Comparison of Satellite Hyperspectral Data in Geological Mapping (Methods Part 2)

In the previous article, "Comparison of Satellite Hyperspectral Data in Geological Mapping (Methods Part 1)",... (See the post dated December 5, 2024)The previous sections introduced data registration, spectral unmixing, spectral abundance, and spectral index of different sensors in the study area. This section continues to introduce related research techniques.

3.3 Comparing sensors by quantitative spectral consistency

Rupsa et al. designed a set of four consistency metrics covering comparisons ranging from broad spectral ranges to narrow spectral ranges specific to particular applications. To maintain interpretability and consistency, Rupsa et al. used the widely used R² score as the basis for comparisons. Additionally, Rabs², an absolute consistency metric, was calculated by comparing the mean square difference in reflectance values ​​(across all bands in each sensor) between each sensor relative to the value of the sensor with the highest standard deviation. This metric ranges from 0 to 1, with a value of 1 indicating perfect data consistency, and values ​​of 0 or negative infinity indicating that the difference between sensors is equal to or greater than the internal variability of the data.

Absolute consistency measures are too conservative because the methods used are typically sensitive only to relative spectral variations, not absolute reflectance. Therefore, researchers proposed a second consistency measure, Rprop², which is calculated using the residuals between the linear regression and the best-fitting linear regression, rather than comparing it to a 1:1 line. This index is equivalent to the R² score of the linear regression for each pair of reflectance measurements, and thus its value ranges from 0 (no correlation) to 1 (perfect correlation).

Where SSR is the sum of residuals of the best-fit linear regression, and SST is the sum of squares of the sums of dependent variables.

To compare the absolute and relative consistency of the sensors, Rupsa et al. resampled all reflectance data to the same 60-meter pixel size as EMIT and adjusted the spectral resolution to approximately 125 bands, the same as HyMap.

Both of these metrics are sensitive to data across the entire spectral range or a selected subset of the spectrum. However, many spectral analyses, such as spectral index analysis and linear unmixing, use only a few specific spectra, meaning that most spectral differences will be irrelevant in these comparisons. Therefore, Rupsa et al. proposed a third consistency metric, Rfeat², specifically designed to compare specific spectral index results. It is not absolute but rather a linear combination of specific pixels (i.e., endmembers). These latent features may be biased by sensor effects and/or atmospheric and topographic correction artifacts, but they can maintain consistency as long as they have the same impact on every pixel in the image. This comparison of latent features is also application-specific and relies on selecting a specific set of endmember pixels that maintain consistent positions across the two datasets. In this way, the researchers used non-negative least squares to linearly unmix the images and calculated the Rfeat² metric by comparing the spectral abundance of the results.

In summary, Rupsa et al. calculated a set of four R² score-based comparative metrics to assess consistency between selected sensors in two study areas. Rabs² measures consistency in raw reflectance estimates, while Rprop² measures consistency in relative spectral variations. Rfeat² and Rlat² are application-specific comparisons, comparing specific spectral indices and linearly unmixed spectral abundances, respectively. Rupsa et al. emphasized that they maintained the original resolution of the spectral data during the spectral analysis and resampled the data to 60 meters in the final comparison. This approach allows for the evaluation of the practical performance of different sensors in geological mapping and the identification of which sensors perform best with specific spectral analysis methods.

 [1]:Chakraborty, R.; Rachdi, I.; Thiele, S.; Booysen, R.; Kirsch, M.; Lorenz, S.; Gloaguen, R.; Sebari, I. A Spectral and Spatial Comparison of Satellite-Based Hyperspectral Data for Geological Mapping. Remote Sens. 2024, 16, 2089. https://doi.org/ 10.3390/rs16122089