Optical coherence tomography (OCT) is a biomedical imaging technique with many current applications. A limitation of the technique is its shallow depth of imaging. A major factor limiting imaging depth in OCT is multiple-scattering of light. This thesis proposes an integrated computational imgaging approach to improve depth of imaging in OCT. In this approach ultrasound patterns are used to modulate the refractive index of tissue. Simulations of the impact of ultrasound on the refractive index are performed, and the results are shown in this thesis. Simulations of the impact of the modulated refractive index on the propagation of light in tissue are needed. But there is no suitable simulator available. Thus, we implemented a Monte Carlo method to solve integral equations that could be used to perform these simulations. Results for integral equations in 1-D and 2-D are shown.

Stimulated Raman scattering (SRS) imaging is a chemical imaging scheme that can visualize cellular content based on intrinsic chemical bond vibrations. To resolve chemicals with overlapping Raman bands, spectroscopic SRS platforms have been developed. To date, endeavors on high-speed instrumentation have achieved spectral acquisition at the microsecond level, enabling in vivo imaging of cells and tissues. Nevertheless, due to the extremely small Raman cross-sections, the current performance of SRS is bounded by a design space that trades off speed, signal fidelity, and spectral bandwidth. The lack of tailored data mining algorithms further limits the chemical information one can extract from the spectroscopic images. My thesis work focuses on developing computational SRS imaging approaches to break the physical tradeoffs and novel data analytical tools to decipher essential chemical information from stimulated Raman spectroscopic images. Utilizing data redundancy of spectroscopic images, we developed two compressive sensing schemes to improve the imaging speed by one order of magnitude without information loss. To break the sensitivity limit, we proposed an ultrafast spectroscopic SRS system and further integrated it with a deep neural network to synergistically achieve microsecond level imaging in the fingerprint region. To improve the chemical specificity and content levels, we implemented a sparsity-regularized spectral unmixing algorithm, realizing multiplexed imaging of up to six major metabolites in a cell. Finally, enabled by advances in low-exposure imaging and spectral unmixing, longitudinal imaging of biofuel synthesis in live cells with sophisticated chemical information is demonstrated. / 2022-09-24T00:00:00Z

X-ray computed tomography (CT) is a popular imaging technique used for reconstructing volumetric properties for a large range of objects. Compared to traditional optical means, CT is a valuable tool for analyzing objects with interesting internal structure or complex geometries that are not accessible with. In this thesis, a variety of applications in computer vision and graphics of inverse problems using tomographic imaging modalities will be presented: The first application focuses on the CT reconstruction with a specific emphasis on recovering thin 1D and 2D manifolds embedded in 3D volumes. To reconstruct such structures at resolutions below the Nyquist limit of the CT image sensor, we devise a new 3D structure tensor prior, which can be incorporated as a regularizer into more traditional proximal optimization methods for CT reconstruction. The second application is about space-time tomography: Through a combination of a new CT image acquisition strategy, a space-time tomographic image formation model, and an alternating, multi-scale solver, we achieve a general approach that can be used to analyze a wide range of dynamic phenomena. Base on the second application, the third one is aiming to improve the tomographic reconstruction of time-varying geometries undergoing faster, non-periodic deformations, by a warp-and-project strategy. Finally, with a physically plausible divergence-free prior for motion estimation, as well as a novel view synthesis technique, we present applications to dynamic fluid imaging (e.g., 4D soot imaging of a combustion process, a mixing fluid process, a fuel injection process, and view synthesis for visible light tomography), which further demonstrates the flexibility of our optimization framework.

Fluorescence microscopy has become an indispensable technology to push fundamental neuroscience by recovering labeled neural structures with high resolution. To enable these studies, the field has adopted the use of low-cost widefield 1-photon epi-fluorescence microscopes to image fixed samples and miniaturized head-mounted miniscopes to monitor neural activity in freely behaving animals. However, fluorescence imaging platforms face a number of challenges such as a limited depth of field (DoF), lack of optical sectioning, and susceptibility to scattering and aberrations which compromises the image quality and signal fidelity. As a result, neural studies are often constrained to a shallow volume near the surface of the sample and are limited by high noise and background. To overcome these challenges, this thesis introduces two novel frameworks that combine pupil engineering with computational imaging to push the performance of miniaturized and tabletop fluorescence neural imaging platforms. These strategies will directly optimize and integrate custom phase elements on the often-vacant pupil plane to enable the encoding of extended fluorescence signals by designing a point spread function (PSF) that exhibits an extended depth of field (EDoF) in scattering media. Next, these strategies will use tailored post processing algorithms to recover that extended information from the resulting images. As a result, this strategy allows for the recovery of sources in an extended neural volume without compromising the optical resolution or imaging speed on the underlying platform. First, this thesis introduces EDoF-Miniscope, a miniaturized neural imaging platform which utilizes a novel physics-informed genetic algorithm to optimize a lightweight binary diffractive optical element (DOE) on the pupil plane. By integrating the binary DOE into a prototype platform, EDoF-Miniscope is able to achieve a 2.8x extension in the DoF between twin imaging foci in neural samples. To enable the recovery of the extended sources, this thesis utilizes a straightforward post-processing filter, which can recover neuronal signals with an SBR down to 1.08. Overall, this framework introduces a generalizable, compact and lightweight solution for augmenting miniscopes with a computational EDoF. Next, I improve upon the proposed framework by designing a flexible 1-photon widefield tabletop platform, entitled EDoF-Tabletop, that exhibits comparable field-of-view (FoV, FoV = 0.6x0.6mm), numerical aperture (NA, NA = 0.5) and aberrations to a miniscope. This platform utilizes a spatial light modulator (SLM) on the pupil plane to rapidly deploy optimized pupil phase profiles without the need of manufacturing, aligning and integrating miniaturized optics. EDoF-Tabletop incorporates a deep optics pipeline, which utilizes novel physical modeling, initialization and training strategies to simultaneously and reliably learn a user-defined EDoFs and a reconstruction using synthetic-only data. As a result, EDoF-Tabletop is able to encode and recover signals from EDoFs up to 140-microns deep in neural samples and 400-microns deep in non-scattering samples. By combining pupil engineering with computational imaging, EDoF-Miniscope and EDoF-Tabletop showcase the potential to enhance neural imaging platforms by extracting information from extended volumes in the brain. By focusing on flexible optimization algorithms and rapid prototyping capabilities, the advancements introduced in this thesis promise broader utility across fluorescence microscopy, where capturing detailed information from complex biological samples is essential for advancing scientific understanding.

<p>The advent of resonant metamaterials with strongly dispersive behavior allowed scientists to design new electromagnetic devices -- including (but not limited to) absorbers, antennas, lenses, holograms, and arguably the most well-known of them all, invisibility cloaks -- exhibiting properties that would otherwise be difficult to obtain. At the heart of these breakthrough designs is our ability to model the behavior of individual metamaterial elements as Lorentzian dipoles, and -- in applications that call for it -- collectively model an entire array of such elements as a homogenous medium with effective electromagnetic properties retrieved from measurements or simulations. </p><p>Of particular interest in the context of this dissertation is a certain type of metamaterials elements which -- while composed entirely of essentially non-magnetic materials -- respond to a magnetic field, can be modeled as magnetic dipoles, and are able to form a material with effective magnetic response. This thesis describes how such ``magnetic metamaterials'' have been utilized by the author when designing devices for applications in wireless power transfer (WPT) and computational imaging. For the former, I discuss in the thesis a metamaterial implementation of a magnetic `superlens' for wireless power transfer enhancements, and a magnetic reflector for near field shielding. For the latter I detail how we model the imaging capabilities of a recently-introduced class of dispersive metamaterial-based leaky apertures that produce pseudo-random measurement modes, and demonstration of novel Lorentzian-constrained holograms able to tailor their radiation patterns. </p><p>To design a magnetic superlens for WPT enhancements, we first demonstrate how an array comprising resonant metamaterial elements can act as an effective medium with negative permeability ($\mu$) and enhance near-field transmission of quasi-static non-resonant coil antennas. We implement a new technique to retrieve all diagonal components of our superlens' permeability, including its normal component, which standard techniques cannot retrieve. We study the effect of different components of the $\mu$ tensor on field enhancements using analytical solutions as well as 2D rotationally-symmetric full-wave simulations which approximate the lens as a disc of equal diameter, enabling highly efficient axisymmetric description of the problem. Our studies indicate enhancements are strongest when all three diagonal components of Re$(\mu)$ are negative, which we attribute to the excitation of surface waves.</p><p>The ability to retrieve permeability's normal component, awarded to us with the implementation of the aforementioned retrieval technique, directly enabled the design of a near field magnetic shield, which -- in contrast to the tripple-negative superlens -- relies on the normal component of $\mu$ assuming values near zero. The thesis discusses the theory behind this phenomenon and explains why such an anisotropic slab is capable of reflecting magnetic fields with component of their wave vector parallel to the slab's surface (fields which contain significant portions of the energy transferred in WPT systems with dipole-like coils). Furthermore, the dispersive nature of the resonant metamaterials used to realize the shield grants us the ability to block certain frequencies while allowing the transmission of other, which can be particularly useful in certain applications; conventional materials used for shielding or electromagnetic interference (EMI) suppression, on the other hand, block frequencies indiscriminately. </p><p>The thesis also discusses a single-pixel, metamaterial-based aperture we designed for computational imaging purposes. This aperture, termed \textit{metaimager}, forms pseudo-random radiation patterns that vary with frequency by leaking energy from a guided mode via a collection of randomly distributed resonant metamaterial elements. The metaimager, then, is able to interrogate a scene without any moving parts or expensive auxiliary hardware (both are common problems which plague synthetic aperture and phased array systems, respectively). While such a structure cannot be homogenized, when modeling its imaging capabilities we still rely on the fact each of its irises can be modeled analytically as a magnetic dipole using a relatively simple Lorentzian expression. Accurate qualitative modeling of such apertures is of paramount importance in the design and optimization stages, since it allows us to save time and money by avoiding prohibitively slow full-wave simulations of such complex structures and unnecessary fabrication processes. </p><p>Lastly, the thesis discusses how such an aperture can be viewed as a hologram in which pixels are realized by the metamaterial elements and the reference wave is realized by the fields that excite them. While the current metaimager implementation produces pseudo-random modes, the last section of the thesis discusses how, by accounting for the Lorentzian constraints of each pixel, a novel metamaterial hologram can be designed to yield tailored radiation patterns. An experiment utilizing a Fraunhofer hologram excited in a free-space illumination configuration indicates tailored modes can indeed be formed by carefully choosing the resonance frequency and location of each metamaterial. While this proof-of-concept example is relatively simple, more sophisticated realizations of such holograms can be explored in future works.</p> / Dissertation

The traditional approach to imaging system design places the sole burden of image formation on optical components. In contrast, a computational imaging system relies on a combination of optics and post-processing to produce the final image and/or output measurement. Therefore, the joint-optimization (JO) of the optical and the post-processing degrees of freedom plays a critical role in the design of computational imaging systems. The JO framework also allows us to incorporate task-specific performance measures to optimize an imaging system for a specific task. In this dissertation, we consider the design of computational imaging systems within a JO framework for two separate tasks: object reconstruction and iris-recognition. The goal of these design studies is to optimize the imaging system to overcome the performance degradations introduced by under-sampled image measurements. Within the JO framework, we engineer the optical point spread function (PSF) of the imager, representing the optical degrees of freedom, in conjunction with the post-processing algorithm parameters to maximize the task performance. For the object reconstruction task, the optimized imaging system achieves a 50% improvement in resolution and nearly 20% lower reconstruction root-mean-square-error (RMSE ) as compared to the un-optimized imaging system. For the iris-recognition task, the optimized imaging system achieves a 33% improvement in false rejection ratio (FRR) for a fixed alarm ratio (FAR) relative to the conventional imaging system. The effect of the performance measures like resolution, RMSE, FRR, and FAR on the optimal design highlights the crucial role of task-specific design metrics in the JO framework. We introduce a fundamental measure of task-specific performance known as task-specific information (TSI), an information-theoretic measure that quantifies the information content of an image measurement relevant to a specific task. A variety of source-models are derived to illustrate the application of a TSI-based analysis to conventional and compressive imaging (CI) systems for various tasks such as target detection and classification. A TSI-based design and optimization framework is also developed and applied to the design of CI systems for the task of target detection, it yields a six-fold performance improvement over the conventional imaging system at low signal-to-noise ratios.

<p>This dissertation studies the coding strategies of computational imaging to overcome the limitation of conventional sensing techniques. The information capacity of conventional sensing is limited by the physical properties of optics, such as aperture size, detector pixels, quantum efficiency, and sampling rate. These parameters determine the spatial, depth, spectral, temporal, and polarization sensitivity of each imager. To increase sensitivity in any dimension can significantly compromise the others. </p><p>This research implements various coding strategies subject to optical multidimensional imaging and acoustic sensing in order to extend their sensing abilities. The proposed coding strategies combine hardware modification and signal processing to exploiting bandwidth and sensitivity from conventional sensors. We discuss the hardware architecture, compression strategies, sensing process modeling, and reconstruction algorithm of each sensing system. </p><p>Optical multidimensional imaging measures three or more dimensional information of the optical signal. Traditional multidimensional imagers acquire extra dimensional information at the cost of degrading temporal or spatial resolution. Compressive multidimensional imaging multiplexes the transverse spatial, spectral, temporal, and polarization information on a two-dimensional (2D) detector. The corresponding spectral, temporal and polarization coding strategies adapt optics, electronic devices, and designed modulation techniques for multiplex measurement. This computational imaging technique provides multispectral, temporal super-resolution, and polarization imaging abilities with minimal loss in spatial resolution and noise level while maintaining or gaining higher temporal resolution. The experimental results prove that the appropriate coding strategies may improve hundreds times more sensing capacity. </p><p>Human auditory system has the astonishing ability in localizing, tracking, and filtering the selected sound sources or information from a noisy environment. Using engineering efforts to accomplish the same task usually requires multiple detectors, advanced computational algorithms, or artificial intelligence systems. Compressive acoustic sensing incorporates acoustic metamaterials in compressive sensing theory to emulate the abilities of sound localization and selective attention. This research investigates and optimizes the sensing capacity and the spatial sensitivity of the acoustic sensor. The well-modeled acoustic sensor allows localizing multiple speakers in both stationary and dynamic auditory scene; and distinguishing mixed conversations from independent sources with high audio recognition rate.</p> / Dissertation

<p>This dissertation explores computational optical imaging methods to circumvent the physical limitations of classical sensing. An ideal imaging system would maximize resolution in time, spectral bandwidth, three-dimensional object space, and polarization. Practically, increasing any one parameter will correspondingly decrease the others.</p><p>Spectrometers strive to measure the power spectral density of the object scene. Traditional pushbroom spectral imagers acquire high resolution spectral and spatial resolution at the expense of acquisition time. Multiplexed spectral imagers acquire spectral and spatial information at each instant of time. Using a coded aperture and dispersive element, the coded aperture snapshot spectral imagers (CASSI) here described leverage correlations between voxels in the spatial-spectral data cube to compressively sample the power spectral density with minimal loss in spatial-spectral resolution while maintaining high temporal resolution.</p><p>Photography is limited by similar physical constraints. Low f/# systems are required for high spatial resolution to circumvent diffraction limits and allow for more photon transfer to the film plain, but require larger optical volumes and more optical elements. Wide field systems similarly suffer from increasing complexity and optical volume. Incorporating a multi-scale optical system, the f/#, resolving power, optical volume and wide field of view become much less coupled. This system uses a single objective lens that images onto a curved spherical focal plane which is relayed by small micro-optics to discrete focal planes. Using this design methodology allows for gigapixel designs at low f/# that are only a few pounds and smaller than a one-foot hemisphere.</p><p>Computational imaging systems add the necessary step of forward modeling and calibration. Since the mapping from object space to image space is no longer directly readable, post-processing is required to display the required data. The CASSI system uses an undersampled measurement matrix that requires inversion while the multi-scale camera requires image stitching and compositing methods for billions of pixels in the image. Calibration methods and a testbed are demonstrated that were developed specifically for these computational imaging systems.</p> / Dissertation

Computational sensing utilizes non-conventional sampling mechanisms along with processing algorithms for accomplishing various sensing tasks. It provides additional flexibility in designing imaging or spectroscopic systems. This dissertation analyzes sampling and signal estimation techniques through three computational sensing systems to accomplish specific tasks. The first is thin long-wave infrared imaging systems through multichannel sampling. Significant reduction in optical system thickness is obtained over a conventional system by modifying conventional sampling mechanisms and applying reconstruction algorithms. In addition, an information theoretic analysis of sampling in conventional as well as multichannel imaging systems is also performed. The feasibility of performing multichannel sampling for imaging is demonstrated using an information theoretic metric. The second system is an application of the multichannel system for the design of compressive low-power video sensors. Two sampling schemes have been demonstrated that utilize spatial as well as temporal aliasing. The third system is a novel computational spectroscopic system for detecting chemicals that utilizes the surface plasmon resonances to encode information about the chemicals that are tested. / Dissertation

<p>The 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. </p><p>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.</p> / Dissertation