Phase retrieval via reweighted Wirtinger flow

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 109. 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.