# Browsing by Subject "Compressed sensing"

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Item Open Access Belief Propagation with Deep Unfolding for High-dimensional Inference in Communication Systems(2019) Lian, MengkeHigh-dimensional probability distributions are important objects in a wide variety of applications for example, most prediction and inference applications focus on computing the posterior marginal of a subset of variables conditioned on observations of another subset of variables. In practice, this is untractable due to the curse of dimensionality. In some problems, high-dimensional joint probability distributions can be represented by factor graphs. For such problems, belief propagation (BP) is a polynomial-time algorithm that provides an efficient approximation of the posterior marginals, and it is exact if the factor graph does not contain cycles. With rapid improvements in machine learning over the past decade, using machine learning techniques to optimize system parameters is an emerging field in communication research.

This thesis considers applying BP for communication systems, and focuses on incorporating domain knowledge into machine learning models. For compressive sensing, two variants of relaxed belief propagation (RBP) algorithm are proposed. One improves the stability over a larger class of measurement matrices and the other reduces the computational complexity when measurement matrix is in the product of several sparse matrices. For optical communication, the non-linear Schrodinger equation is solved by modeling the signal in each step of split-step Fourier method as a multivariate complex Gaussian distribution. Then, the parameters of the Gaussian are tracked through in digital back-propagation. For recursive decoding for Reed–Muller codes, the algebraic structure of the code is utilized and a recursive BP approach for redundant factor graphs is developed for near-optimal decoding. Finally, we use deep unfolding to unroll BP decoding as a recursive neural network and introduce the idea of a the parameter adaptive network to learn the relation between channel SNR and optimal BP weight factors.

Item Open Access Compressive Spectral and Coherence Imaging(2010) Wagadarikar, Ashwin AshokThis dissertation describes two computational sensors that were used to demonstrate applications of generalized sampling of the optical field. The first sensor was an incoherent imaging system designed for compressive measurement of the power spectral density in the scene (spectral imaging). The other sensor was an interferometer used to compressively measure the mutual intensity of the optical field (coherence imaging) for imaging through turbulence. Each sensor made anisomorphic measurements of the optical signal of interest and digital post-processing of these measurements was required to recover the signal. The optical hardware and post-processing software were co-designed to permit acquisition of the signal of interest with sub-Nyquist rate sampling, given the prior information that the signal is sparse or compressible in some basis.

Compressive spectral imaging was achieved by a coded aperture snapshot spectral imager (CASSI), which used a coded aperture and a dispersive element to modulate the optical field and capture a 2D projection of the 3D spectral image of the scene in a snapshot. Prior information of the scene, such as piecewise smoothness of objects in the scene, could be enforced by numerical estimation algorithms to recover an estimate of the spectral image from the snapshot measurement.

Hypothesizing that turbulence between the scene and CASSI would introduce spectral diversity of the point spread function, CASSI's snapshot spectral imaging capability could be used to image objects in the scene through the turbulence. However, no turbulence-induced spectral diversity of the point spread function was observed experimentally. Thus, coherence functions, which are multi-dimensional functions that completely determine optical fields observed by intensity detectors, were considered. These functions have previously been used to image through turbulence after extensive and time-consuming sampling of such functions. Thus, compressive coherence imaging was attempted as an alternative means of imaging through turbulence.

Compressive coherence imaging was demonstrated by using a rotational shear interferometer to measure just a 2D subset of the 4D mutual intensity, a coherence function that captures the optical field correlation between all the pairs of points in the aperture. By imposing a sparsity constraint on the possible distribution of objects in the scene, both the object distribution and the isoplanatic phase distortion induced by the turbulence could be estimated with the small number of measurements made by the interferometer.

Item Open Access Computational Optical Imaging Systems: Sensing Strategies, Optimization Methods, and Performance Bounds(2012) Harmany, Zachary TaylorThe emerging theory of compressed sensing has been nothing short of a revolution in signal processing, challenging some of the longest-held ideas in signal processing and leading to the development of exciting new ways to capture and reconstruct signals and images. Although the theoretical promises of compressed sensing are manifold, its implementation in many practical applications has lagged behind the associated theoretical development. Our goal is to elevate compressed sensing from an interesting theoretical discussion to a feasible alternative to conventional imaging, a significant challenge and an exciting topic for research in signal processing. When applied to imaging, compressed sensing can be thought of as a particular case of computational imaging, which unites the design of both the sensing and reconstruction of images under one design paradigm. Computational imaging tightly fuses modeling of scene content, imaging hardware design, and the subsequent reconstruction algorithms used to recover the images.

This thesis makes important contributions to each of these three areas through two primary research directions. The first direction primarily attacks the challenges associated with designing practical imaging systems that implement incoherent measurements. Our proposed snapshot imaging architecture using compressive coded aperture imaging devices can be practically implemented, and comes equipped with theoretical recovery guarantees. It is also straightforward to extend these ideas to a video setting where careful modeling of the scene can allow for joint spatio-temporal compressive sensing. The second direction develops a host of new computational tools for photon-limited inverse problems. These situations arise with increasing frequency in modern imaging applications as we seek to drive down image acquisition times, limit excitation powers, or deliver less radiation to a patient. By an accurate statistical characterization of the measurement process in optical systems, including the inherent Poisson noise associated with photon detection, our class of algorithms is able to deliver high-fidelity images with a fraction of the required scan time, as well as enable novel methods for tissue quantification from intraoperative microendoscopy data. In short, the contributions of this dissertation are diverse, further the state-of-the-art in computational imaging, elevate compressed sensing from an interesting theory to a practical imaging methodology, and allow for effective image recovery in light-starved applications.

Item Open Access Improving Radar Imaging with Computational Imaging and Novel Antenna Design(2017) Zhu, RuoyuTraditional radar imaging systems are implemented using the focal plane

technique, steering beam antennas, or synthetic aperture imaging. These conventional

methods require either a large number of sensors to form a focal plane array similar to the

idea of an optical camera, or a single transceiver mechanically scanning the field of view.

The former results in expensive systems whereas the latter results in long acquisition time.

Computational imaging methods are widely used for the ability to acquire information

beyond the recorded pixels, thus are ideal options for reducing the number of radar

sensors in radar imaging systems. Novel antenna designs such as the frequency diverse

antennas are capable of optimizing antennas for computational imaging algorithms. This

thesis tries to find a solution for improving the efficiency of radar imaging using a method

that combines computational imaging and novel antenna designs. This thesis first

proposes two solutions to improve the two aspects of the tradeoff respectively, i.e. the

number of sensors and mechanical scanning. A method using time-of-flight imaging

algorithm with a sparse array of antennas is proposed as a solution to reduce the number

of sensors required to estimate a reflective surface. An adaptive algorithm based on the

Bayesian compressive sensing framework is proposed as a solution to minimize

mechanical scanning for synthetic aperture imaging systems. The thesis then explores the

feasibility to further improve radar imaging systems by combining computational

imaging and antenna design methods as a solution. A rapid prototyping method for

manufacturing custom-designed antennas is developed for implementing antenna

designs quickly in a laboratory environment. This method has facilitated the design of a

frequency diverse antenna based on a leaky waveguide design, which can be used under

computational imaging framework to perform 3D imaging. The proposed system is

capable of performing imaging and target localization using only one antenna and

without mechanical scanning, thus is a promising solution to ultimately improve the

efficiency for radar imaging.

Item Open Access Metamaterials for Computational Imaging(2013) Hunt, JohnMetamaterials extend the design space, flexibility, and control of optical material systems and so yield fundamentally new computational imaging systems. A computational imaging system relies heavily on the design of measurement modes. Metamaterials provide a great deal of control over the generation of the measurement modes of an aperture. On the other side of the coin, computational imaging uses the data that that can be measured by an imaging system, which may limited, in an optimal way thereby producing the best possible image within the physical constraints of a system. The synergy of these two technologies - metamaterials and computational imaging - allows for entirely novel imaging systems. These contributions are realized in the concept of a frequency-diverse metamaterial imaging system that will be presented in this thesis. This 'metaimager' uses the same electromagnetic flexibility that metamaterials have shown in many other contexts to construct an imaging aperture suitable for single-pixel operation that can measure arbitrary measurement modes, constrained only by the size of the aperture and resonant elements. It has no lenses, no moving parts, a small form-factor, and is low-cost.

In this thesis we present an overview of work done by the author in the area of metamaterial imaging systems. We first discuss novel transformation-optical lenses enabled by metamaterials which demonstrate the electromagnetic flexibility of metamaterials. We then introduce the theory of computational and compressed imaging using the language of Fourier optics, and derive the forward model needed to apply computational imaging to the metaimager system. We describe the details of the metamaterials used to construct the metaimager and their application to metamaterial antennas. The experimental tools needed to characterize the metaimager, including far-field and near-field antenna characterization, are described. We then describe the design, operation, and characterization of a one-dimensional metaimager capable of collecting two-dimensional images, and then a two-dimensional metaimager capable of collecting two-dimensional images. The imaging results for the one-dimensional metaimager are presented including two-dimensional (azimuth and range) images of point scatters, and video-rate imaging. The imaging results for the two-dimensional metaimager are presented including analysis of the system's resolution, signal-to-noise sensitivity, acquisition rate, human targets, and integration of optical and structured-light sensors. Finally, we discuss explorations into methods of tuning metamaterial radiators which could be employed to significantly increase the capabilities of such a metaimaging system, and describe several systems that have been designed for the integration of tuning into metamaterial imaging systems.