This dissertation develops new techniques employing the Low-rank and Sparse Representation approaches to improve the performance of state-of-the-art algorithms in hyperspectral image analysis. The contributions of this dissertation are outlined as follows. 1) Low-rank and sparse representation approaches, i.e., low-rank representation (LRR) and low-rank subspace representation (LRSR), are proposed for hyperspectral image analysis, including target and anomaly detection, estimation of the number of signal subspaces, supervised and unsupervised classification. 2) In supervised target and unsupervised anomaly detection, the performance can be improved by using the LRR sparse matrix. To further increase detection accuracy, data is partitioned into several highly-correlated groups. Target detection is performed in each group, and the final result is generated from the fusion of the output of each detector. 3) In the estimation of the number of signal subspaces, the LRSR low-rank matrix is used in conjunction with direct rank calculation and soft-thresholding. Compared to the state-of-the-art algorithms, the LRSR approach delivers the most accurate and consistent results across different datasets. 4) In supervised and unsupervised classification, the use of LRR and LRSR low-rank matrices can improve classification accuracy where the improvement of the latter is more significant. The investigation on state-of-the-art classifiers demonstrate that, as a pre-preprocessing step, the LRR and LRSR produce low-rank matrices with fewer outliers or trivial spectral variations, thereby enhancing class separability.

Hyperspectral imagery is often associated with high storage and transmission costs. Dimensionality reduction aims to reduce the time and space complexity of hyperspectral imagery by projecting data into a low-dimensional space such that all the important information in the data is preserved. Dimensionality-reduction methods based on transforms are widely used and give a data-dependent representation that is unfortunately costly to compute. Recently, there has been a growing interest in data-independent representations for dimensionality reduction; of particular prominence are random projections which are attractive due to their computational efficiency and simplicity of implementation. This dissertation concentrates on exploring the realm of computationally fast and efficient random projections by considering projections based on a random Hadamard matrix. These Hadamard-based projections are offered as an alternative to more widely used random projections based on dense Gaussian matrices. Such Hadamard matrices are then coupled with a fast singular value decomposition in order to implement a two-stage dimensionality reduction that marries the computational benefits of the data-independent random projection to the structure-capturing capability of the data-dependent singular value transform. Finally, random projections are applied in conjunction with nonnegative least squares to provide a computationally lightweight methodology for the well-known spectral-unmixing problem. Overall, it is seen that random projections offer a computationally efficient framework for dimensionality reduction that permits hyperspectral-analysis tasks such as unmixing and classification to be conducted in a lower-dimensional space without sacrificing analysis performance while reducing computational costs significantly.

The compressed sensing (CS) model of signal processing, while offering many unique advantages in terms of low-cost sensor design, poses interesting challenges for both signal acquisition and recovery, especially for signals of large size. In this work, we investigate how CS might be applied practically and efficiently in the context of natural video. We make use of a CS video acquisition approach in line with the popular single-pixel camera framework of blind, nonaptive, random sampling while proposing new approaches for the subsequent recovery of the video signal which leverage interrame redundancy to minimize recovery error. We introduce a method of approximation, which we term multihypothesis (MH) frame prediction, to create accurate frame predictions by comparing hypotheses drawn from the spatial domain of chosen reference frames to the non-overlapping, block-by-block CS measurements of subsequent frames. We accomplish this frame prediction via a novel distance-weighted Tikhonov regularization technique. We verify through our experiments that MH frame prediction via distance-weighted regularization provides state-of-the-art performance for the recovery of natural video sequences from blind CS measurements. The distance-weighted regularization we propose need not be limited to just frame prediction for CS video recovery, but may also be used in a variety of contexts where approximations must be generated from a set of hypotheses or training data. To show this, we apply our technique to supervised hyperspectral image (HSI) classification via a novel classifier we term the nearest regularized subspace (NRS) classifier. We show that the distance-weighted regularization used in the NRS method provides greater classification accuracy than state-of-the-art classifiers for supervised HSI classification tasks. We also propose two modifications to the core NRS classifier to improve its robustness to variation of input parameters and and to further increase its classification accuracy.

In this dissertation, the general problem of the dimensionality reduction of hyperspectral imagery is considered. Data dimension can be reduced through compression, in which an original image is encoded into bitstream of greatly reduced size; through application of a transformation, in which a high-dimensional space is mapped into a low-dimensional space; and through a simple process of subsampling, wherein the number of pixels is reduced spatially during image acquisition. All three techniques are investigated in the course of the dissertation. For data compression, an approach to calculate an operational bitrate for JPEG2000 in conjunction with principal component analysis is proposed. It is shown that an optimal bitrate for such a lossy compression method can be estimated while maintaining both class separability as well as anomalous pixels in the original data. On the other hand, the transformation paradigm is studied for spectral dimensionality reduction; specifically, dataindependent random spectral projections are considered, while the compressive projection principal component analysis algorithm is adopted for data reconstruction. It is shown that, by incorporating both spectral and spatial partitioning of the original data, reconstruction accuracy can be improved. Additionally, a new supervised spectral dimensionality reduction approach using a sparsity-preserving graph is developed. The resulting sparse graph-based discriminant analysis is seen to yield superior classification performance at low dimensionality. Finally, for spatial dimensionality reduction, a simple spatial subsampling scheme is considered for a multitemporal hyperspectral image sequence, such that the original image is reconstructed using a sparse dictionary learned from a prior image in the sequence.

Rangeland monitoring is used by land managers for assessing multiple-use management practices on western rangelands. Managers benefit from improved monitoring methods that provide rapid, accurate, cost-effective, and robust measures of rangeland health and ecological trend. In this study, we used a supervised classification image analysis approach to estimate plant cover and bare ground by functional group that can be used to monitor and assess rangeland structure. High-resolution color infrared imagery taken of 40 research plots was acquired with a UltraCam X (UCX) digital camera during summer 2011. Ground estimates of cover were simultaneously collected by the Utah Division of Wildlife Resources' Range Trend Project field crew within these same areas. Image analysis was conducted using supervised classification to determine percent cover from Red, Green, Blue and infrared images. Classification accuracy and mean difference between cover estimates from remote sensed imagery and those obtained from the ground were compared using an accuracy assessment with Kappa statistic and a t-test analysis, respectively. Percent cover estimates from remote sensing ranged from underestimating the surface class (rock, pavement, and bare ground) by 27% to overestimating shrubs by less than 1% when compared to field-based measurements. Overall accuracy of the supervised classification was 91% with a kappa statistic of 0.88. The highest accuracy was observed when classifying surface values (bare ground, rock) which had a user's and producer's accuracy of 92% and 93%, respectively. Although surface cover varied significantly from field-based estimates, plant cover varied only slightly, giving managers an option to assess plant cover effectively and efficiently on greater temporal and spatial extents.

In the past 40 years, floods have become a bane of Mozambique’s inhabitants and economy. The latest of them, caused by the cyclone Idai, has devastated the area resulting in loss of life and property. It was estimated that around 715 000 hectares of farmland was destroyed as a result of the cyclone. The main goal of this thesis was to assess the extent of the flooding and to determine the types of land cover that were affected. This was done in Google Earth Engine, using SAR change detection on Sentinel 1 data to create a mask for the flooded areas, followed by a supervised image classification on Sentinel 2 data to identify the types of land cover that were flooded. Two classifications were done, using imagery from early periods of the country’s plant growing season and later periods of the same season, respectively. The results of both classifications were below standard, with the main problems stemming from difficulties with differentiating between agriculture and roads along with agriculture and vegetation. Multiple ways to improve the results and avoid the errors in future similar projects were discussed, including using multi temporal data and utilizing a road map for the area to create a large amount of training points for the classification. In conclusion, while the results were not as good as was envisioned, the thesis provided ample opportunity to analyze errors and to theorize methods for improving future work.

At Santa Margarita Ranch, California, oak mistletoe (Phoradendron villosum) parasitizes valley oak and blue oak but cannot be found growing on coast live oak despite its abundance and ability to parasitize coast live oak in other areas. It seems as though this species of mistletoe is specializing on certain host oak trees, but the mechanisms of this specialization are unknown. In order to investigate this pattern, we utilized a type of machine learning in GIS called supervised classification as well as a reciprocal transplant study in the field. The three species of oak trees were classified with 87% accuracy using drone imagery and 95% accuracy using open source NAIP imagery. This classification technique could be applied to the whole state of California as long as ground truth points for each species were collected. This could be extremely useful for large scale forest management projects and ecological questions. Unfortunately, the classifier was unsuccessful at distinguishing mistletoe from host and so the number of mistletoe on each host could not be quantified using this technique. The reciprocal transplant study involved collecting mistletoe fruit from individuals growing on each of the three hosts and experimentally applying them back onto all three hosts. This allowed us to test whether there are host races of mistletoe that specialize at growing on certain hosts. We found that seeds from each host origin germinated equally well regardless of where they were dispersed, and seeds survived best on coast live oak, regardless of where they originated from. Based on these results, there must be some mechanism, other than host races, that explains the lack of mistletoe on coast live oaks at Santa Margarita Ranch. Future projects should investigate whether evidence for host races can be found at a later stage of seedling development and the roll of bird dispersers in creating the pattern.

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Class imbalanced datasets constitute a significant portion of the machine learning problems of interest, where recog­nizing the ‘rare class’ is the primary objective for most applications. Traditional linear machine learning algorithms are often not effective in recognizing the rare class. In this research work, a specifically optimized feed-forward artificial neural network (ANN) is proposed and developed to train from moderate to highly imbalanced datasets. The proposed methodology deals with the difficulty in classification task in multiple stages—by optimizing the training dataset, modifying kernel function to generate the gram matrix and optimizing the NN structure. First, the training dataset is extracted from the available sample set through an iterative process of selective under-sampling. Then, the proposed artificial NN comprises of a kernel function optimizer to specifically enhance class boundaries for imbalanced datasets by conformally transforming the kernel functions. Finally, a single hidden layer weighted neural network structure is proposed to train models from the imbalanced dataset. The proposed NN architecture is derived to effectively classify any binary dataset with even very high imbalance ratio with appropriate parameter tuning and sufficient number of processing elements. Effectiveness of the proposed method is tested on accuracy based performance metrics, achieving close to and above 90%, with several imbalanced datasets of generic nature and compared with state of the art methods. The proposed model is also used for classification of a 25GB computed tomographic colonography database to test its applicability for big data. Also the effectiveness of under-sampling, kernel optimization for training of the NN model from the modified kernel gram matrix representing the imbalanced data distribution is analyzed experimentally. Computation time analysis shows the feasibility of the system for practical purposes. This report is concluded with discussion of prospect of the developed model and suggestion for further development works in this direction.