In the past two decades, myriad algorithms to elucidate the characteristics and dynamics of molecular systems have been developed for quantum computers. In this dissertation, we explore how these algorithms can be adapted to other fields, both to closely related subjects such as materials science, and more surprising subjects such as information theory. Special emphasis is placed on the Variational Quantum Eigensolver algorithm adapted to solve band structures of a periodic system; three distinct implementations are developed, each with its own advantages and disadvantages. We also see how unitary quantum circuits designed to model individual electron excitations within a molecule can be modified to prepare a quantum states strictly orthogonal to a space of known states, an important component to solve problems in thermodynamics and spectroscopy. Finally, we see how the core behavior in several quantum algorithms originally developed for quantum chemistry can be adapted to implement compressive sensing, a protocol in information theory for extrapolating large amounts of information from relatively few measurements. This body of work demonstrates that quantum algorithms developed to study molecules have immense interdisciplinary uses in fields as varied as materials science and information theory.

Reduced-control antenna arrays reduce the number of controls required for beamforming while maintaining a given array aperture. A reduced-control array for direction finding (DF), inspired by the concept of compressive sensing (CS), was recently proposed which uses random compression weights for combining antenna-element signals into fewer measurements. However, this compressive array had not been studied in terms of traditional characteristics such as directivity, sidelobe level (SLL) or beamwidth. In this work, random compression weights are shown to be suboptimal and a need for the optimisation of compressive arrays is expressed. Existing codebook optimisation algorithms prove to be the best starting point for the optimisation of compressive arrays, but are computationally complex. A computationally efficient codebook optimisation algorithm is proposed to address this problem, which inspires the compressive-array optimisation algorithm to follow. Compressive antenna arrays are formulated as a generalisation of reduced-control arrays and a framework is presented for their optimisation in terms of SLL. By allowing arbitrary compression weights, compressive arrays are shown to improve on existing reduced-control techniques. A feed network consisting of interconnected couplers and fixed phase shifters is proposed, enabling the implementation of compressive arrays in microwave hardware. The practical feasibility of compressive arrays is illustrated by successfully manufacturing a 3-GHz prototype compressive array with integrated antenna elements. / Thesis (PhD)--University of Pretoria, 2020. / Electrical, Electronic and Computer Engineering / PhD / Unrestricted

High resolution transient/3D imaging technology is of high interest in both scientific research and commercial application. Nowadays, all of the transient imaging methods suffer from low resolution or time consuming mechanical scanning. We proposed a new method based on TCSPC and Compressive Sensing to achieve a high resolution transient imaging with a several seconds capturing process. Picosecond laser sends a serious of equal interval pulse while synchronized SPAD camera's detecting gate window has a precise phase delay at each cycle. After capturing enough points, we are able to make up a whole signal. By inserting a DMD device into the system, we are able to modulate all the frames of data using binary random patterns to reconstruct a super resolution transient/3D image later. Because the low fill factor of SPAD sensor will make a compressive sensing scenario ill-conditioned, We designed and fabricated a diffractive microlens array. We proposed a new CS reconstruction algorithm which is able to denoise at the same time for the measurements suffering from Poisson noise. Instead of a single SPAD senor, we chose a SPAD array because it can drastically reduce the requirement for the number of measurements and its reconstruction time. Further more, it not easy to reconstruct a high resolution image with only one single sensor while for an array, it just needs to reconstruct small patches and a few measurements. In this thesis, we evaluated the reconstruction methods using both clean measurements and the version corrupted by Poisson noise. The results show how the integration over the layers influence the image quality and our algorithm works well while the measurements suffer from non-trival Poisson noise. It's a breakthrough in the areas of both transient imaging and compressive sensing.

Ces dernières années, la théorie mathématique de l'échantillonnage compressé (CS) a émergé en tant que nouvel outil en traitement d'images, permettant notamment de dépasser certaines limites établies par la théorie de l'échantillonnage de Nyquist. En particulier, la théorie du CS établit qu'un signal (une image, une séquence vidéo, etc.) peut être reconstruit à partir d'un faible nombre de mesures linéaires non-adaptatives et aléatoires, pourvu qu'il présente une structure parcimonieuse. Dans la mesure où cette hypothèse se vérifie pour une large classe d'images naturelles, plusieurs applications d'imagerie ont d'ores-et-déjà bénéficié à des titres divers des résultats issus de cette théorie. Le but du travail doctoral présent est d'étudier comment la théorie du CS - et plus généralement les idées et méthodes en relation avec les problèmes de reconstruction de signaux parcimonieux - peuvent être utilisés pour concevoir des dispositifs d'acquisition optiques à haute-résolution spatiale et temporelle pour des applications en imagerie biologique. Nous étudions tout d'abord quelques questions pratiques liées à l'étape de reconstruction nécessairement associée aux systèmes d'acquisition exploitant le CS, ainsi qu'à la sélection des paramètres d'échantillonnage. Nous examinons ensuite comment le CS peut être utilisé dans le cadre d'applications d'échantillonnage de signaux vidéo. Enfin, avec dans l'idée l'utilisation dans des problèmes de débruitage de méthodes inspirées du CS, nous abordons la question de l'estimation d'erreur dans les problèmes de débruitage d'images acquises en conditions de faible luminosité, notamment dans le cadre d'applications de microscopie. / In the past few years, the mathematical theory of compressed sensing (CS) has emerged as a new tool in the image processing field, leading to some progress in surpassing the limits stated by the Nyquist sampling theory. In particular, the CS theory establishes that a signal (image, video, etc.) can be reconstructed from a relatively small subset of non-adaptive linear random measurements, assuming that it presents a sparse structure. As this hypothesis actually holds for a large number of natural images, several imaging applications have already benefited from this theory in various aspects. The goal of the present PhD work is to investigate how the CS theory - and more generally the ideas and methods developed in relation with sparse signal reconstruction problematics - can be used to design efficient optical sensing devices with high spatial and temporal resolution for biological imaging applications. We first investigate some practical issues related to the post-processing stage required by CS acquisition schemes, and to the selection of sampling parameters. We then examine how CS can benefit to video sampling applications. Finally, with the application of CS methods for denoising tasks in mind, we focus on the error estimation issue in image denoising problems for low-light microscopy applications.

The work in this dissertation is focused on two areas within the general discipline of statistical signal processing. First, several new algorithms are developed and exhaustively tested for solving the inverse problem of compressive sensing (CS). CS is a recently developed sub-sampling technique for signal acquisition and reconstruction which is more efficient than the traditional Nyquist sampling method. It provides the possibility of compressed data acquisition approaches to directly acquire just the important information of the signal of interest. Many natural signals are sparse or compressible in some domain such as pixel domain of images, time, frequency and so forth. The notion of compressibility or sparsity here means that many coefficients of the signal of interest are either zero or of low amplitude, in some domain, whereas some are dominating coefficients. Therefore, we may not need to take many direct or indirect samples from the signal or phenomenon to be able to capture the important information of the signal. As a simple example, one can think of a system of linear equations with N unknowns. Traditional methods suggest solving N linearly independent equations to solve for the unknowns. However, if many of the variables are known to be zero or of low amplitude, then intuitively speaking, there will be no need to have N equations. Unfortunately, in many real-world problems, the number of non-zero (effective) variables are unknown. In these cases, CS is capable of solving for the unknowns in an efficient way. In other words, it enables us to collect the important information of the sparse signal with low number of measurements. Then, considering the fact that the signal is sparse, extracting the important information of the signal is the challenge that needs to be addressed. Since most of the existing recovery algorithms in this area need some prior knowledge or parameter tuning, their application to real-world problems to achieve a good performance is difficult. In this dissertation, several new CS algorithms are proposed for the recovery of sparse signals. The proposed algorithms mostly do not require any prior knowledge on the signal or its structure. In fact, these algorithms can learn the underlying structure of the signal based on the collected measurements and successfully reconstruct the signal, with high probability. The other merit of the proposed algorithms is that they are generally flexible in incorporating any prior knowledge on the noise, sparisty level, and so on. The second part of this study is devoted to deployment of mobile sensors in circumstances that the number of sensors to sample the entire region is inadequate. Therefore, where to deploy the sensors, to both explore new regions while refining knowledge in aleady visited areas is of high importance. Here, a new framework is proposed to decide on the trajectories of sensors as they collect the measurements. The proposed framework has two main stages. The first stage performs interpolation/extrapolation to estimate the phenomenon of interest at unseen loactions, and the second stage decides on the informative trajectory based on the collected and estimated data. This framework can be applied to various problems such as tuning the constellation of sensor-bearing satellites, robotics, or any type of adaptive sensor placement/configuration problem. Depending on the problem, some modifications on the constraints in the framework may be needed. As an application side of this work, the proposed framework is applied to a surrogate problem related to the constellation adjustment of sensor-bearing satellites.

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In recent years, sparsity and compressive sensing have attracted significant attention in parameter estimation tasks, including frequency estimation, delay estimation, and localization. Parametric dictionaries collect signals for a sampling of the parameter space and can yield sparse representations for the signals of interest when the sampling is sufficiently dense. While this dense sampling can lead to high coherence in the dictionary, it is possible to leverage structured sparsity models to prevent highly coherent dictionary elements from appearing simultaneously in a signal representation, alleviating these coherence issues. However, the resulting approaches depend heavily on a careful setting of the maximum allowable coherence; furthermore, their guarantees apply to the coefficient vector recovery and do not translate in general to the parameter estimation task. We propose a new algorithm based on optimal sparse approximation measured by earth mover's distance (EMD). Theoretically, we show that EMD provides a better metric for the performance of parametric dictionary-based parameter estimation and $K$-median clustering algorithms has the potential to solve the EMD-optimal sparse approximation problems. Simulations show that the resulting compressive parameter estimation algorithm is better at addressing the coherence issuers without a careful setting of additional parameters.

Typically, inverse imaging problems deal with the reconstruction of images from the sensor measurements where sensors can take form of any imaging modality like camera, radar, hyperspectral or medical imaging systems. In an ideal scenario, we can reconstruct the images via applying an inversion procedure from these sensors’ measurements, but practical applications have several challenges: the measurement acquisition process is heavily corrupted by the noise, the forward model is not exactly known, and non-linearities or unknown physics of the data acquisition play roles. Hence, perfect inverse function is not exactly known for immaculate image reconstruction. To this end, in this dissertation, I propose an automatic sensing and reconstruction scheme based on deep learning within the compressive sensing (CS) framework to solve the computational imaging problems. Here, I develop a data-driven approach to learn both the measurement matrix and the inverse reconstruction scheme for a given class of signals, such as images. This approach paves the way for end-to-end learning and reconstruction of signals with the aid of cascaded fully connected and multistage convolutional layers with a weighted loss function in an adversarial learning framework. I also propose to extend our analysis to introduce data driven models to directly classify from compressed measurements through joint reconstruction and classification. I develop constrained measurement learning framework and demonstrate higher performance of the proposed approach in the field of typical image reconstruction and hyperspectral image classification tasks. Finally, I also propose a single data driven network that can take and reconstruct images at multiple rates of signal acquisition. In summary, this dissertation proposes novel methods on the data driven measurement acquisition for sparse signal reconstruction and classification, learning measurements for given constraints underlying the requirement of the hardware for different applications, and producing a common data driven platform for learning measurements to reconstruct signals at multiple rates. This dissertation opens the path to the learned sensing systems. The future research can use these proposed data driven approaches as the pivotal factors to accomplish task-specific smart sensors in several real-world applications.

High frame rate video (HFV) is an important investigational tool in sciences, engineering and military. In ultrahigh speed imaging, the obtainable temporal, spatial and spectral resolutions are limited by the sustainable throughput of in-camera mass memory, the lower bound of exposure time, and illumination conditions. In order to break these bottlenecks, we propose a new coded video acquisition framework that employs K>1 cameras, each of which makes random measurements of the video signal in both temporal and spatial domains. For each of the K cameras, this multi-camera strategy greatly relaxes the stringent requirements in memory speed, shutter speed, and illumination strength. The recovery of HFV from these random measurements is posed and solved as a large scale l1 minimization problem by exploiting joint temporal and spatial sparsities of the 3D signal. Three coded video acquisition techniques of varied trade o s between performance and hardware complexity are developed: frame-wise coded acquisition, pixel-wise coded acquisition, and column-row-wise coded acquisition. The performances of these techniques are analyzed in relation to the sparsity of the underlying video signal. To make ultra high speed cameras of coded exposure more practical and a fordable, we develop a coded exposure video/image acquisition system by an innovative assembling of multiple rolling shutter cameras. Each of the constituent rolling shutter cameras adopts a random pixel read-out mechanism by simply changing the read out order of pixel rows from sequential to random. Simulations of these new image/video coded acquisition techniques are carried out and experimental results are reported. / Dissertation / Doctor of Philosophy (PhD)

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