In　this　paper,　an　improved　dictionary　learning　method　for　speech　enhancement　is　proposed.　Given　prior　information　of　the　noise,　the　dictionaries　of　speech　and　noise　are　firstly　trained　by　an　approximate　KSVD　algorithm,　respectively.　Then,　the　estimated　short-time　Fourier　transform　(STFT)　magnitudes　of　speech　and　noise　can　be　sparsely　represented　by　multiplying　the　dictionary　with　sparse　coefficients,　which　are　calculated　by　the　least　angle　regression　(LAR)　algorithm.　A　geometrical　stopping　criterion　with　an　adaptive　threshold　is　utilized　to　adjust　the　conventional　stopping　criterion　in　LAR　algorithm　so　that　it　can　increase　the　adaptability　of　LAR.　Next,　we　propose　a　framework　that　utilizes　the　expectation　maximization　(EM)　method　to　refine　the　energy　of　the　estimated　speech　and　noise　in　order　to　obtain　more　accurate　estimation　of　STFT　magnitudes.　Finally,　a　modified　wiener　filter　is　constructed　to　further　eliminate　residual　noise.　When　the　prior　information　of　noise　is　unknown,　an　online　noise　estimation　method　is　applied　to　replace　the　noise　dictionary.　The　test　results　show　that　the　proposed　method　outperforms　the　reference　speech　enhancement　methods.