title: Pitfalls in compressed sensing reconstruction and how to avoid them.
abstract: Multidimensional NMR can provide unmatched spectral resolution, which is crucial when dealing with samples of biological macromolecules. The resolution, however, comes at the high price of long experimental time. Non-uniform sampling (NUS) of the evolution time domain allows to suppress this limitation by sampling only a small fraction of the data, but requires sophisticated algorithms to reconstruct omitted data points. A significant group of such algorithms known as compressed sensing (CS) is based on the assumption of sparsity of a reconstructed spectrum. Several papers on the application of CS in multidimensional NMR have been published in the last years, and the developed methods have been implemented in most spectral processing software. However, the publications rarely show the cases when NUS reconstruction does not work perfectly or explain how to solve the problem. On the other hand, every-day users of NUS develop their rules-of-thumb, which help to set up the processing in an optimal way, but often without a deeper insight. In this paper, we discuss several sources of problems faced in CS reconstructions: low sampling level, missassumption of spectral sparsity, wrong stopping criterion and attempts to extrapolate the signal too much. As an appendix, we provide MATLAB codes of several CS algorithms used in NMR. We hope that this work will explain the mechanism of NUS reconstructions and help readers to set up acquisition and processing parameters. Also, we believe that it might be helpful for algorithm developers.
authors.affiliation: Centre of New Technologies, University of Warsaw, Banacha 2C, 02-097, Warsaw, Poland.|Institute for Spectroscopy, Russian Academy of Sciences, Fizicheskaya 5, Troitsk, Moscow, Russia, 108840.
authors.forename: Alexandra
authors.initials: A
authors.lastname: Shchukina
authors.affiliation: Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Pasteura 5, Warsaw, Poland.
authors.forename: Paweł
authors.initials: P
authors.lastname: Kasprzak
authors.affiliation: Centre of New Technologies, University of Warsaw, Banacha 2C, 02-097, Warsaw, Poland.
authors.forename: Rupashree
authors.initials: R
authors.lastname: Dass
authors.affiliation: Centre of New Technologies, University of Warsaw, Banacha 2C, 02-097, Warsaw, Poland.
authors.forename: Michał
authors.initials: M
authors.lastname: Nowakowski
authors.affiliation: Centre of New Technologies, University of Warsaw, Banacha 2C, 02-097, Warsaw, Poland. k.kazimierczuk@cent.uw.edu.pl.
authors.forename: Krzysztof
authors.identifier: http://orcid.org/0000-0001-9585-1737
authors.initials: K
authors.lastname: Kazimierczuk
mesh_terms: D000465:Algorithms; D000818:Animals; D002645:Chickens; D005583:Fourier Analysis; D005947:Glucose; D008320:Maltose; D008962:Models, Theoretical; D019906:Nuclear Magnetic Resonance, Biomolecular / Q000379:methods*; D018401:Sample Size; D012680:Sensitivity and Specificity; D059629:Signal-To-Noise Ratio; D013049:Spectrin / Q000737:chemistry; D013995:Time; D014994:Xylose
chemical_list: D013049:Spectrin; D008320:Maltose; D014994:Xylose; D005947:Glucose
keywords: CLEAN; Iterative soft thresholding; Iteratively re-weighted least squares; Low-rank; Matching pursuit; Non-uniform sampling