How noise affects the band boundaries in multivariate curve resolution

Abstract

Three models are compared regarding the estimation of the boundaries of the range of feasible bilinear solutions brought about by rotational ambiguity in the presence of noise. A two-component system having significant overlapping between the component profiles in both data modes has been studied using FACPACK, based on the so-called polygon inflation algorithm, and two procedures which estimate the extreme profiles corresponding to maximum and minimum signal contribution function: MCR-BANDS and N-BANDS. These latter two models operate by applying different constraints during the optimization phase. Non-negativity was applied as the only constraint on the retrieved profiles. The results were compared with a simulation based on the addition of identically and independently distributed noise at two levels. An experimental system was also analyzed regarding the combined effect of rotational ambiguity and instrumental noise.