Supplemental Information: Application of Iterative Soft Thresholding for Fast Reconstruction of NMR Data Non-uniformly Sampled with Multidimensional Poisson Gap Scheduling

Sven G. Hyberts1, Alexander G. Milbradt1, Andreas B. Wagner1, 2, Haribabu Arthanari1 and Gerhard Wagner1*.

Contribution from Harvard Medical School, Boston, MA 02115, USA

1Department of Biological Chemistry and Molecular Pharmacology, Harvard Medical School, 240 Longwood Avenue, Boston, Massachusetts 02115, USA.

2Wentworth Institute of Technology, 550 Huntington Avenue, Boston, MA 02115, USA.

*E-mail:

Submitted to JBNMR 1/24/2012

The effect of threshold on the performance of IST reconstructions.

Here we show simulations illustrating the effect of using larger iteration steps in IST iterations. We compare lowering the threshold by factors of 0.75, 0.5 and 0.3 per IST iteration. Supplemental Fig. S1a shows the same synthetic two-line spectrum without noise as used in Fig. 1 of the main text, with a 0.75 iteration threshold. In Figures S1b and S1c the same simulated two-line spectrum was used thresholds of 0.5 and 0.3 were applied, respectively. The reconstruction is still very good when using a factor of 0.5 but there are distortions at the bases of the signals when the top 70% (factor 0.3) of the peaks are removed per iteration. These are due to sinc wiggles because we did not apply apodization functions prior to FFT. Figs S1d, e and f show results of low thresholds when spectra contain noise. In this case, the tallest spikes of the PSF artifacts are interpreted as peaks, and one obtains a baseline full of artifacts, and this should obviously be avoided. However, the observation that the threshold could be lowered initially in large steps before the noise level is reached suggests the use of a dynamic change of the threshold, which could speed up reconstruction dramatically and will be pursued.

Figure S1. Effects of large threshold reduction steps on a synthetic two-line spectrum without (a - c) and with noise (d - f). In all panels 32 points out of 128 were sampled. (a) Same synthetic spectrum reconstruction as in Fig. 1 of the main manuscript with a cut-off 0.75 of the strongest peak in each iteration. (b and c) Effect of lowering the threshold drastically to 0.5 and 0.3. This leads to a faster depletion of the residual but causes distortions at the bases of the lines. (e and f) show simulations with noise. Thresholds of 0.75 and 0.5 have the effect to interpret tallest noise points as peaks, which leads to a spiky baseline, and the weaker signal is not reliably recognized. Lowering the threshold to 0.3 creates serious deterioration of the reconstruction.

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