Phase retrieval via reweighted Wirtinger flow

Abstract

Phase retrieval (PR) is a kind of ill-condition inverse problem which can be found in various applications. Based on the Wirtinger flow (WF) method, a reweighted Wirtinger flow (RWF) method is proposed to deal with the PR problem. In a nutshell, RWF searches the global optimum by solving a series of sub-PR problems with changing weights. Theoretical analyses illustrate that the RWF has a geometric convergence from a deliberate initialization when the weights are bounded by 1 and $\frac{10}{9}$. Numerical tests also show the RWF has a lower sampling complexity compared with the WF. As an essentially adaptive truncated Wirtinger flow (TWF) method, the RWF performs better than the TWF especially when the ratio between sampling number $m$ and length of signal $n$ is small.

© 2017 Optical Society of America

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