We　propose　a　sparse　hidden　Markov　model　(HMM)-based　single-channel　speech　enhancement　method　that　models　the　speech　and　noise　gains　accurately　in　both　stationary　and　non-stationary　environments.　The　objective　function　is　augmented　with　an　l(p)　regularization　term　resulting　in　a　sparse　autoregressive　HMM　(SARHMM).　The　method　encourages　sparsity　in　the　speech-and　noise-modeling,　which　eliminates　the　ambiguity　between　noise　and　speech　spectra　and,　as　a　consequence,　provides　improved　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　an　estimator　to　estimate　the　noise　spectrum.　Then　a　Bayesian　speech　estimator　is　used　to　obtain　the　enhanced　speech.　The　test　results　indicate　that　the　proposed　speech　enhancement　scheme　performs　much　better　than　the　reference　methods　in　non-stationary　environments,　while　providing　state-of-the-art　performance　for　stationary　conditions.