This thesis is focused on speech enhancement techniques based on short-time spectral amplitude (STSA) estimation. In particular, it addresses the weakness of the ?-order minimum mean-square error (MMSE) estimation method that incorporates auditory masking properties (?-masking in short). Two post-processing techniques are proposed to improve the quality of the ?-masking enhanced speech signals. One technique involves non-linear high-frequency regeneration, which uses the lower-band spectral information to re-synthesize the upper-band spectral structure. The other technique involves re-synthesis of the weak spectral components using the autocorrelations of the strong spectral components. In addition to the single-channel speech enhancement methods, a two-channel speech enhancement method for communication in a car environment is also studied. To achieve a better performance, the single-channel ?-masking speech enhancement technique is incorporated within the two-channel enhancement system. The resulting output speech signals have low background noise and the distortion to the speech components is also very low, thus achieving an overall very satisfactory speech enhancement performance.