Low-dimensional subspace models have recently been developed for fast, high-SNR MRSI, by effectively reducing the degrees-of-freedom for the imaging problem. However, low-dimensional linear subspace models may be inadequate in capturing more complicated spectral variations across a general population. This work presents a new approach to model general spectroscopic signals, by learning a nonlinear low-dimensional representation. Specifically, we integrated the well-defined spectral fitting model and a deep autoencoder network to learn the low-dimensional manifold where the high-dimensional spectroscopic signals reside, and applied this learned model for denoising and reconstructing MRSI data. Promising results have been obtained demonstrating the potential of the proposed method.