  Phase retrieval refers to a classical nonconvex problem of recovering a
signal from its Fourier magnitude measurements. Inspired by the compressed
sensing technique, signal sparsity is exploited in recent studies of phase
retrieval to reduce the required number of measurements, known as compressive
phase retrieval (CPR). In this paper, l1 minimization problems are formulated
for CPR to exploit the signal sparsity and alternating direction algorithms are
presented for problem solving. For real-valued, nonnegative image
reconstruction, the image of interest is shown to be an optimal solution of the
formulated l1 minimization in the noise free case. Numerical simulations
demonstrate that the proposed approach is fast, accurate and robust to
measurements noises.
