Determination of optimal sampling wavelengths for reflectance measurement using sparse principal component analysis

In the visible region, material reflectance spectra are typically recorded over the 400–700 nm range at uniformly spaced wavelength intervals (e.g., 1, 5, 10, or 20 nm). However, such uniform sampling strategies neglect the intrinsic spectral characteristics of materials and may fail to capture critical spectral features, particularly when the number of measurement channels are limited. In this study, Sparse Principal Component Analysis (SPCA) was employed to determine the most informative wavelengths for reflectance acquisition when the number of available spectral bands was constrained to 16, 13, 11, 9, and 7. The selected wavelengths were assigned as the central positions of Gaussian filters with very narrow bandwidths (FWHM = 1 nm). These filters were subsequently used to measure the reflectance spectra of 1269 Munsell color chips at a 1-nm spectral resolution. For comparison, reflectance measurements were also simulated using the same Gaussian filters, but with uniformly distributed central wavelengths across the visible spectrum. The reconstruction performances of both approaches were quantitatively evaluated using the Root Mean Square Error (RMSE), Goodness-of-Fit Coefficient (GFC), and color difference (ΔE) values under D65 and A illuminants. The results revealed that reflectance measurements obtained at SPCA-selected wavelengths consistently yielded higher reconstruction accuracy than those derived from uniformly spaced sampling. Specifically, the SPCA-based measurements exhibited lower RMSE and ΔE and higher GFC values, demonstrating the superiority of data-driven wavelength selection under constraints of limited measurement channels.