# 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 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.