  A fundamental problem in phase retrieval is to reconstruct an unknown signal
from a set of magnitude-only measurements. In this work we introduce three
novel quotient intensity-based models (QIMs) based a deep modification of the
traditional intensity-based models. A remarkable feature of the new loss
functions is that the corresponding geometric landscape is benign under the
optimal sampling complexity. When the measurements $ a_i\in \Rn$ are Gaussian
random vectors and the number of measurements $m\ge Cn$, the QIMs admit no
spurious local minimizers with high probability, i.e., the target solution $ x$
is the unique global minimizer (up to a global phase) and the loss function has
a negative directional curvature around each saddle point. Such benign
geometric landscape allows the gradient descent methods to find the global
solution $x$ (up to a global phase) without spectral initialization.
