Hard thresholding pursuit algorithms: Number of iterations Academic Article uri icon


  • 2016 Elsevier Inc. The Hard Thresholding Pursuit algorithm for sparse recovery is revisited using a new theoretical analysis. The main result states that all sparse vectors can be exactly recovered from compressive linear measurements in a number of iterations at most proportional to the sparsity level as soon as the measurement matrix obeys a certain restricted isometry condition. The recovery is also robust to measurement error. The same conclusions are derived for a variation of Hard Thresholding Pursuit, called Graded Hard Thresholding Pursuit, which is a natural companion to Orthogonal Matching Pursuit and runs without a prior estimation of the sparsity level. In addition, for two extreme cases of the vector shape, it is shown that, with high probability on the draw of random measurements, a fixed sparse vector is robustly recovered in a number of iterations precisely equal to the sparsity level. These theoretical findings are experimentally validated, too.

published proceedings


altmetric score

  • 1.75

author list (cited authors)

  • Bouchot, J., Foucart, S., & Hitczenko, P.

citation count

  • 38

complete list of authors

  • Bouchot, Jean-Luc||Foucart, Simon||Hitczenko, Pawel

publication date

  • January 2016