Reconstructing spectra from RGB images by relative error least-squares regression

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 Mean-Relative-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. 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.