We report a new method for SNR-enhancing reconstruction of multi-TE MRSI data. Specifically, we designed a deep complex convolutional autoencoder (DCCAE) to learn a nonlinear low-dimensional model of the high-dimensional multi-TE spectra which allowed for effective separation of molecular signals and noise. A constrained reconstruction formulation is used to incorporate the learned model for denoising spatial-temporal reconstruction. The performance of the learned model and the proposed reconstruction method have been evaluated using both simulation and experimental multi-TE $$$^1$$$H-MRSI data. Results obtained demonstrate superior denoising performance achieved by the proposed method over alternative spatial-spectrally constrained denoising strategies.