A novel second-order calibration algorithm for processing fluorescence data with scattering: Three-direction resection ATLD

The light scattering is common during fluorescence measurements, such as first- and second-order Rayleigh and Raman scatterings, which are not conducive to the decomposition of the multi-way data because it destroys the multi-linear structure. This paper proposed two second-order calibration algorithms, including three-direction resection alternating trilinear decomposition (TDR-ATLD) and three-direction resection self-weight alternating trilinear decomposition (TDR-SWATLD), which are based on an improved trilinear decomposition model for directly decomposition of the three-way fluorescence data with scattering regions removed. Through the simulation data, the proposed algorithms were compared with other three algorithms (ATLD, Interpolation-ATLD, TDR-PARAFAC). The calculation results of three algorithms (TDR-PARAFAC, TDR-ATLD and TDR-SWATLD) are better at small or large scattering widths. Both TDR-ATLD and TDR-SWATLD are insensitive to the number of components and the performance of TDR-ATLD had little fluctuation with different noise levels among the five algorithms. Additionally, TDR-ATLD and TDR-SWATLD are better than other algorithms when dealing with collinear data. The proposed algorithms were also used in two sets of real data, compared with other two algorithms (Interpolation-ATLD and TDR-PARAFAC) for dealing with scattering, the proposed algorithms could deal with fluorescence data with scattering and provided satisfactory results and TDR-ATLD has faster convergence. In general, TDR-ATLD has greater potential and performs better in processing fluorescence data with scattering.