ISD is as fast as L1-minimization but requires fewer measurements.
ISD addresses wrong solutions of L1 construction due to insufficient measurements.
It will learn from such wrong solutions and solve new minimization problems that return a perfect or a better solution.
A demo is given on Pages 4 and 5 of our report.
You can download an efficient implementation of ISD, called threshold-ISD, for recovering signals with fast decaying distributions of nonzeros from compressive measurements. The package includes numerical experiments showing that ISD has significant overall advantages over the classical L1 minimization approach, as well as two other state-of-the-art algorithms: the iterative reweighted L1 minimization algorithm (IRL1) [link] and the iterative reweighted least--squares algorithm (IRLS) [link].