Evaluation Metrics

Spectral resolution enhancement needs to maintain relative peak heights, widths, positions, and shapes as these are of potential interest in a given application. ⁵⁹ It is furthermore important to avoid the introduction of artifacts. ¹⁹ We evaluated improved spectral resolution based on the criteria below. These metrics were applied to the synthetic spectra, which could be best interpreted quantitatively by these methods. For the real spectra, we assessed resolution enhancement qualitatively or semi-quantitatively.

(i) To guard against processing-based spectral distortions, we recorded the root mean square error (RMSE) between the target and resolved sets of spectra

We excluded the featureless parts below channel 200 and above channel 900.

(ii) We assessed the separation of two overlapping peaks, applied here to P8 and P9, as the height of the resolved spectrum’s smallest flanking peak minus the height of the valley between the overlapping peaks relative to the height of the same peak in the target spectrum minus the height of the corresponding valley in the target spectrum

(iii) The reduction in peak HWHM was determined for freestanding peaks as the HWHM in the resolved spectrum relative to the corresponding HWHM in the target spectrum

A ten-step interpolation was used to obtain a more accurate HWHM for the resolved peaks, after processing with the resolution enhancement algorithms. We used P1 for these calculations.

Where quantitative results are desired or correlation dependent analyses need to be performed, the preservation of true peak positions and intensities in resolved spectra are required. Thus, we included in the evaluation (iv) the number of peaks in the first resolved spectrum of the series relative to those in the corresponding truth set, (v) the number of peaks in the resolved spectrum with incorrect positions relative to the truth set, and (vi) the mean deviation of peaks in the resolved spectrum from their correct positions.

Finally, we determined the correlations of the P6 and P7 intensities between the resolved spectra and the truth set because they were the most affected by overlap. If P6 and P7 were resolved, their intensities at the positions of their maxima were used, otherwise the positions used were those of the P6 and P7 maxima in the corresponding truth set. For increasingly well-resolved spectra, the correlation coefficient between P6 of the resolved set and P6 of the truth set (vii) should trend higher and ideally reach unity. In contrast, for increasingly well-resolved spectra, this correlation coefficient for P6 of the resolved set and P7 of the truth set (viii) should trend lower due to diminished overlap. However, as the truth set P7 was constant, a correlation coefficient was undefined. We used instead, where defined, the correlation coefficients between P6 and P7 of the resolved set for this part of the calculation.