  The reconstruction of sparse signals requires the solution of an
$\ell_0$-norm minimization problem in Compressed Sensing. Previous research has
focused on the investigation of a single candidate to identify the support
(index of nonzero elements) of a sparse signal. To ensure that the optimal
candidate can be obtained in each iteration, we propose here an iterative
greedy reconstruction algorithm (GSRA). First, the intersection of the support
sets estimated by the Orthogonal Matching Pursuit (OMP) and Subspace Pursuit
(SP) is set as the initial support set. Then, a hope-tree is built to expand
the set. Finally, a developed decreasing subspace pursuit method is used to
rectify the candidate set. Detailed simulation results demonstrate that GSRA is
more accurate than other typical methods in recovering Gaussian signals, 0--1
sparse signals, and synthetic signals.
