We present a novel method to enhance the SNR for multi-TE MR spectroscopic imaging (MRSI) data by integrating learned nonlinear low-dimensional model and spatial constraints. A deep complex convolutional autoencoder (DCCAE) was developed to learn a nonlinear low-dimensional representation of the high-dimensional multi-TE 1H spectroscopy signals. The learned model significantly reduces the data dimension thus serving as an effective constraint for noise reduction. A reconstruction formulation was proposed to integrate the spatiospectral encoding model, the learned model, and a spatial constraint for an SNR-enhancing reconstruction from multi-TE data. The proposed method has been evaluated using both numerical simulations and in vivo brain MRSI experiments. The superior denoising performance of the proposed over alternative methods was demonstrated, both qualitatively and quantitatively. In vivo multi-TE data was used to assess the improved metabolite quantification reproducibility and accuracy achieved by the proposed method. We expect the proposed SNR-enhancing reconstruction to enable faster and/or higher-resolution multi-TE 1H-MRSI of the brain, potentially useful for various clinical applications.