In this paper, we describe the use of various methods of one-dimensional spectral compression by variable selection as well as principal component analysis (PCA) for compressing multi-dimensional sets of spectral data. We have examined methods of variable selection such as wavelength spacing, spectral derivatives, and spectral integration error. After variable selection, reduced transmission spectra must be decompressed for use. Here we examine various methods of interpolation, e.g., linear, cubic spline and piecewise cubic Hermite interpolating polynomial (PCHIP) to recover the spectra prior to estimating at-sensor radiance. Finally, we compressed multi-dimensional sets of spectral transmittance data from moderate resolution atmospheric transmission (MODTRAN) data using PCA. PCA seeks to find a set of basis spectra (vectors) that model the variance of a data matrix in a linear additive sense. Although MODTRAN data are intricate and are used in nonlinear modeling, their base spectra can be reasonably modeled using PCA yielding excellent results in terms of spectral reconstruction and estimation of at-sensor radiance. The major finding of this work is that PCA can be implemented to compress MODTRAN data with great effect, reducing file size, access time and computational burden while producing high-quality transmission spectra for a given set of input conditions.
Multivariate curve resolution (MCR) using constrained alternating least squares algorithms represents a powerful analysis capability for a quantitative analysis of hyperspectral image data. We will demonstrate the application of MCR using data from a new hyperspectral fluorescence imaging microarray scanner for monitoring gene expression in cells from thousands of genes on the array. The new scanner collects the entire fluorescence spectrum from each pixel of the scanned microarray. Application of MCR with nonnegativity and equality constraints reveals several sources of undesired fluorescence that emit in the same wavelength range as the reporter fluorphores. MCR analysis of the hyperspectral images confirms that one of the sources of fluorescence is due to contaminant fluorescence under the printed DNA spots that is spot localized. Thus, traditional background subtraction methods used with data collected from the current commercial microarray scanners will lead to errors in determining the relative expression of low-expressed genes. With the new scanner and MCR analysis, we generate relative concentration maps of the background, impurity, and fluroescent labels over the entire image. Since the concentration maps of the fluorescent labels are relativly uaffected by the presence of background and impurity emissions, the accuracy and useful dynamic range of the gene expression data are both greatly improved over those obtained by commercial microarray scanners.
In this paper, we describe the use of linear unmixing algorithms to spatially and spectrally separate fluorescence emission signals from fluorophores having highly overlapping emission spectra. Hyperspectral image data for mixtures of Nile Blue and HIDC Iodide in a methanol/polymer matrix were obtained using the Information-efficient Spectral Imaging sensor (ISIS) operated in its Hadamard Transform mode. The data were analyzed with a combination of Principal Components Analysis (PCA), orthogonal rotation, and equality and non-negativity constrained least squares methods. The analysis provided estimates of the pure-component fluorescence emission spectra and the spatial distributions of the fluorophores. In addition, spatially varying interferences from the background and laser excitation were identified and separated. A major finding resulting from this work is that the pure-component spectral estimates are very insensitive to the initial estimates supplied to the alternating least squares procedures. In fact, random number starting points reliably gave solutions that were effectively equivalent to those obtained when measured pure-component spectra were used as the initial estimates. While our proximate application is evaluating the possibility of multivariate quantitation of DNA microarrays, the results of this study should be generally applicable to hyperspectral imagery typical of remote sensing spectrometers.
Field screening of fuel-contaminated soils using laser- induced fluorescence is a cost effective and timely method of characterizing contaminated sites. Data collected with laser-based screening tools are often extensive and difficult to interpret. Pattern recognition algorithms can be utilized to enable less highly trained personnel to identify contaminants. In this work, fluorescence intensity of various hydrocarbon fuels deposited on various soil types was measured as a function of emission wavelength and decay time, generating wavelength-time matrices. The data were arranged into a three mode array and subjected to trilinear decomposition (TLD). The results of the TLD were then utilized in pattern recognition schemes, specifically, linear discrimination and classification and hierarchical cluster analysis. Classification rates and clustering results indicate that these techniques can be very valuable tools in site characterization.
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