  In this paper, we consider compressive/sparse affine phase retrieval proposed
in [B. Gao B, Q. Sun, Y. Wang and Z. Xu, Adv. in Appl. Math., 93(2018),
121-141]. By the lift technique, and heuristic nuclear norm for convex
relaxation of rank and $\ell$ one norm convex relaxation of sparsity, we
establish convex models , which are called compressive affine phase retrieval
via lifting (CAPRL). In order to compute these models, we develop inertial
proximal ADMM for multiple separated operators and also give out its
convergence analysis. Our numerical experiments via proposed algorithm show
that sparse signal can be exactly and stably recovered via CAPRL. We also list
some other applications of our proposed algorithm.
