In　this　paper,　we　propose　a　frequency-domain　speech　enhancement　algorithm　with　phase　estimation,　in　which　the　speech　model　is　modeled　by　a　Gaussian　mixture　model　(GMM)　in　the　log-spectral　domain　and　two　closed-form　log-spectral　amplitude　estimators　for　speech　and　noise　are　derived　directly　by　using　a　Mixture-Maximum　(MIXMAX)　model.　Because　the　accurate　estimation　of　speech　phase　could　help　to　reduce　the　undesired　noise　residues　in　the　enhanced　signal,　our　two　log-spectral　estimators　are　also　used　to　construct　a　geometric　approach　for　phase　estimation　in　each　frequency　bin.　In　order　to　solve　the　ambiguity　problem　in　phase　estimation,　we　utilize　the　complex　linear　predictive　analysis　(CLPA)　and　inconsistency　constraint　to　find　an　appropriate　phase.　Experimental　results　show　that,　in　comparison　with　the　reference　methods,　the　proposed　method　achieves　an　efficient　improvement　in　speech　quality.　©　2016　Asia　Pacific　Signal　and　Information　Processing　Association.