Abstract: A projection/iteration type algorithm is developed for reconstructing signals with sparsity constraints on phases. Recently, similar issues have been reported in a few material science studies. Contrary to the problems studied in the past problems, the sparsity constraint proposed is only applied to the signal phases other than the amplitudes. Thus, no existing non-general algorithms can be directly applied to this problem. The correctness and convergence properties of the algorithm was proven proven in theoretical analysis. Furthermore, its convergence, robustness, and sensitivity to parameters were investigated using numerical simulations. Finally, an application example of computing micro-defects in photoelectronic membranes from the electromagnetic scattering spectrum was presented.