Sampling-based computation of the sets of feasible solutions and feasible bands for noisy data

Multivariate curve resolution often suffers from solution ambiguity, with many nonnegative factorizations fitting the data equally well. Building on the algorithm of Laursen and Hobolth (2022), we present an efficient sampling algorithm that can handle noisy data even containing negative entries. The algorithm iteratively updates factor columns via affine combinations within a nested loop structure, effectively approximating the sets of feasible solutions, the feasible bands, as well as the dual profiles. We apply the algorithm to two in situ FTIR spectroscopic data sets tracking the decomposition and activation of rhodium carbonyl complexes for the hydroformylation process. A comparison against established algorithms for these data sets indicates the robustness and computational efficiency of the algorithm. • Introducing a simple yet efficient sampling of the ambiguity of MCR solutions for noisy data. • Sampling of the sets of feasible solutions and bands without restricting the number of species. • The algorithm is as fast as polygon inflation for systems with three species. • The sampling outperforms all other algorithms for four or more species.