Joint learning of nonlinear representation and projection for fast constrained MRSI reconstruction

Abstract Purpose To develop and evaluate a novel method for computationally efficient reconstruction from noisy MR spectroscopic imaging (MRSI) data. Methods The proposed method features (a) a novel strategy that jointly learns a nonlinear low‐dimensional representation of high‐dimensional spectroscopic signals and a neural‐network‐based projector to recover the low‐dimensional embeddings from noisy/limited data; (b) a formulation that integrates the forward encoding model, a regularizer exploiting the learned representation, and a complementary spatial constraint; and (c) a highly efficient algorithm enabled by the learned projector within an alternating direction method of multipliers (ADMM) framework, circumventing the computationally expensive network inversion subproblem. Results The proposed method has been evaluated using simulations as well as in vivo H and P MRSI data, demonstrating improved performance over state‐of‐the‐art methods, with about 6 fewer averages needed than standard Fourier reconstruction for similar metabolite estimation variances and up to 100 reduction in processing time compared to a prior neural network constrained reconstruction method. Computational and theoretical analyses were performed to offer further insights into the effectiveness of the proposed method. Conclusion A novel method was developed for fast, high‐SNR spatiospectral reconstruction from noisy MRSI data. We expect our method to be useful for enhancing the quality of MRSI or other high‐dimensional spatiospectral imaging data.