Unbiased measurements of reconstruction fidelity of sparsely sampled magnetic resonance spectra

The application of sparse-sampling techniques to NMR data acquisition would benefit from reliable quality measurements for reconstructed spectra. We introduce a pair of noise-normalized measurements, [Image: see text] and [Image: see text], for differentiating inadequate modelling from overfitting. While [Image: see text] and [Image: see text] can be used jointly for methods that do not enforce exact agreement between the back-calculated time domain and the original sparse data, the cross-validation measure [Image: see text] is applicable to all reconstruction algorithms. We show that the fidelity of reconstruction is sensitive to changes in [Image: see text] and that model overfitting results in elevated [Image: see text] and reduced spectral quality.