Joint Learning of Nonlinear Representation and Projection for Fast Constrained MRSI Reconstruction

Learning and utilizing low-dimensional representations for high-dimensional imaging problems is an active research area. We present here a novel method for computationally efficient reconstruction from noisy MR spectroscopic imaging (MRSI) data, a unique high-dimensional molecular imaging modality. 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 joint 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. The proposed method has been evaluated using simulations and different types of in vivo MRSI data, demonstrating robust improved performance over state-of-the-art methods. Computational complexity and algorithm convergence analysis have been performed to offer further insights into the effectiveness of the proposed method.