<p dir="ltr">The past two decades have seen photography shift from the hands of professionals to that of the average smartphone user. However, fitting a camera module in the palm of your hand has come with its own cost. The reduced sensor size, and hence the smaller pixels, has made the image inherently noisier due to fewer photons being captured. To compensate for fewer photons, we can increase the exposure of the camera but this may exaggerate the effect of hand shake, making the image blurrier. The presence of both noise and blur has made the post-processing algorithms necessary to produce a clean and sharp image. </p><p dir="ltr">In this thesis, we discuss various methods of deblurring images in the presence of noise. Specifically, we address the problem of photon-limited deconvolution, both with and without the underlying blur kernel being known i.e. non-blind and blind deconvolution respectively. For the problem of blind deconvolution, we discuss the flaws of the conventional approach of joint estimation of the image and blur kernel. This approach, despite its drawbacks, has been the go-to method for solving blind deconvolution for decades. We then discuss the relatively unexplored kernel-first approach to solving the problem which is numerically stable than the alternating minimization counterpart. We show how to implement this framework using deep neural networks in practice for both photon-limited and noiseless deconvolution problems. </p>

<p dir="ltr">X-ray computed tomography (CT) based on photon counting detectors (PCD) extends standard CT by counting detected photons in multiple energy bins. PCD data can be used to increase the contrast-to-noise ratio (CNR), increase spatial resolution, reduce radiation dose, reduce injected contrast dose, and compute a material decomposition using a specified set of basis materials [1]. Current commercial and prototype clinical photon counting CT systems utilize PCD-CT reconstruction methods that either reconstruct from each spectral bin separately, or first create an estimate of a material sinogram using a specified set of basis materials and then reconstruct from these material sinograms. However, existing methods are not able to utilize simultaneously and in a modular fashion both the measured spectral information and advanced prior models in order to produce a material decomposition. </p><p dir="ltr">We describe an efficient, modular framework for PCD-based CT reconstruction and material decomposition using Multi-Agent Consensus Equilibrium (MACE). Portions of this dissertation appear in [2]. Our method employs a detector proximal map or agent that uses PCD measurements to update an estimate of the path length sinogram. We also create a prior agent in the form of a sinogram denoiser that enforces both physical and empirical knowledge about the material-decomposed sinogram. The sinogram reconstruction is computed using the MACE algorithm, which finds an equilibrium solution between the two agents, and the final image is reconstructed from the estimated sinogram. Importantly, the modularity of our method allows the two agents to be designed, implemented, and optimized independently. Our results on simulated data show a substantial (2-3 times) noise reduction vs conventional maximum likelihood reconstruction when applied to a phantom used to evaluate low contrast detectability. Our results with measured data show an even higher reduction (2-12 times) in noise standard deviation. Lastly, we demonstrate our method on a Lungman phantom that more realistically represents the human body. </p>

Material failure begins with strain between atoms and cascades upward into macroscopic damage such as cracks. Therefore, our ability to predict (and therefore prevent) material failure is largely limited by our understanding of this process. This understanding, however, has been impeded by the difficulty of directly observing such phenomena. In this thesis, I discuss recent advances in Bragg coherent diffraction imaging (BCDI) which produce three-dimensional, mesoscopic images of interior strain in microcrystals. In particular, I present a novel algorithm, based on the concept of cyclic-constrained optimization (CCO), for the rapid, coupled reconstruction of a microcrystal from multiple Bragg diffraction patterns. Using coherent diffraction data collected from the Advanced Photon Source (APS), this algorithm achieves resolution comparable to other multipeak BCDI methods at a fraction of the computational cost. As the rate of data production at coherent X-ray sources worldwide continues to increase, such rapid algorithms will be critical to preventing a data analysis bottleneck. I also present a technique for mapping the orientations of crystal grains on a sample by analyzing the positions of Laue diffraction spots when the crystal is illuminated by a polychromatic beam. Each of these two methods constitute a significant contribution to the field of mesoscopic strain analysis.

<div>There is an increasing need to accurately image objects at a high temporal resolution for different applications in order to analyze the underlying physical, chemical, or biological processes. In this thesis, we use advanced models exploiting the image structure and the measurement process in order to achieve an improved temporal resolution. The thesis is divided into three chapters, each corresponding to a different imaging application.</div><div><br></div><div>In the first chapter, we propose a novel method to localize neurons in fluorescence microscopy images. Accurate localization of neurons enables us to scan only the neuron locations instead of the full brain volume and thus improve the temporal resolution of neuron activity monitoring. We formulate the neuron localization problem as an inverse problem where we reconstruct an image that encodes the location of the neuron centers. The sparsity of the neuron centers serves as a prior model, while the forward model comprises of shape models estimated from training data.</div><div><br></div><div>In the second chapter, we introduce multi-slice fusion, a novel framework to incorporate advanced prior models for inverse problems spanning many dimensions such as 4D computed tomography (CT) reconstruction. State of the art 4D reconstruction methods use model based iterative reconstruction (MBIR), but it depends critically on the quality of the prior modeling. Incorporating deep convolutional neural networks (CNNs) in the 4D reconstruction problem is difficult due to computational difficulties and lack of high-dimensional training data. Multi-Slice Fusion integrates the tomographic forward model with multiple low dimensional CNN denoisers along different planes to produce a 4D regularized reconstruction. The improved regularization in multi-slice fusion allows each time-frame to be reconstructed from fewer measurements, resulting in an improved temporal resolution in the reconstruction. Experimental results on sparse-view and limited-angle CT data demonstrate that Multi-Slice Fusion can substantially improve the quality of reconstructions relative to traditional methods, while also being practical to implement and train.</div><div><br></div><div>In the final chapter, we introduce CodEx, a synergistic combination of coded acquisition and a non-convex Bayesian reconstruction for improving acquisition speed in computed tomography (CT). In an ideal ``step-and-shoot'' tomographic acquisition, the object is rotated to each desired angle, and the view is taken. However, step-and-shoot acquisition is slow and can waste photons, so in practice the object typically rotates continuously in time, leading to views that are blurry. This blur can then result in reconstructions with severe motion artifacts. CodEx works by encoding the acquisition with a known binary code that the reconstruction algorithm then inverts. The CodEx reconstruction method uses the alternating direction method of multipliers (ADMM) to split the inverse problem into iterative deblurring and reconstruction sub-problems, making reconstruction practical. CodEx allows for a fast data acquisition leading to a good temporal resolution in the reconstruction.</div>

<p>There is a great need for accurate image reconstruction in the context of non-destructive evaluation. Major challenges include the ever-increasing necessity for high resolution reconstruction with limited scan and reconstruction time and thus fewer and noisier measurements. In this thesis, we leverage advanced Bayesian modeling of the physical measurement process and probabilistic prior information of the image distribution in order to yield higher image quality despite limited measurement time. We demonstrate in several ways efficient computational performance through the exploitation of more efficient memory access, optimized parametrization of the system model, and multi-pixel parallelization. We demonstrate that by building high-fidelity forward models that we can generate quantitatively reliable reconstructions despite very limited measurement data.</p> <p><br></p> <p>In the first chapter, we introduce an algorithm for estimating isotopic densities from neutron time-of-flight imaging data. Energy resolved neutron imaging (ERNI) is an advanced neutron radiography technique capable of non-destructively extracting spatial isotopic information within a given material. Energy-dependent radiography image sequences can be created by utilizing neutron time-of-flight techniques. In combination with uniquely characteristic isotopic neutron cross-section spectra, isotopic areal densities can be determined on a per-pixel basis, thus resulting in a set of areal density images for each isotope present in the sample. By preforming ERNI measurements over several rotational views, an isotope decomposed 3D computed tomography is possible. We demonstrate a method involving a robust and automated background estimation based on a linear programming formulation. The extremely high noise due to low count measurements is overcome using a sparse coding approach. It allows for a significant computation time improvement, from weeks to a few hours compared to existing neutron evaluation tools, enabling at the present stage a semi-quantitative, user-friendly routine application. </p> <p><br></p> <p>In the second chapter, we introduce the TRINIDI algorithm, a more refined algorithm for the same problem.</p> <p>Accurate reconstruction of 2D and 3D isotope densities is a desired capability with great potential impact in applications such as evaluation and development of next-generation nuclear fuels.</p> <p>Neutron time-of-flight (TOF) resonance imaging offers a potential approach by exploiting the characteristic neutron adsorption spectra of each isotope.</p> <p>However, it is a major challenge to compute quantitatively accurate images due to a variety of confounding effects such as severe Poisson noise, background scatter, beam non-uniformity, absorption non-linearity, and extended source pulse duration. We present the TRINIDI algorithm which is based on a two-step process in which we first estimate the neutron flux and background counts, and then reconstruct the areal densities of each isotope and pixel.</p> <p>Both components are based on the inversion of a forward model that accounts for the highly non-linear absorption, energy-dependent emission profile, and Poisson noise, while also modeling the substantial spatio-temporal variation of the background and flux. </p> <p>To do this, we formulate the non-linear inverse problem as two optimization problems that are solved in sequence.</p> <p>We demonstrate on both synthetic and measured data that TRINIDI can reconstruct quantitatively accurate 2D views of isotopic areal density that can then be reconstructed into quantitatively accurate 3D volumes of isotopic volumetric density.</p> <p><br></p> <p>In the third chapter, we introduce a separable forward model for cone-beam computed tomography (CT) that enables efficient computation of a Bayesian model-based reconstruction. Cone-beam CT is an attractive tool for many kinds of non-destructive evaluation (NDE). Model-based iterative reconstruction (MBIR) has been shown to improve reconstruction quality and reduce scan time. However, the computational burden and storage of the system matrix is challenging. In this paper we present a separable representation of the system matrix that can be completely stored in memory and accessed cache-efficiently. This is done by quantizing the voxel position for one of the separable subproblems. A parallelized algorithm, which we refer to as zipline update, is presented that speeds up the computation of the solution by about 50 to 100 times on 20 cores by updating groups of voxels together. The quality of the reconstruction and algorithmic scalability are demonstrated on real cone-beam CT data from an NDE application. We show that the reconstruction can be done from a sparse set of projection views while reducing artifacts visible in the conventional filtered back projection (FBP) reconstruction. We present qualitative results using a Markov Random Field (MRF) prior and a Plug-and-Play denoiser.</p>

[pt] Câmeras de pixel único consistem em reconstruir computacionalmente imagens em duas dimensões a partir de um conjunto de medidas feitas por um detector de único pixel. Para que se obtenha a informação espacial, um conjunto de padrões de modulação são aplicados à luz transmitida/refletida do objeto e essa informação é combinada com o sinal integral do detector. Primeiro, apresentamos uma visão geral desses sistemas e demonstramos a implementação de uma prova de conceito capaz de fazer aquisição de imagem usando três modos de operação: Varredura, escaneamento por base de Hadamard, e escaneamento por base de Hadamard com sensoriamento compreensivo. Segundo, discutimos como os diferentes parâmetros experimentais do sistema ótico afetam a aquisição. Finalmente, comparamos a performance dos três modos de operação quando usados para a aquisição de images com tamanhos entre (8px, 8px) e (128px, 128px). / [en] Single-pixel imaging consists in computationally reconstructing 2-dimensional images from a set of intensity measurements taken by a singlepoint detector. To derive the spatial information of a scene, a set of modulation patterns are applied to the transmitted/backscattered light from the object and combined with the integral signal on the detector. First, we present an overview of such optical systems and implement a proof of concept that can perform image acquisition using three different modes of operation: Raster scanning, Hadamard basis scanning, and Hadamard compressive sampling. Second, we explore how the different experimental parameters affect image acquisition. Finally, we compare how the three scanning mode perform for acquisition of images of sizes ranging from (8px, 8px) to (128px, 128px).

<p dir="ltr">In this dissertation, efforts and innovations are made to advance subtle pattern mining, edge computing, and system efficiency optimization for biomedical applications, thereby advancing precision medicine big data.</p><p dir="ltr">Brain visual dynamics encode rich functional and biological patterns of the neural system, promising for applications like intention decoding, cognitive load quantization and neural disorder measurement. We here focus on the understanding of the brain visual dynamics for the Amyotrophic lateral sclerosis (ALS) population. We leverage a deep learning framework for automatic feature learning and classification, which can translate the eye Electrooculography (EOG) signal to meaningful words. We then build an edge computing platform on the smart phone, for learning, visualization, and decoded word demonstration, all in real-time. In a further study, we have leveraged deep transfer learning to boost EOG decoding effectiveness. More specifically, the model trained on basic eye movements is leveraged and treated as an additional feature extractor when classifying the signal to the meaningful word, resulting in higher accuracy.</p><p dir="ltr">Efforts are further made to decoding functional Near-Infrared Spectroscopy (fNIRS) signal, which encodes rich brain dynamics like the cognitive load. We have proposed a novel Multi-view Multi-channel Graph Neural Network (mmGNN). More specifically, we propose to mine the multi-channel fNIRS dynamics with a multi-stage GNN that can effectively extract the channel- specific patterns, propagate patterns among channels, and fuse patterns for high-level abstraction. Further, we boost the learning capability with multi-view learning to mine pertinent patterns in temporal, spectral, time-frequency, and statistical domains.</p><p dir="ltr">Massive-device systems, like wearable massive-sensor computers and Internet of Things (IoTs), are promising in the era of big data. The crucial challenge is about how to maximize the efficiency under coupling constraints like energy budget, computing, and communication. We propose a deep reinforcement learning framework, with a pattern booster and a learning adaptor. This framework has demonstrated optimally maximizes the energy utilization and computing efficiency on the local massive devices under a one-center fifteen-device circumstance.</p><p dir="ltr">Our research and findings are expected to greatly advance the intelligent, real-time, and efficient big data harnessing, leveraging deep learning, edge computing, and efficiency optimization.</p>

<pre>Coherent lidar uses a chirped laser pulse for 3D imaging of distant targets.However, existing coherent lidar image reconstruction methods do not account for the system's aperture, resulting in sub-optimal resolution.Moreover, these methods use majorization-minimization for computational efficiency, but do so without a theoretical treatment of convergence.<br> <br>In this work, we present Coherent Lidar Aperture Modeled Plug-and-Play (CLAMP) for multi-look coherent lidar image reconstruction.CLAMP uses multi-agent consensus equilibrium (a form of PnP) to combine a neural network denoiser with an accurate physics-based forward model.CLAMP introduces an FFT-based method to account for the effects of the aperture and uses majorization of the forward model for computational efficiency.We also formalize the use of majorization-minimization in consensus optimization problems and prove convergence to the exact consensus equilibrium solution.Finally, we apply CLAMP to synthetic and measured data to demonstrate its effectiveness in producing high-resolution, speckle-free, 3D imagery.</pre><p></p>

<p><br></p><p dir="ltr">Achieving high optical resolution imaging is one of the most important goals in the history of optics. However, due to finite aperture sizes, a diffraction limit is imposed on optical imaging. Therefore, the Rayleigh limit, which describes the minimum separation at which two point sources are resolvable, has served as a critical limit in optical resolution. Many methods have been studied to break the limit and succeed in resolving nearby sources below the Rayleigh criterion but only beyond a certain distance. Furthermore, it has been demonstrated that quantum-inspired optics techniques maintain consistent variance in estimating the separation of point sources even at low separations, but only with prior information like a known number of sources and equal brightness. Therefore, achieving the ultimate optical resolution remains an open question. This thesis will conclusively address this challenge considering real-world scenarios, i.e., no prior information or controlled lab environment as well as low signal-to-noise ratio (SNR), turbulence, and other practical challenges.</p><p><br></p><p dir="ltr">In information theory, the estimation variance of a random parameter can be quantified using the inverse of Fisher information. By maximizing the Fisher information, one can minimize the variance in estimation. In my thesis, we have shown that the measurement can be accelerated without sacrificing optical resolution using the adaptive mode so that quantum Fisher information per detected photon is maximized. The notable attribute that sets it apart from other quantum-inspired methods is that it does not require any prior information, making it more feasible for practical application. We have further shown that the space domain awareness (SDA) challenge can be effectively handled with the aforementioned approach with a very limited photon budget and even in the presence of turbulence. Toward solving the challenges, we designed a photon statistics-based direct imaging method that can also serve as a baseline method for quantum optics. In my thesis, atmospheric turbulence is also deeply explored and the effect is mitigated using reinforcement learning.</p><p><br></p>

<p dir="ltr">Imaging and sensing through opaque scattering media is a topic of broad interest with a wide range of applications. Methods are impacted by speckle, which refers to grainy patterns of bright and dark spots resulting from coherent interference as light propagates through a randomly scattering medium. This phenomenon is most often considered undesirable in applications. However, it is possible to leverage the information contained in speckle patterns to image hidden objects. In practice, most methods are limited to situations in which the scattering medium is either thin or weakly scattering. This thesis explores a motion-based coherent imaging and sensing method originally developed by prior researchers. This technique takes advantage of heavy scatter and object motion, with no theoretical limit on the amount of scatter. In this method, intensity correlations are performed on speckle images taken with the object at different spatial locations. Prior research led to the development of a theory that describes the relationship between speckle intensity correlations and the object's geometry. This thesis presents substantial new understanding pertaining to the theory that allows for the imaging of general objects in heavily scattering media. Additionally, it is shown that two nominally identical objects can be distinguished through speckle intensity correlations over far-subwavelength translation distances, implying access to the microstructure of objects. Finally, the combining of this method with diffusion-based localization is demonstrated, providing a way to apply this imaging and sensing method without prior knowledge of the object's relative spatial locations.</p>