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In this paper, we consider compressive/sparse affine phase retrieval proposedin [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 convexrelaxation of rank and $\ell$ one norm convex relaxation of sparsity, weestablish convex models , which are called compressive affine phase retrievalvia lifting (CAPRL). In order to compute these models, we develop inertialproximal ADMM for multiple separated operators and also give out itsconvergence analysis. Our numerical experiments via proposed algorithm showthat sparse signal can be exactly and stably recovered via CAPRL. We also listsome other applications of our proposed algorithm.

CAPRL: Signal Recovery from Compressive Affine Phase Retrieval via Lifting