Limitations of Principal Component Analysis for Dimensionality-Reduction for Classification of Hyperspectral Data

It is a popular practice in the remote-sensing community to apply principal component analysis (PCA) on a higher-dimensional feature space to achieve dimensionality-reduction. Several factors that have led to the popularity of PCA include its simplicity, ease of use, availability as part of popular remote-sensing packages, and optimal nature in terms of mean square error. These advantages have prompted the remote-sensing research community to overlook many limitations of PCA when used as a dimensionality-reduction tool for classification and target-detection applications. This thesis addresses the limitations of PCA when used as a dimensionality-reduction technique for extracting discriminating features from hyperspectral data. Theoretical and experimental analyses are presented to demonstrate that PCA is not necessarily an appropriate feature-extraction method for high-dimensional data when the objective is classification or target-recognition. The influence of certain data-distribution characteristics, such as within-class covariance, between-class covariance, and correlation on PCA transformation, is analyzed in this thesis. The classification accuracies obtained using PCA features are compared to accuracies obtained using other feature-extraction methods like variants of Karhunen-Loève transform and greedy search algorithms on spectral and wavelet domains. Experimental analyses are conducted for both two-class and multi-class cases. The classification accuracies obtained from higher-order PCA components are compared to the classification accuracies of features extracted from different regions of the spectrum. The comparative study done on the classification accuracies that are obtained using above feature-extraction methods, ascertain that PCA may not be an appropriate tool for dimensionality-reduction of certain hyperspectral data-distributions, when the objective is classification or target-recognition

An Evaluation of multispectral earth-observing multi-aperture telescope designs for target detection and characterization

Earth-observing satellites have fundamental size and weight design limits since they must be launched into space. These limits serve to constrain the spatial resolutions that such imaging systems can achieve with traditional telescope design strategies. Segmented and sparse-aperture imaging system designs may offer solutions to this problem. Segmented and sparse-aperture designs can be viewed as competing technologies; both approaches offer solutions for achieving finer resolution imaging from space. Segmented-aperture systems offer greater fill factor, and therefore greater signal-to-noise ratio (SNR), for a given encircled diameter than their sparse aperture counterparts, though their larger segments often suffer from greater optical aberration than those of smaller, sparse designs. Regardless, the use of any multi-aperture imaging system comes at a price; their increased effective aperture size and improvement in spatial resolution are offset by a reduction in image quality due to signal loss (less photon-collecting area) and aberrations introduced by misalignments between individual sub-apertures as compared with monolithic collectors. Introducing multispectral considerations to a multi-aperture imaging system further starves the system of photons and reduces SNR in each spectral band. This work explores multispectral design considerations inherent in 9-element tri-arm sparse aperture, hexagonal-element segmented aperture, and monolithic aperture imaging systems. The primary thrust of this work is to develop an objective target detection-based metric that can be used to compare the achieved image utility of these competing multi-aperture telescope designs over a designated design parameter trade space. Characterizing complex multi-aperture system designs in this way may lead to improved assessment of programmatic risk and reward in the development of higher-resolution imaging capabilities. This method assumes that the stringent requirements for limiting the wavefront error (WFE) associated with multi-aperture imaging systems when producing imagery for visual assessment, can be relaxed when employing target detection-based metrics for evaluating system utility. Simple target detection algorithms were used to determine Receiver Operating Characteristic (ROC) curves for the various simulated multi-aperture system designs that could be used in an objective assessment of each system\u27s ability to support target detection activities. Also, a set of regressed equations was developed that allow one to predict multi-aperture system target detection performance within the bounds of the designated trade space. Suitable metrics for comparing the shapes of two individual ROC curves, such as the total area under the curve (AUC) and the sample Pearson correlation coefficient, were found to be useful tools in validating the predicted results of the trade space regression models. And lastly, some simple rules of thumb relating to multi-aperture system design were identified from the inspection of various points of equivalency between competing system designs, as determined from the comparison metrics employed. The goal of this work, the development of a process for simulating multi-aperture imaging systems and comparing them in terms of target detection tasks, was successfully accomplished. The process presented here could be tailored to the needs of any specific multi-aperture development effort and used as a tool for system design engineers

Towards Real-Time Hyperspectral Multi-Image Super-Resolution Reconstruction Applied to Histological Samples

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Interference measurements of non-Abelian e/4 & Abelian e/2 quasiparticle braiding

The quantum Hall states at filling factors $\nu=5/2$ and $7/2$ are expected to have Abelian charge $e/2$ quasiparticles and non-Abelian charge $e/4$ quasiparticles. For the first time we report experimental evidence for the non-Abelian nature of excitations at $\nu=7/2$ and examine the fermion parity, a topological quantum number of an even number of non-Abelian quasiparticles, by measuring resistance oscillations as a function of magnetic field in Fabry-P\'erot interferometers using new high purity heterostructures. The phase of observed $e/4$ oscillations is reproducible and stable over long times (hours) near $\nu=5/2$ and $7/2$, indicating stability of the fermion parity. When phase fluctuations are observed, they are predominantly $\pi$ phase flips, consistent with fermion parity change. We also examine lower-frequency oscillations attributable to Abelian interference processes in both states. Taken together, these results constitute new evidence for the non-Abelian nature of $e/4$ quasiparticles; the observed life-time of their combined fermion parity further strengthens the case for their utility for topological quantum computation.Comment: A significantly revised version; 54 double-column pages containing 14 pages of main text + Supplementary Materials. The figures, which include a number of new figures, are now incorporated into the tex

Expanding Dimensionality in Cinema Color: Impacting Observer Metamerism through Multiprimary Display

Television and cinema display are both trending towards greater ranges and saturation of reproduced colors made possible by near-monochromatic RGB illumination technologies. Through current broadcast and digital cinema standards work, system designs employing laser light sources, narrow-band LED, quantum dots and others are being actively endorsed in promotion of Wide Color Gamut (WCG). Despite artistic benefits brought to creative content producers, spectrally selective excitations of naturally different human color response functions exacerbate variability of observer experience. An exaggerated variation in color-sensing is explicitly counter to the exhaustive controls and calibrations employed in modern motion picture pipelines. Further, singular standard observer summaries of human color vision such as found in the CIE’s 1931 and 1964 color matching functions and used extensively in motion picture color management are deficient in recognizing expected human vision variability. Many researchers have confirmed the magnitude of observer metamerism in color matching in both uniform colors and imagery but few have shown explicit color management with an aim of minimized difference in observer perception variability. This research shows that not only can observer metamerism influences be quantitatively predicted and confirmed psychophysically but that intentionally engineered multiprimary displays employing more than three primaries can offer increased color gamut with drastically improved consistency of experience. To this end, a seven-channel prototype display has been constructed based on observer metamerism models and color difference indices derived from the latest color vision demographic research. This display has been further proven in forced-choice paired comparison tests to deliver superior color matching to reference stimuli versus both contemporary standard RGB cinema projection and recently ratified standard laser projection across a large population of color-normal observers

Incorporating Multiresolution Analysis With Multiclassifiers And Decision Fusion For Hyperspectral Remote Sensing

The ongoing development and increased affordability of hyperspectral sensors are increasing their utilization in a variety of applications, such as agricultural monitoring and decision making. Hyperspectral Automated Target Recognition (ATR) systems typically rely heavily on dimensionality reduction methods, and particularly intelligent reduction methods referred to as feature extraction techniques. This dissertation reports on the development, implementation, and testing of new hyperspectral analysis techniques for ATR systems, including their use in agricultural applications where ground truthed observations available for training the ATR system are typically very limited. This dissertation reports the design of effective methods for grouping and down-selecting Discrete Wavelet Transform (DWT) coefficients and the design of automated Wavelet Packet Decomposition (WPD) filter tree pruning methods for use within the framework of a Multiclassifiers and Decision Fusion (MCDF) ATR system. The efficacy of the DWT MCDF and WPD MCDF systems are compared to existing ATR methods commonly used in hyperspectral remote sensing applications. The newly developed methods’ sensitivity to operating conditions, such as mother wavelet selection, decomposition level, and quantity and quality of available training data are also investigated. The newly developed ATR systems are applied to the problem of hyperspectral remote sensing of agricultural food crop contaminations either by airborne chemical application, specifically Glufosinate herbicide at varying concentrations applied to corn crops, or by biological infestation, specifically soybean rust disease in soybean crops. The DWT MCDF and WPD MCDF methods significantly outperform conventional hyperspectral ATR methods. For example, when detecting and classifying varying levels of soybean rust infestation, stepwise linear discriminant analysis, results in accuracies of approximately 30%-40%, but WPD MCDF methods result in accuracies of approximately 70%-80%

Incorporating Multiresolution Analysis With Multiclassifiers And Decision Fusion For Hyperspectral Remote Sensing

The ongoing development and increased affordability of hyperspectral sensors are increasing their utilization in a variety of applications, such as agricultural monitoring and decision making. Hyperspectral Automated Target Recognition (ATR) systems typically rely heavily on dimensionality reduction methods, and particularly intelligent reduction methods referred to as feature extraction techniques. This dissertation reports on the development, implementation, and testing of new hyperspectral analysis techniques for ATR systems, including their use in agricultural applications where ground truthed observations available for training the ATR system are typically very limited. This dissertation reports the design of effective methods for grouping and down-selecting Discrete Wavelet Transform (DWT) coefficients and the design of automated Wavelet Packet Decomposition (WPD) filter tree pruning methods for use within the framework of a Multiclassifiers and Decision Fusion (MCDF) ATR system. The efficacy of the DWT MCDF and WPD MCDF systems are compared to existing ATR methods commonly used in hyperspectral remote sensing applications. The newly developed methods’ sensitivity to operating conditions, such as mother wavelet selection, decomposition level, and quantity and quality of available training data are also investigated. The newly developed ATR systems are applied to the problem of hyperspectral remote sensing of agricultural food crop contaminations either by airborne chemical application, specifically Glufosinate herbicide at varying concentrations applied to corn crops, or by biological infestation, specifically soybean rust disease in soybean crops. The DWT MCDF and WPD MCDF methods significantly outperform conventional hyperspectral ATR methods. For example, when detecting and classifying varying levels of soybean rust infestation, stepwise linear discriminant analysis, results in accuracies of approximately 30%-40%, but WPD MCDF methods result in accuracies of approximately 70%-80%

Multi-Classifiers And Decision Fusion For Robust Statistical Pattern Recognition With Applications To Hyperspectral Classification

In this dissertation, a multi-classifier, decision fusion framework is proposed for robust classification of high dimensional data in small-sample-size conditions. Such datasets present two key challenges. (1) The high dimensional feature spaces compromise the classifiers’ generalization ability in that the classifier tends to overit decision boundaries to the training data. This phenomenon is commonly known as the Hughes phenomenon in the pattern classification community. (2) The small-sample-size of the training data results in ill-conditioned estimates of its statistics. Most classifiers rely on accurate estimation of these statistics for modeling training data and labeling test data, and hence ill-conditioned statistical estimates result in poorer classification performance. This dissertation tests the efficacy of the proposed algorithms to classify primarily remotely sensed hyperspectral data and secondarily diagnostic digital mammograms, since these applications naturally result in very high dimensional feature spaces and often do not have sufficiently large training datasets to support the dimensionality of the feature space. Conventional approaches, such as Stepwise LDA (S-LDA) are sub-optimal, in that they utilize a small subset of the rich spectral information provided by hyperspectral data for classification. In contrast, the approach proposed in this dissertation utilizes the entire high dimensional feature space for classification by identifying a suitable partition of this space, employing a bank-of-classifiers to perform “local” classification over this partition, and then merging these local decisions using an appropriate decision fusion mechanism. Adaptive classifier weight assignment and nonlinear pre-processing (in kernel induced spaces) are also proposed within this framework to improve its robustness over a wide range of fidelity conditions. Experimental results demonstrate that the proposed framework results in significant improvements in classification accuracies (as high as a 12% increase) over conventional approaches