Application of Two-Dimensional Band-Target Entropy Minimization to Fluorescence Data: Implications for the Recovery of Patterns Arising from Only Bilinear and Not Trilinear Structures

Abstract

Pattern recognition in two-dimensional (2D) spectroscopy, without recourse to spectral libraries, etc., has a number of important potential applications. In the present contribution, two blind source separation techniques (spectral reconstruction) are applied to sets of 2D fluorescence data possessing both Rayleigh scattering and Raman scattering. The two methods used are (1) two-dimensional band-target entropy minimization (2D-BTEM), which models data as a bilinear form (in terms of a weighted sum of 2D patterns) and (2) parallel factor analysis (PARAFAC), which models data as a trilinear form. In addition, an a priori estimate of the number of patterns present is not required by 2D-BTEM but is required in PARAFAC. Both 2D-BTEM and PARAFAC are successfully applied to the real three-component data, and good 2D spectral reconstructions of the three amino acids are achieved. Moreover, 2D-BTEM was also able to recover the 2D Raman scattering directly, whereas PARAFAC did not recover the 2D Raman scatter (the Raman scatter does not possess a trilinear form). The present results suggest that 2D-BTEM can be useful in a wide range of spectroscopic applications for the recovery of underlying 2D patterns.