As the demand of indoor Location-Based Services (LBSs) increases, there is a growing interest in developing an accurate indoor positioning and tracking system on mobile devices. The core location determination problem can be reformulated as a sparse natured problem and thus can be solved by applying the Compressive Sensing (CS) theory. This thesis proposes a compact received signal strength (RSS) based real-time indoor positioning and tracking systems using CS theory that can be implemented on personal digital assistants (PDAs) and smartphones, which are both limited in processing power and memory compared to laptops. The proposed tracking system, together with a simple navigation module is implemented on Windows Mobile-operated smart devices and their performance in different experimental sites are evaluated. Experimental results show that the proposed system is a lightweight real-time algorithm that performs better than other traditional fingerprinting methods in terms of accuracy under constraints of limited processing and memory resources.

Gesture Recognition provides an efficient human-computer interaction for interactive and intelligent computing. In this work, we address the problem of gesture recognition using the theory of random projection and by formulating the recognition problem as an $\ell_1$-minimization problem. The gesture recognition uses a single 3-axis accelerometer for data acquisition and comprises two main stages: a training stage and a testing stage. For training, the system employs dynamic time warping as well as affinity propagation to create exemplars for each gesture while for testing, the system projects all candidate traces and also the unknown trace onto the same lower dimensional subspace for recognition. A dictionary of 18 gestures is defined and a database of over 3,700 traces is created from 7 subjects on which the system is tested and evaluated. Simulation results reveal a superior performance, in terms of accuracy and computational complexity, compared to other systems in the literature.

Gesture Recognition provides an efficient human-computer interaction for interactive and intelligent computing. In this work, we address the problem of gesture recognition using the theory of random projection and by formulating the recognition problem as an $\ell_1$-minimization problem. The gesture recognition uses a single 3-axis accelerometer for data acquisition and comprises two main stages: a training stage and a testing stage. For training, the system employs dynamic time warping as well as affinity propagation to create exemplars for each gesture while for testing, the system projects all candidate traces and also the unknown trace onto the same lower dimensional subspace for recognition. A dictionary of 18 gestures is defined and a database of over 3,700 traces is created from 7 subjects on which the system is tested and evaluated. Simulation results reveal a superior performance, in terms of accuracy and computational complexity, compared to other systems in the literature.

As the demand of indoor Location-Based Services (LBSs) increases, there is a growing interest in developing an accurate indoor positioning and tracking system on mobile devices. The core location determination problem can be reformulated as a sparse natured problem and thus can be solved by applying the Compressive Sensing (CS) theory. This thesis proposes a compact received signal strength (RSS) based real-time indoor positioning and tracking systems using CS theory that can be implemented on personal digital assistants (PDAs) and smartphones, which are both limited in processing power and memory compared to laptops. The proposed tracking system, together with a simple navigation module is implemented on Windows Mobile-operated smart devices and their performance in different experimental sites are evaluated. Experimental results show that the proposed system is a lightweight real-time algorithm that performs better than other traditional fingerprinting methods in terms of accuracy under constraints of limited processing and memory resources.

A Cyber-Physical System integrates computations and dynamics of physical processes. It is an engineering discipline focused on technology with a strong foundation in mathematical abstractions. It shares many of these abstractions with engineering and computer science, but still requires adaptation to suit the dynamics of the physical world. In such a dynamic system, mobility management is one of the key issues against developing a new service. For example, in the study of a new mobile network, it is necessary to simulate and evaluate a protocol before deployment in the system. Mobility models characterize mobile agent movement patterns. On the other hand, they describe the conditions of the mobile services. The focus of this thesis is on mobility modeling in cyber-physical systems. A macroscopic model that captures the mobility of individuals (people and vehicles) can facilitate an unlimited number of applications. One fundamental and obvious example is traffic profiling. Mobility in most systems is a dynamic process and small non-linearities can lead to substantial errors in the model. Extensive research activities on statistical inference and filtering methods for data modeling in cyber-physical systems exist. In this thesis, several methods are employed for multimodal data fusion, localization and traffic modeling. A novel energy-aware sparse signal processing method is presented to process massive sensory data. At baseline, this research examines the application of statistical filters for mobility modeling and assessing the difficulties faced in fusing massive multi-modal sensory data. A statistical framework is developed to apply proposed methods on available measurements in cyber-physical systems. The proposed methods have employed various statistical filtering schemes (i.e., compressive sensing, particle filtering and kernel-based optimization) and applied them to multimodal data sets, acquired from intelligent transportation systems, wireless local area networks, cellular networks and air quality monitoring systems. Experimental results show the capability of these proposed methods in processing multimodal sensory data. It provides a macroscopic mobility model of mobile agents in an energy efficient way using inconsistent measurements.

Group sparsity reveals underlying sparsity patterns and contains rich structural information in data. Hence, exploiting group sparsity will facilitate more efficient techniques for recovering large and complicated data in applications such as compressive sensing, statistics, signal and image processing, machine learning and computer vision. This thesis develops efficient algorithms for solving a class of optimization problems with group sparse solutions, where arbitrary group configurations are allowed and the mixed L21-regularization is used to promote group sparsity. Such optimization problems can be quite challenging to solve due to the mixed-norm structure and possible grouping irregularities. We derive algorithms based on a variable splitting strategy and the alternating direction methodology. Extensive numerical results are presented to demonstrate the efficiency, stability and robustness of these algorithms, in comparison with the previously known state-of-the-art algorithms. We also extend the existing global convergence theory to allow more generality.

Digital image acquisition can be a time consuming process for situations where high spatial resolution is required. As such, optimizing the acquisition mechanism is of high importance for many measurement applications. Acquiring such data through a dynamically small subset of measurement locations can address this problem. In such a case, the measured information can be regarded as incomplete, which necessitates the application of special reconstruction tools to recover the original data set. The reconstruction can be performed based on the concept of sparse signal representation. Recovering signals and images from their sub-Nyquist measurements forms the core idea of compressive sensing (CS). In this work, a CS-based data-guided statistical sparse measurements method is presented, implemented and evaluated. This method significantly improves image reconstruction from sparse measurements. In the data-guided statistical sparse measurements approach, signal sampling distribution is optimized for improving image reconstruction performance. The sampling distribution is based on underlying data rather than the commonly used uniform random distribution. The optimal sampling pattern probability is accomplished by learning process through two methods - direct and indirect. The direct method is implemented for learning a nonparametric probability density function directly from the dataset. The indirect learning method is implemented for cases where a mapping between extracted features and the probability density function is required. The unified model is implemented for different representation domains, including frequency domain and spatial domain. Experiments were performed for multiple applications such as optical coherence tomography, bridge structure vibration, robotic vision, 3D laser range measurements and fluorescence microscopy. Results show that the data-guided statistical sparse measurements method significantly outperforms the conventional CS reconstruction performance. Data-guided statistical sparse measurements method achieves much higher reconstruction signal-to-noise ratio for the same compression rate as the conventional CS. Alternatively, Data-guided statistical sparse measurements method achieves similar reconstruction signal-to-noise ratio as the conventional CS with significantly fewer samples.

The compressive sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by exploiting inherent structure in natural and man-made signals. It has been demonstrated that structured signals can be acquired with just a small number of linear measurements, on the order of the signal complexity. In practice, this enables lower sampling rates that can be more easily achieved by current hardware designs. The primary bottleneck that limits ADC sampling rates is quantization, i.e., higher bit-depths impose lower sampling rates. Thus, the decreased sampling rates of CS ADCs accommodate the otherwise limiting quantizer of conventional ADCs. In this thesis, we consider a different approach to CS ADC by shifting towards lower quantizer bit-depths rather than lower sampling rates. We explore the extreme case where each measurement is quantized to just one bit, representing its sign. We develop a new theoretical framework to analyze this extreme case and develop new algorithms for signal reconstruction from such coarsely quantized measurements. The 1-bit CS framework leads us to scenarios where it may be more appropriate to reduce bit-depth instead of sampling rate. We find that there exist two distinct regimes of operation that correspond to high/low signal-to-noise ratio (SNR). In the measurement compression (MC) regime, a high SNR favors acquiring fewer measurements with more bits per measurement (as in conventional CS); in the quantization compression (QC) regime, a low SNR favors acquiring more measurements with fewer bits per measurement (as in this thesis). A surprise from our analysis and experiments is that in many practical applications it is better to operate in the QC regime, even acquiring as few as 1 bit per measurement. The above philosophy extends further to practical CS ADC system designs. We propose two new CS architectures, one of which takes advantage of the fact that the sampling and quantization operations are performed by two different hardware components. The former can be employed at high rates with minimal costs while the latter cannot. Thus, we develop a system that discretizes in time, performs CS preconditioning techniques, and then quantizes at a low rate.

Compressive sensing (CS) is a novel imaging technology based on the inherent redundancy of natural scenes. The minimum number of required measurements which defines the maximum image compression rate is lower-bounded by the sparsity of the image but is dependent on the type of acquisition patterns employed. Increased measurements by the Rice single pixel camera (SPC) slows down the acquisition process, which may cause the image recovery to be more susceptible to background noise and thus limit CS's application in imaging, detection, or classifying moving targets. In this study, two methods (hybrid-subspace sparse sampling (HSS) for imaging and secant projection on a manifold for classification are applied to solving this problem. For the HSS method, new image pattern are designed via robust principle component analysis (rPCA) on prior knowledge from a library of images to sense a common structure. After measuring coarse scale commonalities, the residual image becomes sparser, and then fewer measurements are needed. For the secant projection case, patterns that can preserve the pairwise distance between data points based on manifold learning are designed via semi-definite programming. These secant patterns turn out to be better in object classification over those learned from PCA. Both methods considerably decrease the number of required measurements for each task when compared with the purely random patterns of a more universal CS imaging system.

Cooperative communication has been shown that it is an effective way to combat the outage caused by channel fading; that is, it provides the spatial diversity for communication. Except for amplify-and-forward (AF) and decode-and-forward (DF), compressed-and-forward (CF) is also an efficient forwarding strategy. In this thesis, we proposed a new CF scheme. In the existing CF protocol, the relay will switch to the DF mode when the source transmitted signal can be recovered by the relay completely; no further compression is made in this scheme. In our proposed, the relay will estimate if the codeword in a block is succeeded decoded, choose the corresponding forwarding methods with LDPC coding; those are based on joint source-channel coding or compressive sensing. At the decode side, a joint decoder with side information that performs sum-product algorithm (SPA) to decode the source message. Simulation results show that the proposed CF scheme can acquire the spatial diversity and outperform AF and DF schemes.