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To address the variation of noise level in non-stationary noise signals, we study the noise gain estimation for speech enhancement using hidden Markov models (HMM). We consider the noise gain as a stochastic process and we approximate the probability density function (PDF) to be log-normal distributed. The PDF parameters are estimated for every signal block using the past noisy signal blocks. The approximated PDF is then used in a Bayesian speech estimator minimizing the Bayes risk for a novel cost function, that allows for an adjustable level of residual noise. As a more computationally efficient alternative, we also derive the maximum likelihood (ML) estimator, assuming the noise gain to be a deterministic parameter. The performance of the proposed gain-adaptive methods are evaluated and compared to two reference methods. The experimental results show significant improvement under noise conditions with time-varying noise energy.