Dynamic Mode Decomposition reveals 23Na Multi-Quantum Coherences and allows incomplete RF Phase-Cycling

Motivation: Sodium (23Na) Multi-Quantum Coherences (MQC) MRI potentially provides richer tissue information. However, separation of the single (SQ) and triple (TQ) quantum coherences is challenging and is done by computing the Fourier transform (FT). Unfortunately, the FT is susceptible to noise and phase-cycle imperfections. Goal(s): To enable reliable frequency separation of the superimposed 23Na MQC signal even with undersampling phase-cycling. Approach: Dynamic Mode Decomposition (DMD) was used to separate the signal components and was tested on numerical simulations, phantom and in vivo brain data acquired at 3T. Results: DMD reliably separated SQ and TQ signal components from 23Na MQC MRI despite missing phase-cycling steps. Impact: DMD reliably separates SQ and TQ signal components and has the potential to enable phase-cycle undersampling below the TQ Nyquist limit to accelerate 23Na MQC MRI. Despite 23Na MQC MRI, every MRI experiment involving phase-cycling could benefit from this approach.