This paper considers a perceptually motivated estimator for single-channel speech enhancement based on statistics and Bayesian estimation in the frequency domain. In detail, we propose a new speech log-spectral amplitude estimator where the cost function is the weighted Euclidean distortion measure of the speech log-spectral amplitude. That cost function is motivated by auditory masking effects of the human hearing system. The statistical assumptions used to develop the proposed estimator are the complex Gaussian distribution and independence of speech, noise discrete Fourier transform coefficients. We evaluate this estimator with speech signals contaminated by various noise sources at different input signal-to-noise ratios and find that it achieves better performance than the well-known minimum mean square error log-spectral amplitude estimator in terms of both noise reduction and speech quality.