A recent breakthrough in information theory known as compressive sensing is one component of an ongoing revolution in data acquisition and processing that guides one to acquire less data yet still recover the same amount of information as traditional techniques, meaning less resources such as time, detector cost, or power are required. Starting from these basic principles, this thesis explores the application of these techniques to imaging. The first laboratory example we introduce is a simple infrared camera. Then we discuss the application of compressive sensing techniques to hyperspectral microscopy, specifically Raman microscopy, which should prove to be a powerful technique to bring the acquisition time for such microscopies down from hours to minutes. Next we explore a novel sensing architecture that uses partial circulant matrices as sensing matrices, which results in a simplified, more robust imaging system. The results of these imaging experiments lead to questions about the performance and fundamental nature of sparse signal recovery with partial circulant compressive sensing matrices. Thus, we present the results of a suite of numerical experiments that show some surprising and suggestive results that could stimulate further theoretical and applied research of partial circulant compressive sensing matrices. We conclude with a look ahead to adaptive sensing procedures that allow real-time, interactive optical signal processing to further reduce the resource demands of an imaging system.

This dissertation presents the fundamental theory and design procedure of the sub-Nyquist rate sampling receiver front-end that exploits signal sparsity by employing Compressive Sensing (CS) techniques. The CS receiver serves as an Analog-to-Information Conversion (AIC) system that works at sampling rates much lower than the Nyquist rate. The performance of a parallel path CS front-end structure that employs current mode sampling techniques is quantified analytically. Useful and fundamental design guidelines that are unique to CS are provided based on the analytical tools. Simulations with IBM 90nm CMOS process verify the theoretical derivations and the circuit implementations. Based on these results, it is shown that instantaneous receiver signal bandwidth of 1.5 GHz and 44 dB of signal to noise plus distortion ratio (SNDR) are achievable in simulations assuming 0.5 ps clock jitter is present. The ADC and front-end core power consumption is estimated to be 120.8 mW. The front-end is fabricated with IBM 90nm CMOS process, and a BPSK sub-Nyquist rate communication system is realized as a prototype in the testing. A 1.25 GHz reference clock with 4.13 ps jitter variance is employed in the test bench. The signal frequency, phase and amplitude can be correctly reconstructed, and the maximum signal SNR obtained in the testing is 40 dB with single tone input and 30 dB with multi-tones test. The CS system has a better FOM than state-of-art Nyquist rate data acquisition systems taking into account the estimated PLL power.

We consider three problems, motivated by questions in computational neuroscience, related to recovering continuous quantities from binary or discrete data or measurements in the context of sparse structure. First, we show that it is possible to recover the norms of sparse vectors given one-bit compressive measurements, and provide associated guarantees. Second, we present a novel algorithm for spike-sorting in neural data, which involves recovering continuous times and amplitudes of events using discrete bases. This method, Continuous Orthogonal Matching Pursuit, builds on algorithms used in compressive sensing. It exploits the sparsity of the signal and proceeds greedily, achieving gains in speed and accuracy over previous methods. Lastly, we present a Bayesian method making use of hierarchical priors for entropy rate estimation from binary sequences. / text

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 / Spread Spectrum (SS) techniques are methods used to deliberately spread the spectrum of transmitted signals in communication systems. The increased bandwidth makes detection of these signals challenging for non-cooperative receivers. In this paper, we investigate detection of Frequency Hopping Spread Spectrum (FHSS) signals from compressive measurements. The theoretical and simulated performances of the proposed methods are compared to those of the conventional methods.

Third generation full-waveform (FW) LIDAR systems image an entire scene by emitting laser pulses in particular directions and measuring the echoes. Each of these echoes provides range measurements about the objects intercepted by the laser pulse along a specified direction. By scanning through a specified region using a series of emitted pulses and observing their echoes, connected 1D profiles of 3D scenes can be readily obtained. This extra information has proven helpful in providing additional insight into the scene structure which can be used to construct effective characterizations and classifications. Unfortunately, massive amounts of data are typically collected which impose storage, processing and transmission limitations. To address these problems, a number of compression approaches have been developed in the literature. These, however, generally require the initial acquisition of large amounts of data only to later discard most of it by exploiting redundancies, thus sampling inefficiently. Based on this, our main goal is to apply efficient and effective LIDAR sampling schemes that achieve acceptable reconstruction quality of the 3D scenes. To achieve this goal, we propose on using compressive sampling by emitting pulses only into random locations within the scene and collecting only the corresponding returned FW signals. Under this framework, the number of emissions would typically be much smaller than what traditional LIDAR systems require. Application of this requires, however, that scenes contain many degrees of freedom. Fortunately, such a requirement is satisfied in most natural and man-made scenes. Here, we propose to use a measure of rank as the measure of degrees of freedom. To recover the connected 1D profiles of the 3D scene, matrix completion is applied to the tensor slices. In this paper, we test our approach by showing that recovery of compressively sampled 1D profiles of actual 3D scenes is possible using only a subset of measurements.

Spread Spectrum (SS) techniques are methods used in communication systems where the spectra of the signal is spread over a much wider bandwidth. The large bandwidth of the resulting signals make SS signals difficult to intercept using conventional methods based on Nyquist sampling. Recently, a novel concept called compressive sensing has emerged. Compressive sensing theory suggests that a signal can be reconstructed from much fewer measurements than suggested by the Shannon Nyquist theorem, provided that the signal can be sparsely represented in a dictionary. In this work, motivated by this concept, we study compressive approaches to detect and decode SS signals. We propose compressive detection and decoding systems based both on random measurements (which have been the main focus of the CS literature) as well as designed measurement kernels that exploit prior knowledge of the SS signal. Compressive sensing methods for both Frequency-Hopping Spread Spectrum (FHSS) and Direct Sequence Spread Spectrum (DSSS) systems are proposed.

With the increasing demand for more wireless multimedia applications, it is desired to design a wireless system with higher data rate. Furthermore, the frequency spectrum has become a limited and valuable resource, making it necessary to utilize the available spectrum efficiently and coexist with other wireless systems. Orthogonal frequency division multiplexing (OFDM) modulation is widely used in communication systems to meet the demand for ever increasing data rates. The major advantage of OFDM over single-carrier transmission is its ability to deal with severe channel conditions without complex equalization. However, OFDM systems suffer from a high peak to average power ratio, and they are sensitive to carrier frequency offset and Doppler spread. This dissertation first focuses on the development of intercarrier interference (ICI) reduction and signal detection algorithms for OFDM systems over time-varying channels. Several ICI reduction algorithms are proposed for OFDM systems over doubly-selective channels. The OFDM ICI reduction problem over time-varying channels is formulated as a combinatorial optimization problem based on the maximum likelihood (ML) criterion. First, two relaxation methods are utilized to convert the ICI reduction problem into convex quadratic programming (QP) problems. Next, a low complexity ICI reduction algorithm applicable to $M$-QAM signal constellations for OFDM systems is proposed. This formulates the ICI reduction problem as a QP problem with non-convex constraints. A successive method is then utilized to deduce a sequence of reduced-size QP problems. For the proposed algorithms, the QP problems are solved by limiting the search in the 2-dimensional subspace spanned by its steepest-descent and Newton directions to reduce the computational complexity. Furthermore, a low-bit descent search (LBDS) is employed to improve the system performance. Performance results are given to demonstrate that the proposed ICI reduction algorithms provide excellent performance with reasonable computational complexity. A low complexity joint semiblind detection algorithm based on the channel correlation and noise variance is proposed which does not require channel state information. The detection problem is relaxed to a continuous non-convex quadratic programming problem. Then an iterative method is utilized to deduce a sequence of reduced-size quadratic programming problems. A LBDS method is also employed to improve the solution of the derived QP problems. Results are given which demonstrate that the proposed algorithm provides similar performance with lower computational complexity compared to that of a sphere decoder. A major challenge to OFDM systems is how to obtain accurate channel state information for coherent detection of the transmitted signals. Thus several channel estimation algorithms are proposed for OFDM systems over time-invariant channels. A channel estimation method is developed to utilize the noncircularity of the input signals to obtain an estimate of the channel coefficients. It takes advantage of the nonzero cyclostationary statistics of the transmitted signals, which in turn allows blind polynomial channel estimation using second-order statistics of the OFDM symbol. A set of polynomial equations are formulated based on the correlation of the received signal which can be used to obtain an estimate of the time domain channel coefficients. Performance results are presented which show that the proposed algorithm provides better performance than the least minimum mean-square error (LMMSE) algorithm at high signal to noise ratios (SNRs), with low computational complexity. Near-optimal performance can be achieved with large OFDM systems. Finally, a CS-based time-domain channel estimation method is presented for OFDM systems over sparse channels. The channel estimation problem under consideration is formulated as a small-scale $l_1$-minimization problem which is convex and admits fast and reliable solvers for the globally optimal solution. It is demonstrated that the magnitudes as well as delays of the significant taps of a sparse channel model can be estimated with satisfactory accuracy by using fewer pilot tones than the channel length. Moreover, it is shown that a fast Fourier transform (FFT) matrix of extended size can be used as a set of appropriate basis vectors to enhance the channel sparsity. This technique allows the proposed method to be applicable to less-sparse OFDM channels. In addition, a total-variation (TV) minimization based method is introduced to provide an alternative way to solve the original sparse channel estimation problem. The performance of the proposed method is compared to several established channel estimation algorithms. / Graduate

Compressed sensing (CS) is an innovative approach of signal processing that facilitates sub-Nyquist processing of bio-signals, such as a neural signal, electrocardiogram (ECG), and electroencephalogram (EEG). This strategy can be used to lower the data rate to realize ultra-low-power performance, As the count of recording channels increases, data volume is increased resulting in impermissible transmitting power. This thesis work presents the implementation of a CMOS-based front-end design with the CS in the standard 180 nm CMOS process. A novel pseudo-random sequence generator is proposed, which consists of two different types of D flip-flops that are used for obtaining a completely random sequence. This thesis work also includes the (reverse electrowetting-on-dielectric) REWOD based energy harvesting model for self-powered bio-sensor which utilizes the electrical energy generated through the process of conversion of mechanical energy to electrical energy. This REWOD based energy harvesting model can be a good alternative to battery usage, particularly for the bio-wearable applications. The comparative analysis of the results generated for voltage, current and capacitance of the rough surface model is compared to that of results of planar surface REWOD.

Η παρούσα εργασία χωρίζεται σε δύο μέρη. Στο πρώτο μέρος μελετάμε το αντικείμενο της Συμπιεσμένης καταγραφής. Το κείμενο εστιάζει στα βασικότερα σημεία της θεωρίας γύρω από την ανακατασκευή αραιών σημάτων από λίγες μετρήσεις, ενώ γίνεται και μία ανασκόπηση των τεχνικών ανακατασκευής. Στο δεύτερο μέρος παρουσιάζονται τα αποτελέσματα της ερευνητικής προσπάθειας γύρω από συγκεκριμένα προβλήματα ανακατασκευής. / -

abstract: As a promising solution to the problem of acquiring and storing large amounts of image and video data, spatial-multiplexing camera architectures have received lot of attention in the recent past. Such architectures have the attractive feature of combining a two-step process of acquisition and compression of pixel measurements in a conventional camera, into a single step. A popular variant is the single-pixel camera that obtains measurements of the scene using a pseudo-random measurement matrix. Advances in compressive sensing (CS) theory in the past decade have supplied the tools that, in theory, allow near-perfect reconstruction of an image from these measurements even for sub-Nyquist sampling rates. However, current state-of-the-art reconstruction algorithms suffer from two drawbacks -- They are (1) computationally very expensive and (2) incapable of yielding high fidelity reconstructions for high compression ratios. In computer vision, the final goal is usually to perform an inference task using the images acquired and not signal recovery. With this motivation, this thesis considers the possibility of inference directly from compressed measurements, thereby obviating the need to use expensive reconstruction algorithms. It is often the case that non-linear features are used for inference tasks in computer vision. However, currently, it is unclear how to extract such features from compressed measurements. Instead, using the theoretical basis provided by the Johnson-Lindenstrauss lemma, discriminative features using smashed correlation filters are derived and it is shown that it is indeed possible to perform reconstruction-free inference at high compression ratios with only a marginal loss in accuracy. As a specific inference problem in computer vision, face recognition is considered, mainly beyond the visible spectrum such as in the short wave infra-red region (SWIR), where sensors are expensive. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2015