Multidimensional NMR inversion without Kronecker products: Multilinear inversion.

Area of Science:

• Nuclear Magnetic Resonance (NMR) Spectroscopy
• Computational Chemistry
• Data Analysis

Background:

• Multidimensional NMR inversion traditionally relies on Kronecker products, which face challenges with non-separable kernels and higher dimensions.
• Existing methods like Lawson-Hanson (LH) and Butler-Reeds-Dawson (BRD) struggle with memory requirements and incorporating arbitrary regularization.
• Kernel compression, crucial for Kronecker product methods, is ill-defined for dimensions three and above.

Purpose of the Study:

• To develop a novel, memory-efficient multidimensional NMR inversion method.
• To overcome the limitations of Kronecker product-based approaches, including handling non-separable kernels and arbitrary regularization.
• To provide a more accessible and versatile tool for analyzing complex NMR data.

Main Methods:

• A minimization-based inversion approach utilizing multilinear forms.
• Avoidance of kernel compression and Kronecker products.
• Implementation requires only a cost function and its first derivative.

Main Results:

• The new method demonstrates significant memory efficiency, using less than 0.1% of the memory required by LH or BRD methods.
• The approach successfully handles non-separable kernels and can be extended to arbitrary dimensions.
• Arbitrary regularization terms and linear constraints can be incorporated into the inversion process.

Conclusions:

• The developed minimization-based method offers a robust and efficient alternative for multidimensional NMR inversion.
• This technique significantly reduces computational resource demands, making complex NMR data analysis more accessible.
• The method's flexibility in handling advanced NMR data features and regularization opens new avenues for research.