  Phase retrieval is an important problem with significant physical and
industrial applications. In this paper, we consider the case where the
magnitude of the measurement of an underlying signal is corrupted by Gaussian
noise. We introduce a convex augmentation approach for phase retrieval based on
total variation regularization. In contrast to popular convex relaxation models
like PhaseLift, our model can be efficiently solved by a modified semi-proximal
alternating direction method of multipliers (sPADMM). The modified sPADMM is
more general and flexible than the standard one, and its convergence is also
established in this paper. Extensive numerical experiments are conducted to
showcase the effectiveness of the proposed method.
