Browsing by Author "Willett, Rebecca M"
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Item Open Access Compressive holography.(2012) Lim, Se HoonCompressive holography estimates images from incomplete data by using sparsity priors. Compressive holography combines digital holography and compressive sensing. Digital holography consists of computational image estimation from data captured by an electronic focal plane array. Compressive sensing enables accurate data reconstruction by prior knowledge on desired signal. Computational and optical co-design optimally supports compressive holography in the joint computational and optical domain. This dissertation explores two examples of compressive holography : estimation of 3D tomographic images from 2D data and estimation of images from under sampled apertures. Compressive holography achieves single shot holographic tomography using decompressive inference. In general, 3D image reconstruction suffers from underdetermined measurements with a 2D detector. Specifically, single shot holographic tomography shows the uniqueness problem in the axial direction because the inversion is ill-posed. Compressive sensing alleviates the ill-posed problem by enforcing some sparsity constraints. Holographic tomography is applied for video-rate microscopic imaging and diffuse object imaging. In diffuse object imaging, sparsity priors are not valid in coherent image basis due to speckle. So incoherent image estimation is designed to hold the sparsity in incoherent image basis by support of multiple speckle realizations. High pixel count holography achieves high resolution and wide field-of-view imaging. Coherent aperture synthesis can be one method to increase the aperture size of a detector. Scanning-based synthetic aperture confronts a multivariable global optimization problem due to time-space measurement errors. A hierarchical estimation strategy divides the global problem into multiple local problems with support of computational and optical co-design. Compressive sparse aperture holography can be another method. Compressive sparse sampling collects most of significant field information with a small fill factor because object scattered fields are locally redundant. Incoherent image estimation is adopted for the expanded modulation transfer function and compressive reconstruction.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 Efficient Inference for High Dimensional Data Under Physical and Human Constraints(2017) Hunt, Xin JiangBig data has become ubiquitous due to the advances of modern sensors -- high-resolution cameras capture millions of pixels at every fraction of a second, from both on the ground and in satellites; high-throughput experiments in biology and physical sciences generate terabytes of data everyday; people post on average 350,000 tweets on Twitter every minute. Big data problems are inherently different from traditional signals due to a few key salient features: high Volume, high Velocity, and high Variety. These three "V"s are the major challenges modern data science faces.
The volume of big data is reflected in both the number of data points, and the dimensionality of each data point. Large numbers of data points put hard constraints on the computational and space complexities of the systems, while high-dimensional data results in the classical "curse of dimensionality". The problem is further complicated by the fact that high-volume data often lacks meaningful labels or thorough annotations, which can make high-dimensional problems ill-posed even when large quantities of data are available.
The velocity of data refers to the speed of data acquisition in streaming data. For instance, commercial video systems usually work at a thirty to sixty per second frame rate, while the new high-speed camera at MIT can capture a stunning one trillion frames per second. High-velocity data requires the system to be both efficient and "online", i.e., to be able to update models and estimates on the fly.
The variety of data includes both data types and data dynamics. Big data often come in multiple sources. For example, healthcare record data may include numerical test readings, images of Ultrasound, CT and MRI scans, and texts of symptom descriptions. A person's Facebook profile is often comprised of various types of data like videos, images, texts, and social interactions. Moreover, the distribution of data can change with time or location, and different applications may have various physical and human constraints that impose further dynamics on the systems. As a result, efficient methods not only need to work with multiple data sources, but also need to adapt to potential dynamics within the data.
Data science focuses on extracting useful information from these challenging data. Most existing methods and analyses fail in the big data setting because they do NOT account for the dynamic environments, limited quantities of labeled data, physical models, or other system constraints. This dissertation describes methods that account for these challenges, and novel insights resulting from those methods.
The first contribution of this dissertation is minimax lower and upper bounds for high-dimensional Poisson inverse problems under physical constraints. In this problem, high dimensionality prevails, and physical constraints invalidate classical measurement matrices.
In addition to the bounds, a novel alternative analysis approach and a weighted LASSO estimator for sparse Poisson inverse problems are proposed to sidestep the technical challenges present in previous work. The next contribution is a method for online data thinning, in which large-scale streaming datasets are winnowed to preserve unique, anomalous, or salient elements for timely expert analysis. This application is challenged by the dimension and velocity of the data, as well as a highly dynamic environment. The last contribution is the development of a real-time interactive search system and an empirical evaluation of a new and various state-of-the-art search algorithms on both simulated and real users. The main challenges in this application are the high data volume, unlabeled data, a finite time horizon, and low processing time due to human interactions.
Item Open Access Exploiting Multi-Look Information for Landmine Detection in Forward Looking Infrared Video(2013) Malof, JordanForward Looking Infrared (FLIR) cameras have recently been studied as a sensing modality for use in landmine detection systems. FLIR-based detection systems benefit from larger standoff distances and faster rates of advance than other sensing modalities, but they also present significant challenges for detection algorithm design. FLIR video typically yields multiple looks at each object in the scene, each from a different camera perspective. As a result each object in the scene appears in multiple video frames, and each time at a different shape and size. This presents questions about how best to utilize such information. Evidence in the literature suggests such multi-look information can be exploited to improve detection performance but, to date, there has been no controlled investigation of multi-look information in detection. Any results are further confounded because no precise definition exists for what constitutes multi-look information. This thesis addresses these problems by developing a precise mathematical definition of "a look", and how to quantify the multi-look content of video data. Controlled experiments are conducted to assess the impact of multi-look information on FLIR detection using several popular detection algorithms. Based on these results two novel video processing techniques are presented, the plan-view framework and the FLRX algorithm, to better exploit multi-look information. The results show that multi-look information can have a positive or negative impact on detection performance depending on how it is used. The results also show that the novel algorithms presented here are effective techniques for analyzing video and exploiting any multi-look information to improve detection performance.
Item Open Access High-Dimensional Inference in Dynamic Environments(2015) Hall, EricThis thesis addresses several challenges unanswered in classical statistics. The first is the problem of sequentially arriving data in changing environments. It is often the case that the order in which data is received can be critically important to accurate inference, and this observation is especially important when the underlying environment generating the data is likely to be changing and one wishes to study the mechanisms driving this change. For instance, in a wide range of applications, including video analytics, social networks, microscopy, and astronomy, analysts must cope with large quantities of high-dimensional data generated by an environment which is known to be changing. Classical methods often fail on such data because they ignore the underlying dynamics, neglect physical models of data generation and statistics, or fail to scale up to high-dimensions both computationally and statistically. While incorporating time-varying, dynamical models can significantly increase statistical accuracy, the difficulty and complexity of learning are increased because there are now two sources of potential errors: observational noise and environmental change. Classical methods which do not account for time variation would attribute all errors to observational noise, while some techniques, such as those used in autoregressive moving average models, would attribute most of the variation to system dynamics. This thesis presents work which learns a systems' dynamics and state simultaneously, while avoiding such strong assumptions.
The second challenge crucial to the learning process is the ability to handle the recent onslaught of information known as ``big data." Two types of challenges big data present are large volumes of data and large dimensionality of data, and algorithmic design must address these challenges. In order to process high volume data algorithms must process data very efficiently in order to complete all its calculations in a reasonable amount of time, while high-dimensional data requires algorithms to perform efficient inference in a potentially vastly underdetermined system. Within both of these regimes analysts face the question of ``how much data must be collected before reliable inference can be guaranteed?" Such questions are typically addressed via sample complexity and regret bounds, but the existing literature on these bounds does not account for the sequential nature and inherent dependencies among the observed data. Methods such as LASSO have become popular in the last decade, as they prove that the amount of data necessary should scale more closely to the low-dimensional subspace on which the data resides, as opposed to the larger, ambient dimension. These types of observations are critical, and the need to find low-dimensional structure in high dimensional signals is of paramount importance and should be addressed in proposed algorithms. Nevertheless, most LASSO analysis does not address streaming data or temporal dependencies common when tracking dynamic environments.
This thesis presents novel algorithms and analyses which address the issues posed by big data in dynamic environments. The first contribution is to propose methods to analyze sequential data in a dynamic environment using online optimization. Online optimization schemes are inherently designed for high volume data, as they receive one datum at a time, make a quick calculation, and then discard it. These methods are additionally adept at processing high-dimensional data, as they incorporate regularization functions that attempt to find low-dimensional structure in high-dimensional data. The proposed online optimization routines account for time varying environments with associated regret bounds, while making minimal assumptions on the underlying system. Unlike previous work in sequential filtering, these methods do not need the dynamical model to be specified a priori, but instead have built-in mechanisms to find the best model within a family of candidate dynamics. The next contribution is to use these methods to analyze data generated by a Hawkes process, a model which is used to characterize complex interactions among a collection of point processes, for instance neurons firing within a network. Using this analysis, network inference on streaming data can be performed with more robustness to poorly-specified model parameters than previously existing methods. Finally, previously unknown sample complexity bounds for a discretized version of the Hawkes process, the log-linear Poisson autoregressive process, are shown and proven. These results, which utilize recent advances in statistical learning theory, show how the assumption of low dimensional structure can greatly aid in the estimation procedure of high dimensional data.
Item Open Access Spectral Image Processing Theory and Methods: Reconstruction, Target Detection, and Fundamental Performance Bounds(2011) Krishnamurthy, KalyaniThis dissertation presents methods and associated performance bounds for spectral image processing tasks such as reconstruction and target detection, which are useful in a variety of applications such as astronomical imaging, biomedical imaging and remote sensing. The key idea behind our spectral image processing methods is the fact that important information in a spectral image can often be captured by low-dimensional manifolds embedded in high-dimensional spectral data. Based on this key idea, our work focuses on the reconstruction of spectral images from photon-limited, and distorted observations.
This dissertation presents a partition-based, maximum penalized likelihood method that recovers spectral images from noisy observations and enjoys several useful properties; namely, it (a) adapts to spatial and spectral smoothness of the underlying spectral image, (b) is computationally efficient, (c) is near-minimax optimal over an anisotropic Holder-Besov function class, and (d) can be extended to inverse problem frameworks.
There are many applications where accurate localization of desired targets in a spectral image is more crucial than a complete reconstruction. Our work draws its inspiration from classical detection theory and compressed sensing to develop computationally efficient methods to detect targets from few projection measurements of each spectrum in the spectral image. Assuming the availability of a spectral dictionary of possible targets, the methods discussed in this work detect targets that either come from the spectral dictionary or otherwise. The theoretical performance bounds offer insight on the performance of our detectors as a function of the number of measurements, signal-to-noise ratio, background contamination and properties of the spectral dictionary.
A related problem is that of level set estimation where the goal is to detect the regions in an image where the underlying intensity function exceeds a threshold. This dissertation studies the problem of accurately extracting the level set of a function from indirect projection measurements without reconstructing the underlying function. Our partition-based set estimation method extracts the level set of proxy observations constructed from such projection measurements. The theoretical analysis presented in this work illustrates how the projection matrix, proxy construction and signal strength of the underlying function affect the estimation performance.
Item Open Access Topics in Online Markov Decision Processes(2015) Guan, PengThis dissertation describes sequential decision making problems in non-stationary environments. Online learning algorithms deal with non-stationary environments, but generally there is no notion of a dynamic state to model future impacts of past actions. State-based models are common in stochastic control settings, but well-known frameworks such as Markov decision processes (MDPs) assume a known stationary environment. In recent years, there has been a growing interest in fusing the above two important learning frameworks and considering an MDP setting in which the cost function is allowed to change arbitrarily over time. A number of online MDP algorithms have been designed to work under various assumptions about the dynamics of state transitions so far and provide performance guarantees, i.e. bounds on the regret defined as the performance gap between the total cost incurred by the learner and the total cost of the best available stationary policy that could have been chosen in hindsight.
However, most of the work in this area has been algorithmic: given a problem, one
would develop an algorithm almost from scratch and prove the performance guarantees on a case-by-case basis. Moreover, the presence of the state and the assumption of an arbitrarily varying environment complicate both the theoretical analysis and the development of computationally efficient methods. Another potential issue is that, by removing distributional assumptions about the mechanism generating the cost sequences, the existing methods have to consider the worst-case scenario, which may render their solutions too conservative in situations where the environment exhibits some degree of predictability.
This dissertation contributes several novel techniques to address the above challenges of the online MDP framework and opens up new research directions for online MDPs.
Our proposed general framework for deriving algorithms in the online MDP setting leads to a unifying view of existing methods and provides a general procedure for constructing new ones. Several new algorithms are developed and analyzed using this framework. We develop convex-analytical algorithms that take advantage of possible regularity of observed sequences, yet maintain the worst case performance guarantees. To further study the convex-analytic methods we applied above, we take a step back to consider the traditional MDP problem and extend the LP approach to MDPs by adding a relative entropy regularization term. A computationally efficient algorithm for this class of MDPs is constructed under mild assumptions on the state transition models. Two-player zero-sum stochastic games are also investigated in this dissertation as an important extension of the online MDP setting. In short, this dissertation provides in-depth analysis of the online MDP problem and answers several important questions in this field.