We proposed here a novel method for computationally efficient reconstruction from noisy MRSI data. The proposed method is characterized by (a) a strategy that jointly learns a nonlinear low-dimensional representation of high-dimensional spectroscopic signals and a projector to recover the low-dimensional embeddings from noisy FIDs; and (b) a formulation that integrates forward encoding model, a spectral constraint from the learned representation and a complementary spatial constraint. The learned projector allows for the derivation of a highly efficient algorithm combining projected gradient descent and ADMM. The proposed method has been evaluated using simulation and in vivo data, demonstrating impressive SNR-enhancing performance.
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