Open AccessReaching the sparse-sampling limit for reconstructing a single peak in a 2D NMR spectrum using iterated maps
Author(s) -
Robert L. Blum,
Jared Rovny,
J. Patrick Loria,
Sean Barrett
Publication year - 2019
Publication title -
journal of biomolecular nmr
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.346
H-Index - 106
eISSN - 1573-5001
pISSN - 0925-2738
DOI - 10.1007/s10858-019-00262-4
Subject(s) - undersampling , iterated function , algorithm , nonuniform sampling , sampling (signal processing) , spectrum (functional analysis) , spectral line , dispersion (optics) , limit (mathematics) , chemistry , computer science , compressed sensing , physics , artificial intelligence , mathematics , detector , mathematical analysis , optics , telecommunications , quantum mechanics , astronomy , quantization (signal processing)
Many of the ubiquitous experiments of biomolecular NMR, including [Formula: see text], [Formula: see text], and CEST, involve acquiring repeated 2D spectra under slightly different conditions. Such experiments are amenable to acceleration using non-uniform sampling spectral reconstruction methods that take advantage of prior information. We previously developed one such technique, an iterated maps method (DiffMap) that we successfully applied to 2D NMR spectra, including [Formula: see text] relaxation dispersion data. In that prior work, we took a top-down approach to reconstructing the 2D spectrum with a minimal number of sparse samples, reaching an undersampling fraction that appeared to leave some room for improvement. In this study, we develop an in-depth understanding of the action of the DiffMap algorithm, identifying the factors that cause reconstruction errors for different undersampling fractions. This improved understanding allows us to formulate a bottom-up approach to finding the lowest number of sparse samples required to accurately reconstruct individual spectral features with DiffMap. We also discuss the difficulty of extending this method to reconstructing many peaks at once, and suggest a way forward.