Abstract:

PhaseLift is a new phase retrieval method that converts phase retrieval problems with nonlinear con-straints into semidefinite programming problems.Phase retrieval problems are translated into Maxcut- like semidefi-nite programming problems (namely PhaseCut) by accurately separating amplitude and phase variables combinedwith the method of PhaseLift.As the computational complexity of PhaseCut increases quickly with the problem size,a PURE- RBR- M algorithm suitable for MaxCut problems is employed to solve PhaseCut.Simulated results show thatPURE- RBR- M algorithm achieves phase retrieval successfully and possesses strong robustness to noise measure-ment; and that it is superior to the interior point algorithm and the greedy algorithm because it runs faster and leadsto a quicker signal reconstruction.

Key words: image processing, PhaseLift, PhaseCut, MaxCut, phase retrieval, semidefinite programming