Reviews: Reshaped Wirtinger Flow for Solving Quadratic System of Equations

Comparing with previous work, including generalized phase retrieval problems, this paper has the following differences: 1) Solves a second order function incorporating absolute values of measurements 2) No step size normalization (or variants) 3) No gradient truncation The key intuition of this paper is that for a measurement ai, x with large magnitude, in the local region near global optima, the sign of ai, x and ai, z are likely to be same. In the case, locally the gradient update of reshaped WF (RWF) is as the same as an equivalent least squares problem. For the objective function including all the measurements, if most the components have reasonably large measurements, those with small measurements contribute less, hence using gradient descent good initialization should give good results. Such intuition is formalized in equation (34) and (35). Yet I have a question -- why don't one consider further truncating components with small magnitude when computing gradient? Just like in robust regression, TWF, etc, we can throw out "wrong" directions.