Sparse Support Recovery with Phase-Only Measurements

Abstract: 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.