Affine phase retrieval for sparse signals via ℓ_1 minimization
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Affine phase retrieval is the problem of recovering signals from the magnitude-only measurements with a priori information. In this paper, we use the ℓ_1 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 ℓ_1 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 ℓ_1 minimization program for affine phase retrieval is stable.
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