Imaging systems play an important role in many diverse applications. Requirements for these applications, however, can lead to complex or sub-optimal designs. Traditionally, imaging systems are designed to yield a visually pleasing representation, or "pretty picture", of the scene or object. Often this is because a human operator is viewing the acquired image to perform a specific task. With digital computers increasingly being used for automation, a large number of algorithms have been designed to accept as input a pretty picture. This isomorphic representation however is neither necessary nor optimal for tasks such as data compression, transmission, pattern recognition or classification. This disconnect between optical measurement and post processing for the final system outcome has motivated an interest in computational imaging (CI). In a CI system the optical sub-system and post-processing sub-system is jointly designed to optimize system performance for a specific task. In these hybrid imagers, the measured image may no longer be a pretty picture but rather an intermediate non-traditional measurement. In this work, applications of non-traditional measurements are considered for computational imaging. Two systems for an image reconstruction task are studied and one system for a detection task is investigated. First, a CI system to extend the field of view is analyzed and an experimental prototype demonstrated. This prototype validates the simulation study and is designed to yield a 3x field of view improvement relative to a conventional imager. Second, a CI system to acquire time-varying natural scenes, i.e. video, is developed. A candidate system using 8x8x16 spatiotemporal blocks yields about 292x compression compared to a conventional imager. Candidate electro-optical architectures, including charge-domain processing, to implement this approach are also discussed. Lastly, a CI system with x-ray pencil beam illumination is investigated for a detection task where system performance is quantified using an information-theoretic metric.

Three problems in compressive sensing, namely, recovery of sparse signals from noise-free measurements, recovery of sparse signals from noisy measurements, and recovery of so called block-sparse signals from noisy measurements, are investigated. In Chapter 2, the reconstruction of sparse signals from noise-free measurements is investigated and three algorithms are developed. The first and second algorithms minimize the approximate L0 and Lp pseudonorms, respectively, in the null space of the measurement matrix using a sequential quasi-Newton algorithm. An efficient line search based on Banach's fixed-point theorem is developed and applied in the second algorithm. The third algorithm minimizes the approximate Lp pseudonorm in the null space by using a sequential conjugate-gradient (CG) algorithm. Simulation results are presented which demonstrate that the proposed algorithms yield improved signal reconstruction performance relative to that of the iterative reweighted (IR), smoothed L0 (SL0), and L1-minimization based algorithms. They also require a reduced amount of computations relative to the IR and L1-minimization based algorithms. The Lp-minimization based algorithms require less computation than the SL0 algorithm. In Chapter 3, the reconstruction of sparse signals and images from noisy measurements is investigated. First, two algorithms for the reconstruction of signals are developed by minimizing an Lp-pseudonorm regularized squared error as the objective function using the sequential optimization procedure developed in Chapter 2. The first algorithm minimizes the objective function by taking steps along descent directions that are computed in the null space of the measurement matrix and its complement space. The second algorithm minimizes the objective function in the time domain by using a CG algorithm. Second, the well known total variation (TV) norm has been extended to a nonconvex version called the TVp pseudonorm and an algorithm for the reconstruction of images is developed that involves minimizing a TVp-pseudonorm regularized squared error using a sequential Fletcher-Reeves' CG algorithm. Simulation results are presented which demonstrate that the first two algorithms yield improved signal reconstruction performance relative to the IR, SL0, and L1-minimization based algorithms and require a reduced amount of computation relative to the IR and L1-minimization based algorithms. The TVp-minimization based algorithm yields improved image reconstruction performance and a reduced amount of computation relative to Romberg's algorithm. In Chapter 4, the reconstruction of so-called block-sparse signals is investigated. The L2/1 norm is extended to a nonconvex version, called the L2/p pseudonorm, and an algorithm based on the minimization of an L2/p-pseudonorm regularized squared error is developed. The minimization is carried out using a sequential Fletcher-Reeves' CG algorithm and the line search described in Chapter 2. A reweighting technique for the reduction of amount of computation and a method to use prior information about the locations of nonzero blocks for the improvement in signal reconstruction performance are also proposed. Simulation results are presented which demonstrate that the proposed algorithm yields improved reconstruction performance and requires a reduced amount of computation relative to the L2/1-minimization based, block orthogonal matching pursuit, IR, and L1-minimization based algorithms. / Graduate

ITC/USA 2011 Conference Proceedings / The Forty-Seventh Annual International Telemetering Conference and Technical Exhibition / October 24-27, 2011 / Bally's Las Vegas, Las Vegas, Nevada / In this paper we study a new streaming Compressive Sensing (CS) technique that aims to replace high speed Analog to Digital Converters (ADC) for certain classes of signals and reduce the artifacts that arise from block processing when conventional CS is applied to continuous signals. We compare the performance of both streaming and block processing methods on several types of signals and quantify the signal reconstruction quality when packet loss is applied to the transmitted sampled data.

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.

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.

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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

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.