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An IHT algorithm for sparse recovery from subexponential measurements

Author

Listed:
  • Simon Foucart

    (Texas A&M University)

  • Guillaume Lecué

    (CREST; ENSAE; CNRS)

Abstract

A matrix whose entries are independent subexponential random variables is not likely to satisfy the classical restricted isometry property in the optimal regime of parameters. However, it is known that uniform sparse recovery is still possible with high probability in the optimal regime if ones uses l1-minimization as a recovery algorithm. We show in this note that such a statement remains valid if one uses a new variation of iterative hard thresholding as a recovery algorithm. The argument is based on a modified restricted isometry property featuring the l1-norm as the inner norm. ;Classification-JEL: 65F10; 15A29; 94A12

Suggested Citation

  • Simon Foucart & Guillaume Lecué, 2017. "An IHT algorithm for sparse recovery from subexponential measurements," Working Papers 2017-31, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2017-31
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