Table 2.
Summary of the effects of 4 common spectral analysis algorithms on the outcomes of the theoretical sensitivity analysis methodology, as applied to the example of detecting a weak fluorescence signal among strong background autofluorescence. The utility of each curve for providing information to the end user is summarized in the 2nd row. Each curve provides different information for examining the response and performance of the analysis algorithm.
| Measured Outcome | TSC (Theoretical Sensitivity Curve) |
TPPC (Thresholded Positive Pixel Curve) |
ROC (Receiver Operator Characteristic Curve) |
|---|---|---|---|
| Algorithm | |||
| Utility of Outcome | Valuable in visualizing the sensitivity linearity of the combined biological sample + imaging hardware + analysis algorithm, as well as potential error associated with measuring the target endmember. High standard deviation (error bars) indicates a high biological variability and potential for misclassification and false-positive detection. | Valuable in assessing the ability to detect positive pixels for a specified detection threshold. This is highly relevant to most biomedical spectral imaging assays, as the end result is often a quantified count (# of expressing cells, # of dividing cells, % of tissue that is pathogenic, etc.). For the majority of scenarios a global threshold is used to make the count, and the TPPC can be used to measure the number of false positive detections and the increase in target endmember signal that is required to detect all true positive pixels. | Valuable as a classical “gold-standard” approach for visualizing the sensitivity and specificity of a spectral imaging assay. The ROC characterizes the spectral imaging classification performance for one specified level of target endmember. |
| LU (Linear Unmixing) | Linear behavior Standard deviation insensitive to scaling factor | Reasonable detection slope indicates the ability to detect weak signals in high autofluorescence regions if the spectra of all endmembers are known a priori | |
| SAM (Spectral Angle Mapper) | Highly nonlinear behavior Standard deviation decreases with increasing scaling factor (as the angle between test pixels and the target endmember decreases) Standard deviation is very high for low background and low signal | Lower detection slope, especially for regions with high autofluorescenec, hence a higher scaling factor may be needed for accurate detection Threshold specified in radians | Improved performance, but may be skewed because SAM is insensitive to intensities |
| CEM (Constrained Energy Minimization) | Nonlinear behavior Standard deviation increases with increasing scaling factor | Much lower detection slope than LU and MF, hence a higher scaling factor will likely be needed for accurate detection and the threshold may need to be increased to compensate | Poor performance for weak signals |
| MF (Matched Filter) | Linear behavior Standard deviation insensitive to scaling factor | Similar detection slope as LU, but right-shifted, indicating a reduced ability to detect very weak signals | Poor performance for very weak signals |