The field of compressive sensing deals with the recovery of a sparse signal from a small set of measurements or linear projections of the signal. In this thesis, we introduce a stochastic framework that allows a collection of correlated sparse signals to be recovered by exploiting both intra and inter signal correlation. Our approach differs from others by not assuming that the collection of sparse signals have a common support or a common component; in some cases, this assumption does not hold true. Imagine a simplified cognitive radio problem, where users can send a single tone (sine-wave) in a finite number of frequencies; it is desired to find the used frequencies over a large area (creation of a radio map). This is a sparse problem; however, as we move spatially, the occuppied frequencies change, thus voiding the assumption of a common support/component. Our solution to multi sparse signal recovery addresses this problem, where signals that are close geographically are highly correlated and their support gradually changes as the distance between signals grow. Our approach consists of the creation of a probabilistic model that accounts for inter and intra signal correlation and then using belief propagation to calculate the posterior distribution of the signals and perform recovery.

ITC/USA 2013 Conference Proceedings / The Forty-Ninth Annual International Telemetering Conference and Technical Exhibition / October 21-24, 2013 / Bally's Hotel & Convention Center, Las Vegas, NV / Compressive Sensing (CS) is a set of techniques that can faithfully acquire a signal from sub- Nyquist measurements, provided the class of signals have certain broadly-applicable properties. Reconstruction (or exploitation) of the signal from these sub-Nyquist measurements requires a forward model - knowledge of how the system maps signals to measurements. In high-dimensional CS systems, determination of this forward model via direct measurement of the system response to the complete set of impulse functions is impractical. In this paper, we will discuss the development of a parameterized forward model for the Adaptive, Feature-Specific Spectral Imaging Classifier (AFSSI-C), an experimental compressive spectral image classifier. This parameterized forward model drastically reduces the number of calibration measurements.

User/relay selection is a simple technique that achieves spatial diversity in multiuser networks. However, for user/relay selection algorithms to make a selection decision, channel state information (CSI) from all cooperating users/relays is usually required at a central node. This requirement poses two important challenges. Firstly, CSI acquisition generates a great deal of feedback overhead (air-time) that could result in significant transmission delays. Secondly, the fed-back channel information is usually corrupted by additive noise. This could lead to transmission outages if the central node selects the set of cooperating relays based on inaccurate feedback information. Motivated by the aforementioned challenges, we propose a limited feedback user/relay selection scheme that is based on the theory of compressed sensing. Firstly, we introduce a limited feedback relay selection algorithm for a multicast relay network. The proposed algorithm exploits the theory of compressive sensing to first obtain the identity of the “strong” relays with limited feedback air-time. Following that, the CSI of the selected relays is estimated using minimum mean square error estimation without any additional feedback. To minimize the effect of noise on the fed-back CSI, we introduce a back-off strategy that optimally backs-off on the noisy received CSI. In the second part of the thesis, we propose a feedback reduction scheme for full-duplex relay-aided multiuser networks. The proposed scheme permits the base station (BS) to obtain channel state information (CSI) from a subset of strong users under substantially reduced feedback overhead. More specifically, we cast the problem of user identification and CSI estimation as a block sparse signal recovery problem in compressive sensing (CS). Using existing CS block recovery algorithms, we first obtain the identity of the strong users and then estimate their CSI using the best linear unbiased estimator (BLUE). Moreover, we derive the error covariance matrix of the post-detection noise to be used in the back-off strategy. In addition to this, we provide exact closed form expressions for the average maximum equivalent SNR at the destination user. The last part of the thesis treats the problem of user selection in a network MIMO setting. We propose a distributed user selection strategy that is based on a well known technique called semi-orthogonal user selection when the zero-forcing beamforming (ZFBF) is adopted. Usually this technique requires perfect channel state information at the transmitter (CSIT) which might not be available or need large feedback overhead. Instead, we propose a distributed user selection technique where no communication between base stations is needed. In order to reduce the feedback overhead, each user set a timer that is inversely proportional to his channel quality indicator (CQI). This technique will allow only the user with the highest CQI to feedback provided that the transmission time is shorter than the difference between his timer and the second strongest user timer, otherwise a collision will occur. In the case of collision, we propose another feedback strategy that is based on the theory of compressive sensing, where collision is allowed and each user encode its feedback using Gaussian codewords and feedback the combination at the same time with other users. We prove that the problem can be formulated as a block sparse recovery problem and that this approach is agnostic on the transmission time, thus it could be a good alternative to the timer approach when collision is dominant. Simulation results show that the proposed CS-based selection algorithms yield a rate performance that is close to the ones achieved when perfect CSI is available while consuming a small amount of feedback.

Cementitious materials obtained from different sources, while evaluated and classified by the same methods and criteria, often produce concrete with compressive strength variance despite other inputs remaining constant. The focus of this thesis was to enumerate and illustrate the possible compressive strength variation when cementitious material sources are interchanged, and investigate the influence that aggregate can have on this variation. This was accomplished by compiling and analyzing compressive strength data from previous research initiatives, and concluded that coefficient of variation (COV) and range values at the 14-, 28-, and 56-day timeframes due to a cement source change varied between 15.3% and 18.1% and 1,988 psi and 2,728 psi in concrete, and 16.1% and 22.9% and 3,406 psi and 5,884 psi in paste or mortar. Concrete that included supplementary cementitious material (SCM) displayed up to 4.1% higher COV values versus non-SCM mixtures, and specific aggregate/cementitious material combinations influenced compressive strength variability.

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Recent research has shown that compressible signals can be recovered from a very limited number of measurements by minimizing nonconvex functions that closely resemble the L0-norm function. These functions have sparse minimizers and, therefore, are called sparsity-promoting functions (SPFs). Recovery is achieved by solving a nonconvex optimization problem when using these SPFs. Contemporary methods for the solution of such difficult problems are inefficient and not supported by robust convergence theorems. New signal-recovery methods for compressive sensing that can be used to solve nonconvex problems efficiently are proposed. Two categories of methods are considered, namely, sequential convex formulation (SCF) and proximal-point (PP) based methods. In SCF methods, quadratic or piecewise-linear approximations of the SPF are employed. Recovery is achieved by solving a sequence of convex optimization problems efficiently with state-of-the-art solvers. Convex problems are formulated as regularized least-squares, second-order cone programming, and weighted L1-norm minimization problems. In PP based methods, SPFs that entail rich optimization properties are employed. Recovery is achieved by iteratively performing two fundamental operations, namely, computation of the PP of the SPF and projection of the PP onto a convex set. The first operation is performed analytically or numerically by using a fast iterative method. The second operation is performed efficiently by computing a sequence of closed-form projectors. The proposed methods have been compared with the leading state-of-the-art signal-recovery methods, namely, the gradient-projection method of Figueiredo, Nowak, and Wright, the L1-LS method of Kim, Koh, Lustig, Boyd, and Gorinevsky, the L1-Magic method of Candes and Romberg, the spectral projected-gradient L1-norm method of Berg and Friedlander, the iteratively reweighted least squares method of Chartrand and Yin, the difference-of-two-convex-functions method of Gasso, Rakotomamonjy, and Canu, and the NESTA method of Becker, Bobin, and Candes. The comparisons concerned the capability of the proposed and competing algorithms in recovering signals in a wide range of test problems and also the computational efficiency of the various algorithms. Simulation results demonstrate that improved reconstruction performance, measurement consistency, and comparable computational cost are achieved with the proposed methods relative to the competing methods. The proposed methods are robust, are supported by known convergence theorems, and lead to fast convergence. They are, as a consequence, particularly suitable for the solution of hard recovery problems of large size that entail large dynamic range and, are, in effect, strong candidates for use in many real-world applications. / Graduate / 0544 / eng.flavio.teixeira@gmail.com

Computational imaging and sensing leverages the joint-design of optics, detectors and processing to overcome the performance bottlenecks inherent to the traditional imaging paradigm. This novel imaging and sensing design paradigm essentially allows new trade-offs between the optics, detector and processing components of an imaging system and enables broader operational regimes beyond the reach of conventional imaging architectures, which are constrained by well-known Rayleigh, Strehl and Nyquist rules amongst others. In this dissertation, we focus on scalability aspects of these novel computational imaging architectures, their design and implementation, which have far-reaching impacts on the potential and feasibility of realizing task-specific performance gains relative to traditional imager designs. For the extended depth of field (EDoF) computational imager design, which employs a customized phase mask to achieve defocus immunity, we propose a joint-optimization framework to simultaneously optimize the parameters of the optical phase mask and the processing algorithm, with the system design goal of minimizing the noise and artifacts in the final processed image. Using an experimental prototype, we demonstrate that our optimized system design achieves higher fidelity output compared to other static designs from the literature, such as the Cubic and Trefoil phase masks. While traditional imagers rely on an isomorphic mapping between the scene and the optical measurements to form images, they do not exploit the inherent compressibility of natural images and thus are subject to Nyquist sampling. Compressive sensing exploits the inherent redundancy of natural images, basis of image compression algorithms like JPEG/JPEG2000, to make linear projection measurements with far fewer samples than Nyquist for the image forming task. Here, we present a block wise compressive imaging architecture which is scalable to high space-bandwidth products (i.e. large FOV and high resolution applications) and employs a parallelizable and non-iterative piecewise linear reconstruction algorithm capable of operating in real-time. Our compressive imager based on this scalable architecture design is not limited to the imaging task and can also be used for automatic target recognition (ATR) without an intermediate image reconstruction. To maximize the detection and classification performance of this compressive ATR sensor, we have developed a scalable statistical model of natural scenes, which enables the optimization of the compressive sensor projections with the Cauchy-Schwarz mutual information metric. We demonstrate the superior performance of this compressive ATR system using simulation and experiment. Finally, we investigate the fundamental resolution limit of imaging via the canonical incoherent quasi-monochromatic two point-sources separation problem. We extend recent results in the literature demonstrating, with Fisher information and estimator mean square error analysis, that a passive optical mode-sorting architecture with only two measurements can outperform traditional intensity-based imagers employing an ideal focal plane array in the sub-Rayleigh range, thus overcoming the Rayleigh resolution limit.

Thesis advisor: Willie J. Padilla / This thesis will describe the implementation of novel imaging applications with electromagnetic metamaterials. Metamaterials have proven to be host to a multitude of interesting physical phenomena and give rich insight electromagnetic theory. This thesis will explore not only the physical theory that give them their interesting electromagnetic properties, but also the many applications of metamaterials. There is a strong need for efficient, low cost imaging solutions, specifically in the longer wavelength regime. While this technology has often been at a standstill due to the lack of natural materials that can effectively operate at these wavelengths, metamaterials have revolutionized the creation of devices to fit these needs. Their scalability has allowed them to access regimes of the electromagnetic spectrum previously unobtainable with natural materials. Along with metamaterials, mathematical techniques can be utilized to make these imaging systems streamlined and effective. Chapter 1 gives a background not only to metamaterials, but also details several parts of general electromagnetic theory that are important for the understanding of metamaterial theory. Chapter 2 discusses one of the most ubiquitous types of metamaterials, the metamaterial absorber, examining not only its physical mechanism, but also its role in metamaterial devices. Chapter 3 gives a theoretical background of imaging at longer wavelengths, specifically single pixel imaging. Chapter 3 also discusses the theory of Compressive Sensing, a mathematical construct that has allowed sampling rates that can exceed the Nyquist Limit. Chapter 4 discusses work that utilizes photoexcitation of a semiconductor to modulate THz radiation. These physical methods were used to create a dynamic THz spatial light modulator and implemented in a single pixel imaging system in the THz regime. Chapter 5 examines active metamaterial modulation through depletion of carriers in a doped semiconductor via application of a bias voltage and its implementation into a similar single pixel imaging system. Additionally, novel techniques are used to access masks generally unobtainable by traditional single pixel imagers. Chapter 6 discusses a completely novel way to encode spatial masks in frequency, rather than time, to create a completely passive millimeter wave imager. Chapter 7 details the use of telecommunication techniques in a novel way to reduce image acquisition time and further streamline the THz single pixel imager. Finally, Chapter 8 will discuss some future outlooks and draw some conclusions from the work that has been done. / Thesis (PhD) — Boston College, 2015. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

Magnetic Resonance Imaging (MRI) is an essential instrument in clinical diag- nosis; however, it is burdened by a slow data acquisition process due to physical limitations. Compressive Sensing (CS) is a recently developed mathematical framework that o ers signi cant bene ts in MRI image speed by reducing the amount of acquired data without degrading the image quality. The process of image reconstruction involves solving a nonlinear constrained optimization problem. The reduction of reconstruction time in MRI is of signi cant bene t. We reformulate sparse MRI reconstruction as a Second Order Cone Program (SOCP).We also explore two alternative techniques to solving the SOCP prob- lem directly: NESTA and speci cally designed SOCP-LB. / UOIT

Composite materials have been more and more used in aircraft primary structures such as wing and fuselage. The aim of this thesis is to identify an effective way to optimize composite wing structure, especially the stiffened skin panels for minimum weight subject to stiffness and strength constraints. Many design variables (geometrical dimensions, ply angle proportion and stacking sequence) are involved in the optimum design of a composite stiffened panel. Moreover, in order to meet practical design, manufacturability and maintainability requirements should be taken into account as well, which makes the optimum design problem more complicated. In this thesis, the research work consists of three steps: Firstly, attention is paid to metallic stiffened panels. Based on the study of Emero’s optimum design method and buckling analysis, a VB program IPO, which employs closed form equations to obtain buckling load, is developed to facilitate the optimization process. The IPO extends the application of Emero’s method to an optimum solution based on user defined panel dimensional range to satisfy practical design constraints. Secondly, the optimum design of a composite stiffened panel is studied. Based on the research of laminate layup effects on buckling load and case study of bucking analysis methods, a practical laminate database (PLDB) concept is presented, upon which the optimum design procedure is established. By employing the PLDB, laminate equivalent modulus and closed form equations, a VB program CPO is developed to achieve the optimum design of a composite stiffened panel. A multi-level and step-length-adjustable optimization strategy is applied in CPO, which makes the optimization process efficient and effective. Lastly, a composite outer wing box, which is related to the author’s GDP work, is optimized by CPO. Both theoretical and practical optimum solutions are obtained and the results are validated by FE analysis.