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Acoustic models trained with clean speech signals suffer in the presence of background noise. In some situations, only a limited amount of noisy data of the new environment is available based on which the clean models could be adapted. A feature compensation approach employing polynomial regression of the signal-to-noise ratio (SNR) is proposed in this paper. While clean acoustic models remain unchanged, a bias which is a polynomial function of utterance SNR is estimated and removed from the noisy feature. Depending on the amount of noisy data available, the algorithm could be flexibly carried out at different levels of granularity. Based on the Euclidean distance, the similarity between the residual distribution and the clean models are estimated and used as the confidence factor in a back-end weighted Viterbi decoding (WVD) algorithm. With limited amounts of noisy data, the feature compensation algorithm outperforms maximum likelihood linear regression (MLLR) for the Aurora2 database. Weighted Viterbi decoding further improves recognition accuracy.