  In this paper, we develop a novel framework to optimally design spectral
estimators for phase retrieval given measurements realized from an arbitrary
model. We begin by deconstructing spectral methods, and identify the
fundamental mechanisms that inherently promote the accuracy of estimates. We
then propose a general formalism for spectral estimation as approximate Bregman
loss minimization in the range of the lifted forward model that is tractable by
a search over rank-1, PSD matrices. Essentially, by the Bregman loss approach
we transcend the Euclidean sense alignment based similarity measure between
phaseless measurements in favor of appropriate divergence metrics over
$\mathbb{R}^M_+$. To this end, we derive spectral methods that perform
approximate minimization of KL-divergence, and the Itakura-Saito distance over
phaseless measurements by using element-wise sample processing functions. As a
result, our formulation relates and extends existing results on model dependent
design of optimal sample processing functions in the literature to a model
independent sense of optimality. Numerical simulations confirm the
effectiveness of our approach in problem settings under synthetic and real data
sets.
