Effective modeling of high dimensional data is crucial in information processing and machine learning. Classical subspace methods have been very effective in such applications. However, over the past few decades, there has been considerable research towards the development of new modeling paradigms that go beyond subspace methods. This dissertation focuses on the study of sparse models and their interplay with modern machine learning techniques such as manifold, ensemble and graph-based methods, along with their applications in image analysis and recovery. By considering graph relations between data samples while learning sparse models, graph-embedded codes can be obtained for use in unsupervised, supervised and semi-supervised problems. Using experiments on standard datasets, it is demonstrated that the codes obtained from the proposed methods outperform several baseline algorithms. In order to facilitate sparse learning with large scale data, the paradigm of ensemble sparse coding is proposed, and different strategies for constructing weak base models are developed. Experiments with image recovery and clustering demonstrate that these ensemble models perform better when compared to conventional sparse coding frameworks. When examples from the data manifold are available, manifold constraints can be incorporated with sparse models and two approaches are proposed to combine sparse coding with manifold projection. The improved performance of the proposed techniques in comparison to sparse coding approaches is demonstrated using several image recovery experiments. In addition to these approaches, it might be required in some applications to combine multiple sparse models with different regularizations. In particular, combining an unconstrained sparse model with non-negative sparse coding is important in image analysis, and it poses several algorithmic and theoretical challenges. A convex and an efficient greedy algorithm for recovering combined representations are proposed. Theoretical guarantees on sparsity thresholds for exact recovery using these algorithms are derived and recovery performance is also demonstrated using simulations on synthetic data. Finally, the problem of non-linear compressive sensing, where the measurement process is carried out in feature space obtained using non-linear transformations, is considered. An optimized non-linear measurement system is proposed, and improvements in recovery performance are demonstrated in comparison to using random measurements as well as optimized linear measurements.

Motion capture using cost-effective sensing technology is challenging and the huge success of Microsoft Kinect has been attracting researchers to uncover the potential of using this technology into computer vision applications. In this thesis, an upper-body motion analysis in a home-based system for stroke rehabilitation using novel RGB-D camera - Kinect is presented. We address this problem by first conducting a systematic analysis of the usability of Kinect for motion analysis in stroke rehabilitation. Then a hybrid upper body tracking approach is proposed which combines off-the-shelf skeleton tracking with a novel depth-fused mean shift tracking method. We proposed several kinematic features reliably extracted from the proposed inexpensive and portable motion capture system and classifiers that correlate torso movement to clinical measures of unimpaired and impaired. Experiment results show that the proposed sensing and analysis works reliably on measuring torso movement quality and is promising for end-point tracking. The system is currently being deployed for large-scale evaluations.

In this thesis, quantitative evaluation of quality of movement during stroke rehabilitation will be discussed. Previous research on stroke rehabilitation in hospital has been shown to be effective. In this thesis, we study various issues that arise when creating a home-based system that can be deployed in a patient's home. Limitation of motion capture due to reduced number of sensors leads to problems with design of kinematic features for quantitative evaluation. Also, the hierarchical three-level tasks of rehabilitation requires new design of kinematic features. In this thesis, the design of kinematic features for a home based stroke rehabilitation system will be presented. Results of the most challenging classifier are shown and proves the effectiveness of the design. Comparison between modern classification techniques and low computational cost threshold based classification with same features will also be shown.

Diabetic retinopathy (DR) is a common cause of blindness occurring due to prolonged presence of diabetes. The risk of developing DR or having the disease progress is increasing over time. Despite advances in diabetes care over the years, DR remains a vision-threatening complication and one of the leading causes of blindness among American adults. Recent studies have shown that diagnosis based on digital retinal imaging has potential benefits over traditional face-to-face evaluation. Yet there is a dearth of computer-based systems that can match the level of performance achieved by ophthalmologists. This thesis takes a fresh perspective in developing a computer-based system aimed at improving diagnosis of DR images. These images are categorized into three classes according to their severity level. The proposed approach explores effective methods to classify new images and retrieve clinically-relevant images from a database with prior diagnosis information associated with them. Retrieval provides a novel way to utilize the vast knowledge in the archives of previously-diagnosed DR images and thereby improve a clinician's performance while classification can safely reduce the burden on DR screening programs and possibly achieve higher detection accuracy than human experts. To solve the three-class retrieval and classification problem, the approach uses a multi-class multiple-instance medical image retrieval framework that makes use of spectrally tuned color correlogram and steerable Gaussian filter response features. The results show better retrieval and classification performances than prior-art methods and are also observed to be of clinical and visual relevance.

Recent advances in camera architectures and associated mathematical representations now enable compressive acquisition of images and videos at low data-rates. While most computer vision applications of today are composed of conventional cameras, which collect a large amount redundant data and power hungry embedded systems, which compress the collected data for further processing, compressive cameras offer the advantage of direct acquisition of data in compressed domain and hence readily promise to find applicability in computer vision, particularly in environments hampered by limited communication bandwidths. However, despite the significant progress in theory and methods of compressive sensing, little headway has been made in developing systems for such applications by exploiting the merits of compressive sensing. In such a setting, we consider the problem of activity recognition, which is an important inference problem in many security and surveillance applications. Since all successful activity recognition systems involve detection of human, followed by recognition, a potential fully functioning system motivated by compressive camera would involve the tracking of human, which requires the reconstruction of atleast the initial few frames to detect the human. Once the human is tracked, the recognition part of the system requires only the features to be extracted from the tracked sequences, which can be the reconstructed images or the compressed measurements of such sequences. However, it is desirable in resource constrained environments that these features be extracted from the compressive measurements without reconstruction. Motivated by this, in this thesis, we propose a framework for understanding activities as a non-linear dynamical system, and propose a robust, generalizable feature that can be extracted directly from the compressed measurements without reconstructing the original video frames. The proposed feature is termed recurrence texture and is motivated from recurrence analysis of non-linear dynamical systems. We show that it is possible to obtain discriminative features directly from the compressed stream and show its utility in recognition of activities at very low data rates.

In this thesis, we consider the problem of fast and efficient indexing techniques for time sequences which evolve on manifold-valued spaces. Using manifolds is a convenient way to work with complex features that often do not live in Euclidean spaces. However, computing standard notions of geodesic distance, mean etc. can get very involved due to the underlying non-linearity associated with the space. As a result a complex task such as manifold sequence matching would require very large number of computations making it hard to use in practice. We believe that one can device smart approximation algorithms for several classes of such problems which take into account the geometry of the manifold and maintain the favorable properties of the exact approach. This problem has several applications in areas of human activity discovery and recognition, where several features and representations are naturally studied in a non-Euclidean setting. We propose a novel solution to the problem of indexing manifold-valued sequences by proposing an intrinsic approach to map sequences to a symbolic representation. This is shown to enable the deployment of fast and accurate algorithms for activity recognition, motif discovery, and anomaly detection. Toward this end, we present generalizations of key concepts of piece-wise aggregation and symbolic approximation for the case of non-Euclidean manifolds. Experiments show that one can replace expensive geodesic computations with much faster symbolic computations with little loss of accuracy in activity recognition and discovery applications. The proposed methods are ideally suited for real-time systems and resource constrained scenarios.

Photovoltaics (PV) is an important and rapidly growing area of research. With the advent of power system monitoring and communication technology collectively known as the "smart grid," an opportunity exists to apply signal processing techniques to monitoring and control of PV arrays. In this paper a monitoring system which provides real-time measurements of each PV module's voltage and current is considered. A fault detection algorithm formulated as a clustering problem and addressed using the robust minimum covariance determinant (MCD) estimator is described; its performance on simulated instances of arc and ground faults is evaluated. The algorithm is found to perform well on many types of faults commonly occurring in PV arrays. Among several types of detection algorithms considered, only the MCD shows high performance on both types of faults.

Advancements in computer vision and machine learning have added a new dimension to remote sensing applications with the aid of imagery analysis techniques. Applications such as autonomous navigation and terrain classification which make use of image classification techniques are challenging problems and research is still being carried out to find better solutions. In this thesis, a novel method is proposed which uses image registration techniques to provide better image classification. This method reduces the error rate of classification by performing image registration of the images with the previously obtained images before performing classification. The motivation behind this is the fact that images that are obtained in the same region which need to be classified will not differ significantly in characteristics. Hence, registration will provide an image that matches closer to the previously obtained image, thus providing better classification. To illustrate that the proposed method works, naïve Bayes and iterative closest point (ICP) algorithms are used for the image classification and registration stages respectively. This implementation was tested extensively in simulation using synthetic images and using a real life data set called the Defense Advanced Research Project Agency (DARPA) Learning Applied to Ground Robots (LAGR) dataset. The results show that the ICP algorithm does help in better classification with Naïve Bayes by reducing the error rate by an average of about 10% in the synthetic data and by about 7% on the actual datasets used.