This research using Hyperspectral imaging involves recognizing targets through spatial and spectral matching and spectral un-mixing of data ranging from remote sensing to medical imaging kernels for clinical studies based on Hyperspectral data-sets generated using the VFTHSI [Visible Fourier Transform Hyperspectral Imager], whose high resolution Si detector makes the analysis achievable. The research may be broadly classified into (I) A Physically Motivated Correlation Formalism (PMCF), which places both spatial and spectral data on an equivalent mathematical footing in the context of a specific Kernel and (II) An application in RF plasma specie detection during carbon nanotube growing process. (III) Hyperspectral analysis for assessing density and distribution of retinopathies like age related macular degeneration (ARMD) and error estimation enabling the early recognition of ARMD, which is treated as an ill-conditioned inverse imaging problem. The broad statistical scopes of this research are two fold-target recognition problems and spectral unmixing problems. All processes involve experimental and computational analysis of Hyperspectral data sets is presented, which is based on the principle of a Sagnac Interferometer, calibrated to obtain high SNR levels.

PMCF computes spectral/spatial/cross moments and answers the question of how optimally the entire hypercube should be sampled and finds how many spatial-spectral pixels are required precisely for a particular target recognition. Spectral analysis of RF plasma radicals, typically Methane plasma and Argon plasma using VFTHSI has enabled better process monitoring during growth of vertically aligned multi-walled carbon nanotubes by instant registration of the chemical composition or density changes temporally, which is key since a significant correlation can be found between plasma state and structural properties.

A vital focus of this dissertation is towards medical Hyperspectral imaging applied to retinopathies like age related macular degeneration targets taken with a Fundus imager, which is akin to the VFTHSI. Detection of the constituent components in the diseased hyper-pigmentation area is also computed. The target or reflectance matrix is treated as a highly ill-conditioned spectral un-mixing problem, to which methodologies like inverse techniques, principal component analysis (PCA) and receiver operating curves (ROC) for precise spectral recognition of infected area.

The region containing ARMD was easily distinguishable from the spectral mesh plots over the entire band-pass area. Once the location was detected the PMCF coefficients were calculated by cross correlating a target of normal oxygenated retina with the deoxygenated one. The ROCs generated using PMCF shows 30% higher detection probability with improved accuracy than ROCs based on Spectral Angle Mapper (SAM). By spectral unmixing methods, the important endmembers/carotenoids of the MD pigment were found to be Xanthophyl and lutein, while β-carotene which showed a negative correlation in the unconstrained inverse problem is a supplement given to ARMD patients to prevent the disease and does not occur in the eye. Literature also shows degeneration of meso-zeaxanthin. Ophthalmologists may assert the presence of ARMD and commence the diagnosis process if the Xanthophyl pigment have degenerated 89.9%, while the lutein has decayed almost 80%, as found deduced computationally. This piece of current research takes it to the next level of precise investigation in the continuing process of improved clinical findings by correlating the microanatomy of the diseased fovea and shows promise of an early detection of this disease.