Systematic reduction of hyperspectral images for high-throughput plastic characterization.

Hyperspectral Imaging (HSI) combines microscopy and spectroscopy to assess the spatial distribution of spectroscopically active compounds in objects, and has diverse applications in food quality control, pharmaceutical processes, and waste sorting. However, due to the large size of HSI datasets, it can be challenging to analyze and store them within a reasonable digital infrastructure, especially in waste sorting where speed and data storage resources are limited. Additionally, as with most spectroscopic data, there is significant redundancy, making pixel and variable selection crucial for retaining chemical information. Recent high-tech developments in chemometrics enable automated and evidence-based data reduction, which can substantially enhance the speed and performance of Non-Negative Matrix Factorization (NMF), a widely used algorithm for chemical resolution of HSI data. By recovering the pure contribution maps and spectral profiles of distributed compounds, NMF can provide evidence-based sorting decisions for efficient waste management. To improve the quality and efficiency of data analysis on hyperspectral imaging (HSI) data, we apply a convex-hull method to select essential pixels and wavelengths and remove uninformative and redundant information. This process minimizes computational strain and effectively eliminates highly mixed pixels. By reducing data redundancy, data investigation and analysis become more straightforward, as demonstrated in both simulated and real HSI data for plastic sorting.

Multivariate Curve Resolution Slicing of Multiexponential Time-Resolved Spectroscopy Fluorescence Data.

Time-resolved fluorescence spectroscopy (TRFS), i.e., measurement of fluorescence decay curves for different excitation and/or emission wavelengths, provides specific and sensitive local information on molecules and on their environment. However, TRFS relies on multiexponential data fitting to derive fluorescence lifetimes from the measured decay curves and the time resolution of the technique is limited by the instrumental response function (IRF). We propose here a multivariate curve resolution (MCR) approach based on data slicing to perform tailored and fit-free analysis of multiexponential fluorescence decay curves. MCR slicing, taking as a basic framework the multivariate curve resolution-alternating least-squares (MCR-ALS) soft-modeling algorithm, relies on a hybrid bilinear/trilinear data decomposition. A key feature of the method is that it enables the recovery of individual components characterized by decay profiles that are only partially describable by monoexponential functions. For TRFS data, not only pure multiexponential tail information but also shorter time delay information can be decomposed, where the signal deviates from the ideal exponential behavior due to the limited time resolution. The accuracy of the proposed approach is validated by analyzing mixtures of three commercial dyes and characterizing the mixture composition, lifetimes, and associated contributions, even in situations where only ternary mixture samples are available. MCR slicing is also applied to the analysis of TRFS data obtained on a photoswitchable fluorescent protein (rsEGFP2). Three fluorescence lifetimes are extracted, along with the profile of the IRF, highlighting that decomposition of complex systems, for which individual isomers are characterized by different exponential decays, can also be achieved.

Joint selection of essential pixels and essential variables across hyperspectral images.

An approach is proposed and illustrated for the joint selection of essential samples and essential variables of a data matrix in the frame of spectral unmixing. These essential features carry the signals required to linearly recover all the information available in the rows and columns of a data set. Working with hyperspectral images, this approach translates into the selection of essential spectral pixels (ESPs) and essential spatial variables (ESVs). This results in a highly-reduced data set, the benefits of which can be minimized computational effort, meticulous data mining, easier model building as well as better problem understanding or interpretation. Working with both simulated and real data, we show that (i) reduction rates of over 99% can be typically obtained, (ii) multivariate curve resolution - alternating least squares (MCR-ALS) can be easily applied on the reduced data sets and (iii) the full distribution maps and spectral profiles can be readily obtained from the reduced profiles and the reduced data sets (without using the full data matrix).

Second-order universal calibration.

Quantification and qualification of an analyte of interest in pharmaceutical tablets from different manufacturers/companies are a hard task because of the potential presence of various interfering molecules. Indeed, the composition of the tablets covers a wide range of interferents which can be even unknown. As a consequence, we propose to determine the concentration of an analyte of interest regardless of the interferents using the concept of universal calibration. Universal calibration paves the way to the quantification of a specific chemical entity in samples with various compositions and different interferents. This is possible by the trilinear structure of analyte's signal. In fact, the second-order advantage resulting from the second-order universal calibration models is exploited. However, a new second-order calibration strategy was conducted in this work using Trilinear Factor Extraction (TFE). A simulated data set was exemplified to highlight the ability of the proposed procedure in order to accurate extraction of the analyte's concentration profile. Additionally, two real data sets were also explored in order to test the TFE method. In the first case, Acetaminophen was quantified using fluorescence spectroscopy in tablets with different formulations from 6 companies. In the second experimental data, a peptide (Valine-Tyrosine-Valine) was successfully quantified in different samples using spectrofluorimetric data. Finally, these real data sets were analyzed by Multivariate Curve resolution - Alternating Least-Squares (MCR-ALS) under non-negativity and trilinearity constraints for the sake of comparison. The calculated Root Mean Square Error of Predictions (RMSEP) of Acetaminophen were 0.028 and 0.026 for the MCR-ALS and TFE models, respectively. On the other hand, for the second experimental data set, the RMSEP were 0.216 and 0.165, respectively. Finally, based on a paired t-test, the results of MCR-ALS and TFE were not significantly different.

Essential Spectral Pixels for Multivariate Curve Resolution of Chemical Images.

We propose a methodology to select essential spectral pixels (ESPs) of chemical images. These pixels are on the outer envelope of the principal component scores of the data and can be identified by convex-hull computation. As ESPs carry all the linearly mixed spectral information, large hyperspectral images can be dramatically reduced before multivariate curve resolution (MCR) analysis. We investigated chemical images of different spectroscopies, sizes, and complexities and show that the analysis of full data sets of hundreds of thousands of spectral pixels only require a few tenths of them.

Multi-excitation hyperspectral autofluorescence imaging for the exploration of biological samples.

Many plant tissues can be observed thanks to autofluorescence of their cell wall components. Hyperspectral autofluorescence imaging using confocal microscopy is a fast and efficient way of mapping fluorescent compounds in samples with a high spatial resolution. However a huge spectral overlap is observed between molecular species. As a consequence, a new data analysis approach is needed in order to fully exploit the potential of this spectroscopic technique and extract unbiased chemical information about complex biological samples. The objective of this work is to evaluate multi-excitation hyperspectral autofluorescence imaging to identify biological components in wheat grains during their development through their spectral profiles and corresponding contribution maps using Multivariate Curve Resolution - Alternating Least-Squares (MCR-ALS), a signal unmixing algorithm under proper constraints. For this purpose two different scenarios are used: 1) analyzing the total spectral domain of data sets using MCR-ALS under non negativity constraint in both spectral and spatial modes; 2) analyzing a reduced spectral domain of data sets using MCR-ALS under non negativity in both modes and trilinearity constraint in spectral mode. Considering the original instrumental setup and our data analysis approach, we will demonstrate that extracted contribution maps and spectral profiles of constituents can provide complementary information used to identify molecules in complex biological samples.

Effect of image processing constraints on the extent of rotational ambiguity in MCR-ALS of hyperspectral images.

Hyperspectral imaging is a way to explore the spatial and spectral information of the different compounds in chemical or biological samples. In addition, multivariate curve resolution - alternating least squares (MCR-ALS) can be used to extract this information based on the bilinearity assumption. However, it is well-known that using proper constraints can reduce the amount of uncertainty in the results of MCR, which is called rotational ambiguity. In MCR-ALS analysis of hyperspectral images, different image processing techniques, such as model fitting, image segmentation or sparse image recovery can be applied as spatial constraints. In this contribution, we aim to investigate how the use of these spatial constraints limits the extent of rotational ambiguity of MCR-ALS solutions. For this purpose, we evaluate the extent of rotational ambiguity and use Borgen plots to visualize it. We show on simulations and real hyperspectral imaging data that accuracy of the results is improved when spatial constraints are applied.

Strategy To Obtain Accurate Analytical Solutions in Second-Order Multivariate Calibration with Curve Resolution Methods.

A novel procedure is described for processing the second-order data matrices with multivariate curve resolution-alternating least-squares; while the data set is nontrilinear and severe profile overlapping occurs in the instrumental data modes. The area of feasible solutions can be reduced to a unique solution by including/considering the area correlation constraint, besides the traditional constraints (i.e., non-negativity, unimodality, species correspondence, etc.). The latter is implemented not only for the unknown samples but also for all calibration samples, regardless of their interferent content. The area of correlation constraint was specially designed to remove rotational ambiguity in the chemical data sets when information about calibration samples is at hand. In this contribution a comprehensive strategy is developed to uniquely unravel nontrilinear data sets or data sets with severely overlapped profiles in the instrumental data modes. The approach is illustrated with simulated and experimental data sets. Borgen plots are employed to adequately visualize the extent of rotational ambiguity under non-negativity constraint.