We　propose　a　sparse　hidden　Markov　model　(HMM)-based　single-　channel　speech　enhancement　method　that　models　the　speech　and　noise　gains　accurately　in　non-　stationary　noise　environments.　Autoregressive　models　are　employed　to　describe　the　speech　and　noise　in　a　unified　framework　and　the　speech　and　noise　gains　are　modeled　as　random　processes　with　memory.　The　likelihood　criterion　for　finding　the　model　parameters　is　augmented　with　an　l(p)　regularization　term　resulting　in　a　sparse　autoregressive　HMM　(SARHMM)　system　that　encourages　sparsity　in　the　speech-　and　noise-　modeling.　In　the　SARHMM　only　a　small　number　of　HMM　states　contribute　significantly　to　the　model　of　each　particular　observed　speech　segment.　As　it　eliminates　ambiguity　between　noise　and　speech　spectra,　the　sparsity　of　speech　and　noise　modeling　helps　to　improve　the　tracking　of　the　changes　of　both　spectral　shapes　and　power　levels　of　non-stationary　noise.　Using　the　modeled　speech　and　noise　SARHMMs,　we　first　construct　a　noise　estimator　to　estimate　the　noise　power　spectrum.　Then,　a　Bayesian　speech　estimator　is　derived　to　obtain　the　enhanced　speech　signal.　The　subjective　and　objective　test　results　indicate　that　the　proposed　speech　enhancement　scheme　can　achieve　a　larger　segmental　SNR　improvement,　a　lower　log-　spectral　distortion　and　a　better　speech　quality　in　stationary　noise　conditions　than　state-of-the-art　reference　methods.　The　advantage　of　the　new　method　is　largest　for　non-stationary　noise　conditions.