  Proximal algorithms have gained popularity in recent years in large-scale and
distributed optimization problems. One such problem is the phase retrieval
problem, for which proximal operators have been proposed recently. The phase
retrieval problem commonly refers to the task of recovering a target signal
based on the magnitude of linear projections of that signal onto known vectors,
usually under the presence of noise. A more general problem is the
multispectral phase retrieval problem, where sums of these magnitudes are
observed instead. In this paper we study the proximal operator for this
problem, which appears in applications like X-ray solution scattering. We show
that despite its non-convexity, all local minimizers are global minimizers,
guaranteeing the optimality of simple descent techniques. An efficient linear
time exact Newton method is proposed based on the structure of the problem's
Hessian. Initialization criteria are discussed and the computational
performance of the proposed algorithm is compared to that of traditional
descent methods. The studied proximal operator can be used in a distributed and
parallel scenarios using an ADMM scheme and allows for exploiting the spectral
characteristics of the problem's measurement matrices, known in many physical
sensing applications, in a way that is not possible with non-splitted
optimization algorithms. The dependency of the proximal operator on the rank of
these matrices, instead of their dimension, can greatly reduce the memory and
computation requirements for problems of moderate to large size (N>10000) when
these measurement matrices admit a low-rank representation.
