Spectral reconstruction (SR) algorithms attempt to map RGB- to hyperspectral-images. Classically, simple pixel-based regression is used to solve for this SR mapping and more recently patch-based Deep Neural Networks (DNN) are considered (with a modest performance increment). For either method, the 'training' process typically minimizes a Mean-Squared-Error (MSE) loss. Curiously, in recent research, SR algorithms are evaluated and ranked based on a relative percentage error, so-called MeanRelative-Absolute Error (MRAE), which behaves very differently from the MSE loss function. The most recent DNN approaches - perhaps unsurprisingly - directly optimize for this new MRAE error in training so as to match this new evaluation criteria.<br/> In this paper, we show how we can also reformulate pixelbased regression methods so that they too optimize a relative spectral error. Our Relative Error Least-Squares (RELS) approach minimizes an error that is similar to MRAE. Experiments demonstrate that regression models based on RELS deliver better spectral recovery, with up to a 10% increment in mean performance and a 20% improvement in worst-case performance depending on the method.
Pigments characterization on paintings is usually made with X-ray fluorescence, traditional false color photography and optical microscopy. The use of optical techniques based on reflectance spectra, like reflectance spectrophotometry or hyperspectral imaging, is limited today to some case studies. We would like to improve these optical techniques for pigment characterization, because they are non-invasive and can give a lot of information. After comparing the ways to calibrate to reflectance spectrophotometry and hyperspectral imaging, we develop the two techniques for the specific study of pigments. We develop a Matlab program to analyze (identify and quantify) reflectance spectra given by spectrophotometry, and a new methodology based on false color composites to use hyperspectral images in a simple way. The choice of the spectral bands to identify pigments takes its roots in the maximization of spectral differences, and leads to the generation of 3 false color composites - called variable composites FC1, FC2 and FC3 - to distinguish the pigments of the four categories (blue, red, yellow and green). The results of spectrophotometry and variable composites on a painting of the 17th century by French painter Eustache Le Sueur are encouraging and consistent with other techniques' results. Our results should promote the use of spectrophotometry and hyperspectral imaging for pigment characterization in the future.