Constraining shape smoothness in multivariate curve resolution–alternating least squares
Résumé
The resolution of complex multicomponent hyperspectral images with multivariate curve resolution–alternating least squares is mainly performed by using a limited number of constraints on the pure constituent distribution maps, such as non-negativity or local constraints. This work proposes a constraint that works with the spatial information of the whole image and has been given the name shape smoothness constraint. Contrary to local constraints, shape smoothness constraint imposes a global character on the distribution map pattern. It uses two-dimensional P-splines to enforce smoothness of the global spatial features of the distribution maps generated within the alternating least squares procedure. This allows revealing main pattern(s) in the spatial data leaving high-frequency signals, corresponding to fine-scale structures in the image. This approach has been successfully applied on several simulated examples where imposing shape smoothness resulted in the recovery of the correct pattern for the image objects, which in turn provided more accurate distribution maps and spectral profiles. It was also shown that when information about the smoothness of the pattern(s) of the image constituents holds, the constraint can be a flexible and robust alternative for the resolution of real hyperspectral imaging data.