According to the encoding and decoding mechanism of binaural cue coding (BCC), in this paper, the speech and noise are considered as left channel signal and right channel signal of the BCC framework, respectively. Subsequently, the speech signal is estimated from noisy speech when the inter-channel level difference (ICLD) and inter-channel correlation (ICC) between speech and noise are given. In this paper, exact inter-channel cues and the pre-enhanced inter-channel cues are used for speech restoration. The exact inter-channel cues are extracted from clean speech and noise, and the pre-enhanced inter-channel cues are extracted from the pre-enhanced speech and estimated noise. After that, they are combined one by one to form a codebook. Once the pre-enhanced cues are extracted from noisy speech, the exact cues are estimated by a mapping between the pre-enhanced cues and a prior codebook. Next, the estimated exact cues are used to obtain a time-frequency (T-F) mask for enhancing noisy speech based on the decoding of BCC. In addition, in order to further improve accuracy of the T-F mask based on the inter-channel cues, the deep neural network (DNN)-based method is proposed to learn the mapping relationship between input features of noisy speech and the T-F masks. Experimental results show that the codebook-driven method can achieve better performance than conventional methods, and the DNN-based method performs better than the codebook-driven method.