A new approach to compressed sensing for NMR

Area of Science:

• Nuclear Magnetic Resonance (NMR) Spectroscopy
• Signal Processing
• Computational Chemistry

Background:

• Compressed sensing (CS) is a promising technique for analyzing nonuniformly sampled NMR data.
• Existing CS algorithms for NMR face challenges including poor convergence and uncertainty regarding spectral sparsity requirements.
• Comparison with Maximum Entropy (MaxEnt) reconstruction is difficult due to differing formalisms.

Purpose of the Study:

• To develop a unified formalism for comparing CS and MaxEnt reconstruction in NMR.
• To introduce a novel CS algorithm for NMR spectrum analysis.
• To address limitations of current CS methods, such as artifact generation and causality issues.

Main Methods:

• Development of a theoretical framework to place CS and MaxEnt on equal footing for NMR spectrum analysis.
• Introduction of a new CS algorithm that restricts l1 norm computation to the real channel for complex spectra.
• Ensuring causality in the CS reconstruction process.

Main Results:

• The proposed formalism enables direct critical comparison between CS and MaxEnt reconstruction methods.
• The new CS algorithm effectively ameliorates artifacts associated with l1 norm minimization on complex spectra.
• Preliminary 1D NMR results validate the improved performance of the novel CS approach.

Conclusions:

• The developed formalism provides a robust basis for understanding and comparing CS and MaxEnt in NMR.
• The novel CS algorithm offers enhanced accuracy and reliability for NMR spectrum analysis.
• This work advances the application of compressed sensing in nuclear magnetic resonance spectroscopy.