In this paper, we propose a novel scheme to learn high-level representative features and conduct classification for hyperspectral image (HSI) data in an automatic fashion. The proposed method is a collaboration of a wavelet-based extended morphological profile (WTEMP) and a deep autoencoder (DAE) ("WTEMP-DAE"), with the aim of exploiting the discriminative capability of DAE when using WTEMP features as the input. Each part of WTEMP-DAE is ingenious and contributes to the final classification performance. Specifically, in WTEMP-DAE, the spatial information is extracted from the WTEMP, which is then joined with the wavelet denoised spectral information to form the spectral-spatial description of HSI data. The obtained features are fed into DAE as the original input, where the good weights and bias of the network are initialized through unsupervised pre-training. Once the pro-training is completed, the reconstruction layers are discarded and a logistic regression (LR) layer is added to the top of the network to perform supervised fine-tuning and classification. Experimental results on two real HSI data sets demonstrate that the proposed strategy improves classification performance in comparison with other state-of-the-art hand-crafted feature extractors and their combinations.