Two gain forms of spectral amplitude subtraction are derived theoretically without neglecting the correlation of speech and noise spectrum during the period of a frame. In the implementation, the constrained gain is expressed as a function of noncausal a priori SNR (Signal-to-Noise Ratio). Noise and noncausal a priori SNR are estimated from the multitaper spectrum of the noisy signal with algorithms modified to be suitable for the multitaper spectrum. Objective evaluations show that in case of white Gaussian noise the proposed method outperforms some methods based on LSA (Log Spectral Amplitude) in terms of MBSD (Modified Bark Spectral Distortion), segmental SNR and overall SNR, and informal listening tests show that speech reconstructed in this way has little speech distortion and musical noise is nearly inaudible even at low SNR. Two gain forms of spectral amplitude subtraction are derived theoretically without spectral sensitivity of the correlation of speech and noise spectrum during the period of a frame. In the implementation, the constrained gain is expressed as a function of non-a priori SNR (Signal-to-Noise Ratio ) Noise and noncausal a priori SNR are estimated from the multitaper spectrum of the noisy signal with algorithms modified to be suitable for the multitaper spectrum. Objective evaluations show that in case of white Gaussian noise the proposed method outperforms some methods based on LSA (Log Spectral Amplitude) in terms of MBSD (Modified Bark Spectral Distortion), segmental SNR and overall SNR, and informal listening tests show that speech reconstructed in this way has little speech distortion and musical noise is nearly inaudible even at low SNR.