Sparse signal recovery in Hilbert spaces

@article{Pope2012SparseSR,
  title={Sparse signal recovery in Hilbert spaces},
  author={Graeme Pope and Helmut B{\"o}lcskei},
  journal={2012 IEEE International Symposium on Information Theory Proceedings},
  year={2012},
  pages={1463-1467}
}
  • G. PopeH. Bölcskei
  • Published 21 May 2012
  • Computer Science
  • 2012 IEEE International Symposium on Information Theory Proceedings
This paper reports an effort to consolidate numerous coherence-based sparse signal recovery results available in the literature. We present a single theory that applies to general Hilbert spaces with the sparsity of a signal defined as the number of (possibly infinite-dimensional) subspaces participating in the signal's representation. Our general results recover uncertainty relations and coherence-based recovery thresholds for sparse signals, block-sparse signals, multi-band signals, signals… 

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