Progress on Hard Thresholding Pursuit
Jean-Luc Bouchot, Drexel University
Location: Stevenson 1307
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 incomplete linear measurements in a number of iterations at most proportional to the sparsity level as soon as the measurement matrix obeys a 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 two extreme cases of the vector shape, it is also 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.