Generalized notions of sparsity and restricted isometry property. Part I: A unified framework

Marius Junge, Kiryung Lee

Research output: Contribution to journalArticlepeer-review


The restricted isometry property (RIP) is an integral tool in the analysis of various inverse problems with sparsity models. Motivated by the applications of compressed sensing and dimensionality reduction of low-rank tensors, we propose generalized notions of sparsity and provide a unified framework for the corresponding RIP, in particular when combined with isotropic group actions. Our results extend an approach by Rudelson and Vershynin to a much broader context including commutative and noncommutative function spaces. Moreover, our Banach space notion of sparsity applies to affine group actions. The generalized approach in particular applies to high-order tensor products.

Original languageEnglish (US)
Pages (from-to)157-193
Number of pages37
JournalInformation and Inference
Issue number1
StatePublished - Mar 1 2020


  • Banach space
  • Compressed sensing
  • Dimensionality reduction
  • Restricted isometry property

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Numerical Analysis
  • Statistics and Probability
  • Computational Theory and Mathematics


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