions on lower sets. Math. Comp. 87(311), 1415–1450 (2018)
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