Doctor of Philosophy, The Ohio State University, 2017, Electrical and Computer Engineering

Passive radar is a type of radar sensor that exploits non-cooperative radio frequency transmissions to detect, localize and track targets of interest. A plethora of sources of illumination were suggested in previous work including many wireless communication signals such as GSM, OFDM, WIFI, DVB-T and DTV. Using these ubiquitously available sources of RF energy enables covert operation, however this comes with the penalty of lower performance in terms of sensitivity, resolution, and ambiguity when compared to active monostatic radar systems. Improving passive radar system performance through improved receive processing algorithms has been the focus of researchers in the past few decades. In our work, we propose alternative processing techniques that can improve detection performance in two distinct problem settings. First, we study widely separated passive radar receiver scenarios, most notably with direct path signal obstruction and imprecise knowledge of transmitter positions. In this setting, the joint detection of the target and active propagation paths can be posed as a model order selection problem. We formulate a composite detection problem with unknown reference transmitted signal parameters and unknown model order. We derive penalty terms for Bayesian Information Criterion (BIC) and Exponentially Embedded Family (EEF) methods of model order selection. Simulation experiments show that properly modified BIC outperforms the alternatives at low and high SNR. Second, we consider passive radar systems that employ randomly subsampled antenna arrays with access to a noisy copy of the transmitted signal. In this setting, the sparsity of targets within a discretized angle-range-Doppler domain is a natural assumption. Hence, we propose applying spatial compressive sensing with matched filtering techniques to a collocated randomly subsampled passive antenna array system to accomplish a system with higher angular resolution and lower hardware complexity. A sp (open full item for complete abstract)

Committee: Emre Ertin (Advisor) Subjects: Electrical Engineering

Master of Science in Electrical Engineering (MSEE), Wright State University, 2017, Electrical Engineering

Compressive sensing (CS) is an active research field focused on finding solutions to sparse linear inverse problems, i.e. estimating a signal using fewer linear measurements than there are unknowns. The assumption of signal sparsity makes solutions to this otherwise ill-posed problem possible and has lead to a number of technological innovations such as smaller and less expensive cameras that capture high resolution imagery, low-power radar systems, and accelerated MRI scanners. In this thesis, we present the development of a hardware CS imaging system using a Digital Micromirror Device (DMD) providing spatial light modulation via an array of micromirrors that can be programmatically controlled to produce automated measurements. Additionally, we develop a number of new DMD-specific calibration models intended to capture the physical attributes of micromirrors and the end-to-end data collection system. Algorithms are derived to fit the calibration models from training data, and resultant CS reconstructions demonstrate a substantial reduction in image estimation error while reducing the number of required measurements by fifty percent, relative to current baseline calibration methods.

Committee: Joshua Ash Ph.D. (Advisor); Arnab Shaw Ph.D. (Committee Member); Vince Velten Ph.D. (Committee Member) Subjects: Electrical Engineering

Doctor of Philosophy, The Ohio State University, 2014, Electrical and Computer Engineering

Across numerous disciplines, the ability to generate high-dimensional datasets is driving an enormous demand for increasingly efficient ways of both capturing and processing this data. A promising recent trend for addressing these needs has developed from the recognition that, despite living in high-dimensional ambient spaces, many datasets have vastly smaller intrinsic dimensionality. When capturing (sampling) such datasets, exploiting this realization permits one to dramatically reduce the number of samples that must be acquired without losing the salient features of the data. When processing such datasets, the reduced intrinsic dimensionality can be leveraged to allow reliable inferences to be made in scenarios where it is infeasible to collect the amount of data that would be required for inference using classical techniques. To date, most approaches for taking advantage of the low intrinsic dimensionality inherent in many datasets have focused on identifying succinct (i.e., sparse) representations of the data, seeking to represent the data using only a handful of "significant" elements from an appropriately chosen dictionary. While powerful in their own right, such approaches make no additional assumptions regarding possible relationships between the significant elements of the dictionary. In this dissertation, we examine ways of incorporating knowledge of such relationships into our sampling and processing schemes. One setting in which it is possible to dramatically improve the efficiency of sampling schemes concerns the recovery of temporally correlated, sparse time series, and in the first part of this dissertation we summarize our work on this important problem. Central to our approach is a Bayesian formulation of the recovery problem, which allows us to access richly expressive models of signal structure. While Bayesian sparse linear regression algorithms have often been shown to outperform their non-Bayesian counterparts, this frequently come (open full item for complete abstract)

Committee: Philip Schniter PhD (Advisor); Lee Potter PhD (Committee Member); Per Sederberg PhD (Committee Member) Subjects: Computer Science; Electrical Engineering

Doctor of Philosophy, The Ohio State University, 2014, Electrical and Computer Engineering

Recent developments in compressive sensing (CS) combined with increasing demands for effective high-dimensional inference techniques across a variety of disciplines have motivated extensive research into algorithms exploiting various notions of parsimony, including sparsity and low-rank constraints. In this dissertation, we extend the generalized approximate message passing (GAMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of CS, to handle several classes of bilinear inference problems. First, we consider a general form of noisy CS where there is uncertainty in the measurement matrix as well as in the measurements. Matrix uncertainty is motivated by practical cases in which there are imperfections or unknown calibration parameters in the signal acquisition hardware. While previous work has focused on analyzing and extending classical CS algorithms like the LASSO and Dantzig selector for this problem setting, we propose a new algorithm called Matrix Uncertain GAMP (MU-GAMP) whose goal is minimization of mean-squared error of the signal estimates in the presence of these uncertainties, without attempting to estimate the uncertain measurement matrix itself. Next, we extend GAMP to the generalized-bilinear case, in which the measurement matrix is estimated jointly with the signals of interest, enabling its application to matrix completion, robust PCA, dictionary learning, and related matrix-factorization problems. We derive this Bilinear GAMP (BiG-AMP) algorithm as an approximation of the sum-product belief propagation algorithm in the high-dimensional limit, where central limit theorem arguments and Taylor-series approximations apply, and under the assumption of statistically independent matrix entries with known priors. In addition, we propose an adaptive damping mechanism that aids convergence under finite problem sizes, an expectation-maximization (EM)-based method to automatically tune the parameters of the assu (open full item for complete abstract)

Committee: Philip Schniter (Advisor); Lee Potter (Committee Member); Emre Ertin (Committee Member) Subjects: Electrical Engineering

Master of Science, The Ohio State University, 2014, Electrical and Computer Engineering

Radar images are created from measurements of the electromagnetic field scattered from an object or scene of interest. The scattered field defines the radar signature as a function of frequency and aspect angle. High resolution radar images and radar signatures are used for target recognition, tracking, and hardware-in-the-loop testing. High resolution radar images of electrically large targets may require a large amount of data to be measured, stored, and processed. A sparse representation of this data may allow the radar signature to be efficiently measured, stored, and rapidly reconstructed on demand. Compressed sensing is applied to obtain the sparse representation without measuring the full data set. “Compressed sensing” has different interpretations, but in this thesis it refers to using non-adaptive, random samples of the measured signal, with no a priori knowledge of the signal. According to compressed sensing theory, this is possible if the radar signature can be expressed in terms of a sparse basis. If a signal y can be approximated by K non-zero coefficients in the sparse basis (“K-sparse”), the coefficients may be obtained with random sampling of the signal at sub-Nyquist rates provided that K is much smaller than the total number of Nyquist samples. The random sampling is non-adaptive (i.e., future samples are independent of previous samples) and the number of samples required is primarily related to the sparseness of the signal, and not the bandwidth nor the size of the dictionary from which the basis functions are selected. The objective of this thesis is to investigate the effectiveness of physical basis functions, defined as point scatter functions with frequency-dependent amplitudes characteristic of physical scattering mechanisms, to provide an improved sparse basis in which to expand radar signatures. The goal is to represent a radar signature accurately with the fewest terms possible and with the fewest measurements. Use of physical basi (open full item for complete abstract)

Committee: Robert Burkholder (Advisor); Lee Potter (Committee Member) Subjects: Electrical Engineering; Electromagnetics

Doctor of Philosophy, The Ohio State University, 2021, Electrical and Computer Engineering

Passive radar systems use signals of opportunity to illuminate targets instead of dedicated radar transmitters. The signals of opportunity have lower bandwidth than dedicated active radar systems, leading to poor downrange resolution. Multiple signals of opportunity can be coherently combined to increase the overall bandwidth of the system, and therefore create finer resolution images. These signals are usually separated in the frequency domain (non-contiguous), which causes large unwanted grating lobe artifacts in the image when using back-projection or Fourier transform based imaging. Additionally, the signals of opportunity may be completely uncorrelated and transmitting from different locations. This dissertation investigates methods of combining these signals to create images with higher resolution than if only a single signal of opportunity were used. A method to quickly estimate bistatic scattered electric fields from complex targets is augmented with new models. The targets are first decomposed into a set of canonical geometries with closed-form solutions. Then the total scattered field of the target is found as the superposition of the scattered fields from the individual geometries. The canonical geometries used are plates, dihedrals, and trihedrals. A closed-form solution for the non-90° dihedral is introduced and verified with iterative physical optics. Bistatic SAR images of complex targets can be predicted in seconds using the total scattered fields from the canonical geometries, whereas it would take hours using a physical optics solver. Approaches of combining signals for 1D passive radar imaging are then examined. The signals may be non-contiguous in frequency, and originate from transmitters not located at the same position. A calibration method is developed to align the downrange responses, and coherently combine the two signals. A compressive sensing-based algorithm is used to combine the non-contiguous frequency data, and is shown to mitigat (open full item for complete abstract)

Committee: Robert Burkholder (Advisor); Brian Joseph (Committee Member); Fernando Teixeira (Committee Member); Joel Johnson (Committee Member) Subjects: Electrical Engineering

Master of Science in Computer Engineering (MSCE), Wright State University, 2021, Computer Engineering

We consider the problem of compressive synthetic aperture radar (SAR) imaging with the goal of reconstructing SAR imagery in the presence of undersampled phase history. While this problem is typically considered in compressive sensing (CS) literature, we consider a variety of deep learning approaches where a deep neural network (DNN) is trained to form SAR imagery from limited data. At the cost of computationally intensive offline training, on-line test-time DNN-SAR has demonstrated orders of magnitude faster reconstruction than standard CS algorithms. A limitation of the DNN approach is that any change to the operating conditions necessitates a costly retraining procedure. In this work, we consider development of DNN methods that are robust to discrepancies between training and testing conditions. We examine several approaches to this problem, including using input-layer dropout, augmented data support indicators, and DNN-based robust approximate message passing.

Committee: Joshua Ash Ph.D. (Advisor); Tanvi Banerjee Ph.D. (Committee Member); Mateen Rizki Ph.D. (Committee Member) Subjects: Computer Engineering; Computer Science; Electrical Engineering

Doctor of Philosophy, The Ohio State University, 2019, Electrical and Computer Engineering

We present novel realizations of computational terahertz (THz) imaging techniques based on compressive sensing and phase-retrieval algorithms and a single-pixel THz sensor. Imaging in the THz band covering 300 GHz-10 THz is being considered for key applications in biomedical imaging, security screening and non-destructive evaluation. State-of-the-art in THz imaging is based on mechanical raster scanning using a single, high-performance sensor. Such raster-scanning imagers are rather bulky and suffer from very low frame-rates, as well as mechanical noise due to the moving parts in the hardware. Alternatively, multi-detector imagers such as THz focal plane arrays (FPAs) can speed-up image acquisition time, potentially reaching real-time video rates. However, such devices require complex and expensive fabrication and they typically exhibit limited sensitivity due to additional noise introduced by the read-out circuit. In this dissertation, we demonstrate novel THz imaging techniques based on a single THz sensor that concurrently circumvent the slow acquisition time and mechanical noise of raster scan imaging. This is achieved by using an optically reconfigurable spatial wave modulation scheme to "serialize'' the scene measurements. Subsequently, compressive sensing (CS) and reconstruction algorithms are employed to computationally generate 2D images of the scene from a set of serial measurements, each corresponding to a different spatial modulation. Similar to well-developed optical CS methods, compressive THz imaging allows far fewer measurements than the conventional Nyquist rate to accurately reconstruct sparse scenes. In addition, compressive THz reconstruction exhibits better signal-to-noise (SNR) performance compared to the FPA cameras. To enable the study and experimental demonstration of various computational imaging algorithms, we realize a generalized compressive THz imaging setup using conventional quasi-optical components and a semiconductor-based ph (open full item for complete abstract)

Committee: Kubilay Sertel (Advisor); Niru K. Nahar (Committee Member); Fernando Teixeira (Committee Member); Robert Burkholder (Committee Member) Subjects: Electrical Engineering; Electromagnetics; Optics

Doctor of Philosophy, The Ohio State University, 2017, Electrical and Computer Engineering

Multi-Input Multi-output (MIMO) radar is an emerging technology that is attracting the attention of researchers for both civilian and military applications. Unlike a standard phased array radar, which transmits a phase shifted version of a single waveform, MIMO radars can transmit independent waveforms across each of it's transmit antennas. Judicious choice of these waveforms results in improvement in target detection performance, improvement in angular estimation accuracy, and reduction in minimum detectable velocity. The work in this thesis is broadly divided into two categories.\\ In the first part, combining the advantages of MIMO array and software defined radar architecture, we present the design, implementation, and validation of a Software Defined MIMO radar test bed for distributed MIMO radar research. The micro radars discuss here are low power, small form factor radar systems that use high speed Field Programmable Gate Array (FPGA) and a custom designed RF Frontend operating at X-band (10.5 GHz). They can be used individually or more than one micro-SDRs can be synchronized for MIMO experimentation. Real world experimentation results to validate the functioning of the radar testbed is also presented. \\ Conventional radar systems, in order to achieve smaller range resolution transmit waveforms with several hundred megahertz or gigahertz bandwidth. Traditionally match filtering is used to recover the information content at the receiver. However, for implementing match filtering the Analog to Digital converter (ADC) must sample the received signal Nyquist rate which is at least twice the bandwidth of transmit signal. This puts a constraint on the maximum available bandwidth of a radar receiver. On the other hand, stretch processing which converts range estimation problem into frequency estimation problem. Even though this significantly reduces the sampling rate needed, the received signal is still bound by Nyquist constraint. To overcome this limitatio (open full item for complete abstract)

Committee: Emre Ertin (Advisor); Bibyk Steven (Committee Member); Roblin Patrick (Committee Member) Subjects: Electrical Engineering

Master of Science, The Ohio State University, 2017, Electrical and Computer Engineering

Liver fibrosis, a common feature of many chronic liver diseases, is associated with an increase in liver stiffness. While biopsy is the clinical standard for staging fibrosis, this invasive procedure is prone to error and places the patient at risk for health complications. Magnetic resonance elastography (MRE) is a noninvasive clinical tool for staging liver fibrosis. However, MRE requires patients to perform lengthy breath holds exceeding 15 seconds for each slice in each encoding direction, which limits its clinical application. Therefore, we propose a new data acquisition and processing method to reduce MRE scan time. The proposed method, called Bayesian method for magnetic resonance Elastography using Approximate Message passing (BEAM) utilizes a combination of several features to accelerate reconstruction. Pseudorandom sampling of k-space promotes incoherent aliasing, which allows compressive recovery via enforcement of sparsity in wavelet domain. Additionally, a spatially varying magnitude constraint is applied across offsets and polarities to exploit structure unique to MRE. BEAM is validated using retrospectively downsampled phantom data and prospectively downsampled in vivo liver data (n = 86). Analysis of BEAM reconstructions demonstrate accurate quantification of mean liver stiffness up to an acceleration factor of R = 6. Bland Altman analysis indicates that BEAM (R = 6) has a bias of -0.04 kPa and limits of agreement of -0.36 – +0.28 kPa when compared to the clinical standard liver MRE technique with traditional GRAPPA (R = 1.4). This study demonstrates that by exploiting spatial sparsity and magnitude consistency, it is feasible to reduce the scan time of liver MRE by an additional factor of 4 while maintaining accurate mean stiffness quantification. This potentially enables collection of four liver slices, as per clinical protocol, within a single breath hold.

Committee: Rizwan Ahmad (Advisor); Arunark Kolipaka (Advisor) Subjects: Biomedical Engineering; Biomedical Research; Electrical Engineering; Engineering; Medical Imaging; Radiology

MS, University of Cincinnati, 2015, Engineering and Applied Science: Electrical Engineering

A wide variety of error sources affect accuracy of the basic GPS measurements of pseudorange (also known as code-phase) and integrated Doppler (also known as carrier-phase). Among these are satellite clock and ephemeris errors, ionospheric delay, tropospheric delay, receiver dynamic tracking error, multipath and thermal noise. Multipath is the dominant error source in high precision GPS applications as others sources can be countered with differential measurements. Multipath errors result when the receiver receives the direct or line-of-sight (LOS) satellite signal via multiple paths and processes the combined signal as if it were only the direct. This causes anomalies in determining user's location and velocity. Large time-delay multipath are easily separated by correlators in a GPS receiver due to easy separation of correlation peaks. Medium and small time-delay multipath are more difficult to detect and separate since the correlation peaks are not separated, but rather distorted from the shape of that of a single path. Many solutions have been proposed to estimate LOS in the presence of multipath, almost all of them require faster sampling than the Nyquist rate. This in turn requires a large bandwidth on the RF frontend, i.e., a large pre-correlation bandwidth. A large bandwidth RF frontend admits more noise, and is also more prone to interference. Therefore a narrowband solution would be more desirable. However, tradeoff is that not enough samples are contained in a correlation peak, making it very difficult, if not impossible, to detect LOS and mitigate multipath. In this thesis we present a novel method to reconstruct high-sampling rate (super-Nyquist rate) correlation functions from low-sampling rate (Nyquist-rate) correlation functions using the new signal processing paradigm of compressive sampling or compressive sensing (CS). Since the correlation function of GPS signals is sparse, with only a few high peaks, it is suitable to apply the CS theor (open full item for complete abstract)

Committee: H. Howard Fan Ph.D. (Committee Chair); Eric T. Vinande Ph.D. (Committee Member); Xuefu Zhou Ph.D. (Committee Member) Subjects: Electrical Engineering

Doctor of Philosophy, The Ohio State University, 2015, Electrical and Computer Engineering

In recent years, there have been massive increases in both the dimensionality and sample sizes of data due to ever-increasing consumer demand coupled with relatively inexpensive sensing technologies. These high-dimensional datasets bring challenges such as complexity, along with numerous opportunities. Though many signals of interest live in a high-dimensional ambient space, they often have a much smaller inherent dimensionality which, if leveraged, lead to improved recoveries. For example, the notion of sparsity is a requisite in the compressive sensing (CS) field, which allows for accurate signal reconstruction from sub-Nyquist sampled measurements given certain conditions. When recovering a sparse signal from noisy compressive linear measurements, the distribution of the signal's non-zero coefficients can have a profound effect on recovery mean-squared error (MSE). If this distribution is apriori known, then one could use computationally efficient approximate message passing (AMP) techniques that yield approximate minimum MSE (MMSE) estimates or critical points to the maximum a posteriori (MAP) estimation problem. In practice, though, the distribution is unknown, motivating the use of robust, convex algorithms such as LASSO-which is nearly minimax optimal-at the cost of significantly larger MSE for non-least- favorable distributions. As an alternative, this dissertation focuses on empirical-Bayesian techniques that simultaneously learn the underlying signal distribution using the expectation-maximization (EM) algorithm while recovering the signal. These techniques are well-justified in the high-dimensional setting since, in the large system limit under specific problem conditions, the MMSE version of AMP's posteriors converge to the true posteriors and a generalization of the resulting EM procedure yields consistent parameter estimates. Furthermore, in many practical applications, we can exploit additional signal structure beyond simple sparsity for improve (open full item for complete abstract)

Committee: Philip Schniter (Advisor); Lee Potter (Committee Member); Yuejie Chi (Committee Member) Subjects: Electrical Engineering

MS, University of Cincinnati, 2014, Engineering and Applied Science: Electrical Engineering

Compressive Sensing is a new signal processing paradigm that reconstructs a signal that is sampled at a frequency much lower than the Nyquist Rate with very high accuracy. Compressive Sensing is a ground breaking technology that has improved data acquisition in many applications including Imaging, Radar and Communication Systems. It can be applied to any signal that is inherently sparse or can be represented sparsely in some domain. On the other hand, Inverse Synthetic Aperture Radar (ISAR) Imaging is a technique of imaging moving targets with a stationary radar. Unlike Synthetic Aperture Radar (SAR), the necessary angular diversity to image the entire target is provided by target motion. ISAR naturally lends itself to Compressive Sensing due to the sparse nature of the target scene. In fact, Compressive Sensing's inherent properties such as robustness to noise and minimal data acquisition have been thoroughly exploited to produce good images of a target scene in ISAR. ISAR imagery in itself is complex because the moving targets typically cause a blur in the resultant image if the motion parameters are unknown. This can be countered by using motion compensation schemes which nullify the blurred effect due to target motion. This thesis proposes a simplified scheme to estimate the complex motion parameters such as Range, Velocity and Acceleration. Furthermore, this thesis proposes the use of sparse probing frequencies to apply Compressive Sensing for multiple targets, hence retrieving an ISAR image of good quality.

Committee: H. Howard Fan Ph.D. (Committee Chair); William Wee Ph.D. (Committee Member); Xuefu Zhou Ph.D. (Committee Member) Subjects: Electrical Engineering

Master of Science (M.S.), University of Dayton, 2014, Electro-Optics

Tomography is a technique to reconstruct the 3-dimensional (3D) profile of the object. In multi-angle holographic tomography (MAHT), data from different projections with different angles are recorded by an in-line Gabor hologram setup, and the 2-dimensional (2D) shapes of the object for different angles are reconstructed and combined to form a true 3D profile. A one-shot MAHT setup with 3 angles is built and the main issues involved in this technique are discussed. Compressive sensing (CS) is a new alternative to the conventional Fresnel approach for digital holographic reconstruction for sparse objects, and can show a good performance with respect to the depth of focus and working range. The performance of the Fresnel approach, the transfer function approach and the CS approach for holographic reconstruction is compared with respect to the depth of focus, twin-image effect and the computation time, which helps us determine the optimum approach to use in one-shot MAHT.

Committee: Partha Banerjee (Advisor); Joseph Haus (Committee Member); Imad Agha (Committee Member) Subjects: Optics

Doctor of Philosophy (PhD), Wright State University, 2012, Engineering PhD

Sensors capable of collecting wide area motion imagery (WAMI), video synthetic aperture radar (SAR), and other high frame rate sensor modalities provide massive amounts of high-resolution data. Such data allows for the use of multiple images in exploitation tasks which may have traditionally used single images or single pairs of images. One such task is change detection. This dissertation presents new statistical methods for change detection that provide for the exploitation of multiple images per pass. Uncertainty in image registration can degrade change detection performance. Registration accuracy is analyzed, and the impact of registration uncertainty is propagated to the registered imagery. A statistical understanding of this uncertainty is incorporated into the sequential change detection algorithm to mitigate performance degradation due to registration errors. Theoretical results are verified through simulation experiments and with measured data sets.

Committee: Brian Rigling PhD (Advisor); Fred Garber PhD (Committee Member); John Gallagher PhD (Committee Member); Micheal Temple PhD (Committee Member); William Pierson PhD (Committee Member) Subjects: Computer Science; Electrical Engineering; Engineering; Statistics

MS, University of Cincinnati, 2012, Engineering and Applied Science: Electrical Engineering

Compressed Sensing reconstructs the signal / image from a significantly less number of samples violating the Nyquist criteria. It exploits the sparsity present in the signal /image. Medical Imaging techniques like MRI (Magnetic Resonance Imaging), MRA (Magnetic Resonance Angiography), PET (Positron Emission Tomography) and MRSI (Magnetic Resonance Spectroscopic Imaging) are very popular and powerful medical tools and are used throughout the globe. The drawback associated with these important tools is that they have very slow data acquisition processes. On the other hand, all natural images are sparse in nature in some transform domain. Magnetic Resonance Angiograms are sparse in the image domain itself. More complex images like Magnetic Resonance Imaging of brain is sparse in some transform domain like Wavelet Transform etc. Compressed Sensing using this property of the medical images could significantly change the concept of scanning associated with the devices used in the sense that Compressed Sensing when applied could speed up the scanning process by a large margin. Using the inherent sparsity in the medical images, Compressed Sensing undersamples the k-space by acquiring very small amount of data from it and reconstructs the original image using non-linear optimization method. In this thesis, we have worked on the sampling schemes or patterns used to undersample the k-space or the Fourier space of different medical imaging techniques. Our sampling scheme when compared to the ones proposed by Dr. Lustig[1, 2] in his work, gives a better output. For a proper comparison, same amount of the data was acquired and the results were compared.

Committee: H. Howard Fan PhD (Committee Chair); T. Douglas Mast PhD (Committee Member); William Wee PhD (Committee Member) Subjects: Electrical Engineering

Master of Science, The Ohio State University, 2012, Electrical and Computer Engineering

We propose a factor-graph-based approach to joint channel-estimation-and-decoding (JCED) of bit-interleaved coded orthogonal frequency division multiplexing (BICMOFDM) over a Rayleigh Fading channel. A Basis Expansion model is applied to reduce inter-carrier interference (ICI) caused by channel variation over time. Guard interval structure is introduce to reduce inter-symbol interference (ISI) caused by multi-path delay. In contrast to existing designs, our is capable of exploiting not only sparsity in sampled channel taps but also time variation in both the tap amplitudes and the tap support. In order to exploit these channel-tap structures, we adopt a twostate Gaussian mixture prior in conjunction with a Gauss-Markov model on the tap amplitude trajectories and a discrete Binary Markov model on the tap state trajectories. For loopy belief propagation, we exploit the Generalized Approximate Message Passing algorithm (GAMP) recently developed in the context of compressive sensing, and show that it can be successfully coupled with soft-input soft-output decoding, as well as Markov trajectory inference, through a sum-product framework. We try to find out the optimal scheme to utilize the most of channel capacity as well as getting effective bit error rate (BER).

Committee: Philip Schniter Dr. (Advisor); Lee Potter Dr. (Committee Member) Subjects: Electrical Engineering

Master of Science, The Ohio State University, 2012, Electrical and Computer Engineering

We present a framework that leverages compressive sensing (CS) for tomographic echo imaging in two dimensions, a specific type of imaging problem that is of interest to both military and civilian researchers. We establish CS guarantees for certain types of far-field tomographic imaging of sparse scenes. Typically, CS guarantees for common tomographic systems can be difficult to establish because of the structure imposed by uniform sampling of echoes. This introduces a high level of coherence between measurements from different nearby reflectors. We overcome these difficulties by introducing randomness in the placement of several monostatic radar sites surrounding the scene and by making simplifying assumptions based on practical engineering constraints. We use a wideband signal to interrogate the scene, allowing for high-resolution imaging. Our main result shows that with high probability, the system model satisfies the restricted isometry property (RIP) under a certain set of assumptions and restrictions. The number of radar sites required to meet RIP is a function of the desired imaging resolution and the RIP parameters. We compare this result to empirical trials and show that there are significant limitations to the practical use of the bounds proven. However, there is value in the novel approach to proving RIP for this type of two-dimensional system. Our results indicate that we can produce a similar image using less sensors with CS compared to more sensors with traditional imaging algorithms that assume no information about the unknown scene.

Committee: Lee Potter PhD (Advisor); Emre Ertin PhD (Committee Member); Phillip Schniter PhD (Committee Member) Subjects: Applied Mathematics; Electrical Engineering

Doctor of Philosophy, Case Western Reserve University, 2013, Applied Mathematics

Signal/image processing and reconstruction based on mathematical modeling and computational techniques have been well developed and still attract much attention due to their broad applications. It becomes challenging to build mathematical models if the given data lacks some certainties. Prior information, including geometric priors, high frequency priors, spatially variant intensity variations and image regularities, assists to establish mathematical models by providing a more accurate description of the underlying signal/image. We have been exploring applications of the extracted prior information in two directions: integrating prior information into the image denoising explained in nonlocal means (NL-means) denoising framework; enhancing the compressive sensing signal/image reconstruction with the guidance of prior information. The first topic is geometric information based image denoising, where we develop a segmentation boosted image denoising scheme, balancing the removal of excessive noise and preservation of fine features. By virtue of segmentation algorithms and more general geometry extraction schemes, we are able to obtain the phase or geometric prior information. Based on the NL-means method, we introduce a mutual position function to ensure that averaging is only taken over pixels in the same image phase. To further improve the performance, we provide the respective selection scheme for the convolution kernel and the weight function. To address the unreliable segmentation due to the presence of excessive noise, the phase prior is relaxed to a more general geometric prior. The second topic is prior information guided compressive sensing signal/image reconstruction. Concerning the 1D signal reconstruction, we extract high frequency subbands as prior to boost the subsequent reconstruction. In 2D image reconstruction realm, we propose a novel two-stage intensity variation prior guided image reconstruction method using pixel-to-pixel varying weights ass (open full item for complete abstract)

Committee: Weihong Guo (Advisor); Daniela Calvetti (Committee Member); Erkki Somersalo (Committee Member); David Wilson (Committee Member) Subjects: Applied Mathematics