Multidimensional NMR inversion without Kronecker products: Multilinear inversion

Area of Science:

• Chemistry
• Spectroscopy
• Computational Science

Background:

• Multidimensional NMR inversion traditionally relies on Kronecker products, facing challenges with non-separable kernels and higher dimensions.
• Existing methods like Lawson-Hanson (LH) and Butler-Reeds-Dawson (BRD) struggle with memory requirements and limitations in handling arbitrary regularization.

Purpose of the Study:

• To develop a novel, memory-efficient multidimensional NMR inversion method.
• To overcome limitations of Kronecker product-based methods, including non-separable kernels and arbitrary regularization.

Main Methods:

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

Main Results:

• The new method requires less than 0.1% of the memory used by LH or BRD algorithms.
• Successfully performs multidimensional NMR inversion without kernel compression or Kronecker products.
• Demonstrates adaptability to non-separable kernels, arbitrary dimensions, linear constraints, and regularization terms.

Conclusions:

• The developed minimization-based method offers a significant advancement in multidimensional NMR data processing.
• Provides a flexible, memory-efficient, and easily implementable solution for complex NMR inversion challenges.
• Opens possibilities for analyzing more intricate NMR sequences and datasets.