Christopher L. Stork

Hyperspectral Confocal Fluorescence Imaging: Exploring Alternative Multivariate Curve Resolution Approaches

Hyperspectral confocal fluorescence microscopy, when combined with multivariate curve resolution (MCR), provides a powerful new tool for improved quantitative imaging of multi-fluorophore samples. Generally, fully non-negatively constrained models are used in the constrained alternating least squares MCR analyses of hyperspectral images since real emission components are expected to have non-negative pure emission spectra and concentrations. However, in this paper, we demonstrate four separate cases in which partially constrained models are preferred over the fully constrained MCR models. These partially constrained MCR models can sometimes be preferred when system artifacts are present in the data or where small perturbations of the major emission components are present due to environmental effects or small geometric changes in the fluorescing species. Here we demonstrate that in the cases of hyperspectral images obtained from multicomponent spherical beads, autofluorescence from fixed lung epithelial cells, fluorescence of quantum dots in aqueous solutions, and images of mercurochrome-stained endosperm portions of a wild-type corn seed, these alternative, partially constrained MCR analyses provide improved interpretability of the MCR solutions. Often the system artifacts or environmental effects are more readily described as first and/or second derivatives of the main emission components in these alternative MCR solutions since they indicate spectral shifts and/or spectral broadening or narrowing of the emission bands, respectively. Thus, this paper serves to demonstrate the need to test alternative partially constrained models when analyzing hyperspectral images with MCR methods.

Advantages of clustering in the phase classification of hyperspectral materials images.

Despite the many demonstrated applications of factor analysis (FA) in analyzing hyperspectral materials images, FA does have inherent mathematical limitations, preventing it from solving certain materials characterization problems. A notable limitation of FA is its parsimony restriction, referring to the fact that in FA the number of components cannot exceed the chemical rank of a dataset. Clustering is a promising alternative to FA for the phase classification of hyperspectral materials images. In contrast with FA, the phases extracted by clustering do not have to be parsimonious. Clustering has an added advantage in its insensitivity to spectral collinearity that can result in phase mixing using FA. For representative energy dispersive X-ray spectroscopy materials images, namely a solder bump dataset and a braze interface dataset, clustering generates phase classification results that are superior to those obtained using representative FA-based methods. For the solder bump dataset, clustering identifies a Cu-Sn intermetallic phase that cannot be isolated using FA alone due to the parsimony restriction. For the braze interface sample that has collinearity among the phase spectra, the clustering results do not exhibit the physically unrealistic phase mixing obtained by multivariate curve resolution, a commonly utilized FA algorithm.

Solving Inverse Radiation Transport Problems with Multi-Sensor Data in the Presence of Correlated Measurement and Modeling Errors

Inverse radiation transport focuses on identifying the configuration of an unknown radiation source given its observed radiation signatures. The inverse problem is traditionally solved by finding the set of transport model parameter values that minimizes a weighted sum of the squared differences by channel between the observed signature and the signature pre dicted by the hypothesized model parameters. The weights are inversely proportional to the sum of the variances of the measurement and model errors at a given channel. The traditional implicit (often inaccurate) assumption is that the errors (differences between the modeled and observed radiation signatures) are independent across channels. Here, an alternative method that accounts for correlated errors between channels is described and illustrated using an inverse problem based on the combination of gam ma and neutron multiplicity counting measurements.

Accounting for correlated errors in inverse radiation transport problems

Inverse radiation transport focuses on identifying the configuration of an unknown radiation source given its observed radiation signatures. The inverse problem is solved by finding the set of transport model variables that minimizes a weighted sum of the squared differences by channel between the observed signature and the signature predicted by the hypothesized model parameters. The weights per channel are inversely proportional to the sum of the variances of the measurement and model errors at a given channel. In the current treatment, the implicit assumption is that the errors (differences between the modeled and observed radiation signatures) are independent across channels. In this paper, an alternative method that accounts for correlated errors between channels is described and illustrated for inverse problems based on gamma spectroscopy.