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This paper presents a new algorithm for noise compensation in the log-spectral domain. We first note that using a Gaussian mixture assumption a compensation algorithm in the log-spectral domain is completely defined by three parameters for each Gaussian component: the noisy speech mean, the noisy speech variance, and the covariance of clean and noisy speech. Starting from a well known mismatch function we propose two new approximations which allow deriving analytical expressions for the above mentioned parameters, and hence develop a new noise compensation algorithm in the log-spectral domain. In addition to theoretical derivations we discuss implementation issues of the proposed method and analyze its computational complexity. Experimental results for digit recognition in the car reveal that the proposed technique significantly outperform the baseline, and first order VTS. For example at 10 db signal to noise ratio the baseline, first order VTS, and the proposed method lead to recognition accuracies 82.6%, 85.5%, and 90.1%. The superiority of the proposed method to VTS can be attributed to the accuracy of the employed approximations. The compensation algorithm is also found to be more accurate and faster than an approximate numerical integration technique.