Compressed Sensing With Nonlinear Observations and Related Nonlinear Optimization Problems

  title={Compressed Sensing With Nonlinear Observations and Related Nonlinear Optimization Problems},
  author={Thomas Blumensath},
  journal={IEEE Transactions on Information Theory},
  • T. Blumensath
  • Published 8 May 2012
  • Computer Science
  • IEEE Transactions on Information Theory
Nonconvex constraints are valuable regularizers in many optimization problems. In particular, sparsity constraints have had a significant impact on sampling theory, where they are used in compressed sensing and allow structured signals to be sampled far below the rate traditionally prescribed. Nearly, all of the theory developed for compressed sensing signal recovery assumes that samples are taken using linear measurements. In this paper, we instead address the compressed sensing recovery… 

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