A Fast-Iterative Algorithm Based on the Wirtinger Flow for Phase Retrieval

Can PEI, Zheng-ming JIANG, Qiang LI, Lei HUANG, Ji-hong ZHANG


Reconstructing the original complex signal using amplitude-only measurements is referred to as the phase retrieval problem. In this paper, we develop a fast-iterative phase retrieval algorithm that can be considered as an enhanced version of the well-known Wirtinger Flow (WF) algorithm. The original WF algorithm is based on gradient descent scheme to tackle the phase recovery problem, however, the convergence speed of this WF algorithm is very slow. Compared with the original WF algorithm, the proposed fast-iterative WF (FWF) algorithm has a faster convergence speed, with an acceptable little more computational complexity. The proposed FWF algorithm is preferable not only due to its accelerated convergence speed but also due to its ability to converge to the global optimum. Experimental results show that the FWF algorithm is superior to the state-of-the-art algorithms in terms of the convergence speed.


Phase retrieval, Wirtinger Flow algorithm, Gradient descent


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