Incoherence of Partial-Component Sampling in multidimensional NMR

• Main Authors: Monajemi, Hatef, Donoho, David L, Hoch, Jeffrey C, Schuyler, Adam D
• Format: Journal Article
• Language: English
• Published: 06.02.2017
• Subjects: Statistics - Applications
• DOI: 10.48550/arxiv.1702.01830

In NMR spectroscopy, undersampling in the indirect dimensions causes reconstruction artifacts whose size can be bounded using the so-called {\it coherence}. In experiments with multiple indirect dimensions, new undersampling approaches were recently proposed: random phase detection (RPD) \cite{Maciejewski11} and its generalization, partial component sampling (PCS) \cite{Schuyler13}. The new approaches are fully aware of the fact that high-dimensional experiments generate hypercomplex-valued free induction decays; they randomly acquire only certain low-dimensional components of each high-dimensional hypercomplex entry. We provide a classification of various hypercomplex-aware undersampling schemes, and define a hypercomplex-aware coherence appropriate for such undersampling schemes; we then use it to quantify undersampling artifacts of RPD and various PCS schemes.