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Abstract PurposeTo develop and evaluate a novel method for computationally efficient reconstruction from noisy MR spectroscopic imaging (MRSI) data. MethodsThe 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. ResultsThe 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. ConclusionA 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.
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This content will become publicly available on June 30, 2027
Simultaneous Model Discovery and State Estimation under High Data Corruption
This paper proposes a sparse regression strategy for discovery of ordinary differential equations from incomplete and noisy data. Inference is performed over both equation parameters and state variables using a statistically motivated likelihood function. Sparsity is enforced by a selection algorithm which iteratively removes terms and compares models using statistical information criteria. Large scale optimization is performed using a second-order variant of the Levenberg--Marquardt method, where the gradient and Hessian are computed via automatic differentiation. The proposed method is illustrated and tested on several systems with varying levels of noisy and incomplete data. Comparisons are made to a state-of-the-art algorithm for system identification, demonstrating competitiveness of the proposed approach.
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- Award ID(s):
- 2407033
- PAR ID:
- 10694387
- Publisher / Repository:
- Society for Industrial and Applied Mathematics
- Date Published:
- Journal Name:
- SIAM Journal on Applied Dynamical Systems
- Volume:
- 25
- Issue:
- 2
- ISSN:
- 1536-0040
- Page Range / eLocation ID:
- 1439 to 1467
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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