Many speech enhancement systems have been proposed to enhance a speech signal corrupted by various kinds of noise. However, most of them suffer from a quantity of residual noise containments and serious speech distortion. After careful study on the research topic of speech enhancement, we find that a speech enhancement algorithm adapted by the auditory masking properties of the human ear performs better than the other state-of-the-art methods. It is attributed to the fact that residual noise with small magnitude is inaudible to the human ear. Preserving it does not cause annoying effect, but brings the benefit of reducing speech distortion in the enhanced speech. However, the annoying musical residual noise still exists and is apparent in the spectrogram. The major reason is the incorrect estimation on the noise level, yielding musical residual tones with strong energy to randomly appear over neighbor subbands and in successive frames. Thus, how to reduce the effect of musical residual is an import task for speech enhancement. Many residual noise reduction algorithms produce serious speech distortion and echo effect, resulting in the quality of enhanced speech to be deteriorated. In this project, we aim at improving the performances of the reduction of residual noise and of the preservation of speech quality by speech enhancement and post-processing techniques. Firstly, we will design an improved version of complementary denoising algorithm to efficiently remove the background noise, while the speech distortion is kept at a low level and the residual noise should be apparent for detection. In turn, an iterative-two-dimensional spectrogram filtering technique will be developed for significantly reducing the spectra of musical residual noise. Accordingly, the quality of the enhanced speech is improved.