  Sparse support recovery (SSR) is an important part of the compressive sensing
(CS). Most of the current SSR methods are with the full information
measurements. But in practice the amplitude part of the measurements may be
seriously destroyed. The corrupted measurements mismatch the current SSR
algorithms, which leads to serious performance degeneration. This paper
considers the problem of SSR with only phase information. In the proposed
method, the minimization of the l1 norm of the estimated sparse signal enforces
sparse distribution, while a nonzero constraint of the uncorrupted random
measurements' amplitudes with respect to the reconstructed sparse signal is
introduced. Because it only requires the phase components of the measurements
in the constraint, it can avoid the performance deterioration by corrupted
amplitude components. Simulations demonstrate that the proposed phase-only SSR
is superior in the support reconstruction accuracy when the amplitude
components of the measurements are contaminated.
