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In this paper, we propose a nonlinear regression method for speech enhancement, whose idea approximates the log spectra of clean speech with the inputs of the log spectra of noisy speech and estimated noise. We compared both subjective and objective assessments on regression-enhanced speech to those obtained through spectral subtraction (SS) and short-time spectral amplitude (STSA) methods. Our subjective evaluation experiments, which included Mean Opinion Score (MOS) and Pairwise Preference Test (PPT), show that the proposed regression-based speech enhancement method provides consistent improvements in overall quality in all seven driving conditions. The proposed method also performs the best in most objective measures.