The data and code provided here are supplementary information for the paper “Incoherence of Partial Component Sampling in multidimensional NMR" by H. Monajemi, D.L. Donoho, J.C. Hoch, and A.D. Schuyler. Please read INSTRUCTION.TXT for reproducing the results of the article. Abstract of the article: In NMR spectroscopy, random 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.
The data and code provided here are supplementary information for the paper “Incoherence of Partial Component Sampling in multidimensional NMR" by H. Monajemi, D.L. Donoho, J.C. Hoch, and A.D. Schuyler. Please read INSTRUCTION.TXT for reproducing the results of the article. Abstract of the article: In NMR spectroscopy, random 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.