HERO: A Memory-Efficient and Fast Structured Low-Rank Reconstruction Algorithm for Accelerated Hypercomplex NMR.

Area of Science:

• Chemistry
• Spectroscopy
• Data Science

Background:

• Non-uniform sampling (NUS) accelerates Nuclear Magnetic Resonance (NMR) spectroscopy data acquisition.
• Structured low-rank methods excel at preserving spectral fidelity in NMR data by leveraging inherent redundancies.
• High-dimensional NMR applications of these methods are hindered by substantial memory and computational demands.

Purpose of the Study:

• To develop a memory-efficient structured low-rank reconstruction algorithm for high-dimensional NMR spectroscopy.
• To overcome the computational and memory limitations of existing NUS reconstruction techniques.

Main Methods:

• Proposed a reformulated Alternating Direction Method of Multipliers (ADMM) scheme.
• Avoided explicit construction of large block Hankel matrices.
• Reduced reliance on computationally intensive matrix multiplications.

Main Results:

• Achieved significant reductions in both computational and memory complexity for four-dimensional (4D) NMR reconstructions.
• Demonstrated over 90% memory usage reduction compared to existing matrix factorization approaches.
• Maintained spectral accuracy during reconstruction.

Conclusions:

• The developed algorithm enables practical and scalable applications of structured low-rank reconstruction to high-dimensional NMR.
• Significantly enhances the utility of Non-Uniform Sampling (NUS) in real-world NMR spectroscopy scenarios.
• The code is publicly available for further research and application.