Effect of image processing constraints on the extent of rotational ambiguity in MCR-ALS of hyperspectral images

Abstract

Hyperspectral imaging is a way to explore the spatial and spectral information of the different compounds in chemical or biological samples. In addition, multivariate curve resolution - alternating least squares (MCR-ALS) can be used to extract this information based on the bilinearity assumption. However, it is well-known that using proper constraints can reduce the amount of uncertainty in the results of MCR, which is called rotational ambiguity. In MCR-ALS analysis of hyperspectral images, different image processing techniques, such as model fitting, image segmentation or sparse image recovery can be applied as spatial constraints. In this contribution, we aim to investigate how the use of these spatial constraints limits the extent of rotational ambiguity of MCR-ALS solutions. For this purpose, we evaluate the extent of rotational ambiguity and use Borgen plots to visualize it. We show on simulations and real hyperspectral imaging data that accuracy of the results is improved when spatial constraints are applied.

Keywords: Alternating least squares; Area of feasible solutions; Borgen plot; Multivariate curve resolution; Spatial constraints; Uncertainty.