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

Non-uniform sampling is essential in NMR spectroscopy to accelerate data acquisition without compromising spectral information. Among the various NUS reconstruction techniques, such as compressive sensing and maximum entropy, structured low-rank methods are particularly effective in preserving spectral fidelity by exploiting the inherent redundancies in NMR data. However, their application to high-dimensional NMR remains limited due to the high memory and computational cost associated with nuclear norm minimization or matrix factorization methods, both of which rely on large intermediate variables. In this work, we propose a memory-efficient structured low-rank reconstruction algorithm that avoids explicit construction of block Hankel matrices and reduces the dependence on large matrix multiplications through a reformulated Alternating Direction Method of Multipliers scheme. In contrast to existing matrix factorization approaches, our algorithm significantly lowers both computational and memory complexity, achieving four-dimensional (4D) NMR reconstructions with more than a 90% reduction in memory usage while maintaining accuracy. This advancement enables practical and scalable applications of structured low-rank reconstruction to high-dimensional NMR, greatly enhancing the utility of NUS in real-world scenarios. The code is available at https://github.com/EricLin1993/HERO.