Affine phase retrieval is the problem of recovering signals from the
magnitude-only measurements with a priori information. In this paper, we use
the β1β minimization to exploit the sparsity of signals for affine phase
retrieval, showing that O(klog(en/k)) Gaussian random measurements are
sufficient to recover all k-sparse signals by solving a natural β1β
minimization program, where n is the dimension of signals. For the case where
measurements are corrupted by noises, the reconstruction error bounds are given
for both real-valued and complex-valued signals. Our results demonstrate that
the natural β1β minimization program for affine phase retrieval is stable.Comment: 22 page