Computing upper and lower bounds on linear functional outputs from linear coercive partial differential equations

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2003.Includes bibliographical references (p. 115-123).Uncertainty about the reliability of numerical approximations frequently undermines the utility of field simulations in the engineering design process: simulations are often not trusted because they lack reliable feedback on accuracy, or are more costly than needed because they are performed with greater fidelity than necessary in an attempt to bolster trust. In addition to devitalized confidence, numerical uncertainty often causes ambiguity about the source of any discrepancies when using simulation results in concert with experimental measurements. Can the discretization error account for the discrepancies, or is the underlying continuum model inadequate? This thesis presents a cost effective method for computing guaranteed upper and lower bounds on the values of linear functional outputs of the exact weak solutions to linear coercive partial differential equations with piecewise polynomial forcing posed on polygonal domains. The method results from exploiting the Lagrangian saddle point property engendered by recasting the output problem as a constrained minimization problem. Localization is achieved by Lagrangian relaxation and the bounds are computed by appeal to a local dual problem. The proposed method computes approximate Lagrange multipliers using traditional finite element discretizations to calculate a primal and an adjoint solution along with well known hybridization techniques to calculate interelement continuity multipliers. At the heart of the method lies a local dual problem by which we transform an infinite-dimensional minimization problem into a finite-dimensional feasibility problem.(cont.) The computed bounds hold uniformly for any level of refinement, and in the asymptotic convergence regime of the finite element method, the bound gap decreases at twice the rate of the H¹-norm measure of the error in the finite element solution. Given a finite element solution and its output adjoint solution, the method can be used to provide a certificate of precision for the output with an asymptotic complexity that is linear in the number of elements in the finite element discretization. The complete procedure computes approximate outputs to a given precision in polynomial time. Local information generated by the procedure can be used as an adaptive meshing indicator. We apply the method to Poisson's equation and the steady-state advection-diffusion-reaction equation.by Alexander M. Sauer-Budge.Ph.D

Speckle Effects in Target-in-the-Loop Laser Beam Projection Systems

In target-in-the-loop laser beam projection scenarios typical of remote sensing, directed energy, and adaptive optics applications, a transmitted laser beam propagates through an optically inhomogeneous medium toward a target, scatters off the target’s rough surface, and returns back to the transceiver plane. Coherent beam scattering off the randomly rough surface results in strong speckle modulation in the transceiver plane. This speckle modulation has been a long-standing challenge that limits performance of remote sensing, active imaging, and adaptive optics techniques. Using physics-based models of laser beam scattering off a randomly rough surface, we show that received speckle-field spatial and temporal characteristics can be used to evaluate the intensity distribution of the beam projected onto the target. We derive analytical expressions that directly couple the measured target-return wave statistical characteristics, or ‘speckle metrics’, with characteristics of the laser beam intensity distribution on the target surface. We also show how measured speckle metrics can be utilized for evaluation of laser beam quality at the target surface and for adaptive compensation of atmospheric turbulence-induced phase aberrations

Computational Algorithms for Improved Synthetic Aperture Radar Image Focusing

High-resolution radar imaging is an area undergoing rapid technological and scientific development. Synthetic Aperture Radar (SAR) and Inverse Synthetic Aperture Radar (ISAR) are imaging radars with an ever-increasing number of applications for both civilian and military users. The advancements in phased array radar and digital computing technologies move the trend of this technology towards higher spatial resolution and more advanced imaging modalities. Signal processing algorithm development plays a key role in making full use of these technological developments.In SAR and ISAR imaging, the image reconstruction process is based on using the relative motion between the radar and the scene. An important part of the signal processing chain is the estimation and compensation of this relative motion. The increased spatial resolution and number of receive channels cause the approximations used to derive conventional algorithms for image reconstruction and motion compensation to break down. This leads to limited applicability and performance limitations in non-ideal operating conditions.This thesis presents novel research in the areas of data-driven motion compensation and image reconstruction in non-cooperative ISAR and Multichannel Synthetic Aperture Radar (MSAR) imaging. To overcome the limitations of conventional algorithms, this thesis proposes novel algorithms leading to increased estimation performance and image quality. Because a real-time imaging capability is important in many applications, special emphasis is placed on the computational aspects of the algorithms.For non-cooperative ISAR imaging, the thesis proposes improvements to the range alignment, time window selection, autofocus, time-frequency-based image reconstruction and cross-range scaling procedures. These algorithms are combined into a computationally efficient non-cooperative ISAR imaging algorithm based on mathematical optimization. The improvements are experimentally validated to reduce the computational burden and significantly increase the image quality under complex target motion dynamics.Time domain algorithms offer a non-approximated and general way for image reconstruction in both ISAR and MSAR. Previously, their use has been limited by the available computing power. In this thesis, a contrast optimization approach for time domain ISAR imaging is proposed. The algorithm is demonstrated to produce improved imaging performance under the most challenging motion compensation scenarios. The thesis also presents fast time domain algorithms for MSAR. Numerical simulations confirm that the proposed algorithms offer a reasonable compromise between computational speed and image quality metrics

Advances in Sonar Technology

The demand to explore the largest and also one of the richest parts of our planet, the advances in signal processing promoted by an exponential growth in computation power and a thorough study of sound propagation in the underwater realm, have lead to remarkable advances in sonar technology in the last years.The work on hand is a sum of knowledge of several authors who contributed in various aspects of sonar technology. This book intends to give a broad overview of the advances in sonar technology of the last years that resulted from the research effort of the authors in both sonar systems and their applications. It is intended for scientist and engineers from a variety of backgrounds and even those that never had contact with sonar technology before will find an easy introduction with the topics and principles exposed here

Probabilistic photometric redshift estimation in massive digital sky surveys via machine learning

The problem of photometric redshift estimation is a major subject in astronomy, since the need of estimating distances for a huge number of sources, as required by the data deluge of the recent years. The ability to estimate redshifts through spectroscopy does not scale with this avalanche of data. Photometric redshifts provide the required redshift estimates at the cost of some precision. The success of several forthcoming missions is highly dependent on the availability of photometric redshifts. The purpose of this thesis is to provide innovative methods for photometric redshift estimation. Two models are proposed. The first is fully-automatized, based on the combination of a convolutional neural network with a mixture density network, to predict probabilistic multimodal redshifts directly from images. The second model is features-based, performing a massive combination of photometric parameters to apply a forward selection in a huge feature space. The proposed models perform very efficiently compared to some of the most common models used in the literature. An important part of the work is dedicated to the correct estimation of the errors and prediction quality. The proposed models are very general and can be applied to different topics in astronomy and beyond

Event-based Vision: A Survey

Event cameras are bio-inspired sensors that differ from conventional frame cameras: Instead of capturing images at a fixed rate, they asynchronously measure per-pixel brightness changes, and output a stream of events that encode the time, location and sign of the brightness changes. Event cameras offer attractive properties compared to traditional cameras: high temporal resolution (in the order of microseconds), very high dynamic range (140 dB vs. 60 dB), low power consumption, and high pixel bandwidth (on the order of kHz) resulting in reduced motion blur. Hence, event cameras have a large potential for robotics and computer vision in challenging scenarios for traditional cameras, such as low-latency, high speed, and high dynamic range. However, novel methods are required to process the unconventional output of these sensors in order to unlock their potential. This paper provides a comprehensive overview of the emerging field of event-based vision, with a focus on the applications and the algorithms developed to unlock the outstanding properties of event cameras. We present event cameras from their working principle, the actual sensors that are available and the tasks that they have been used for, from low-level vision (feature detection and tracking, optic flow, etc.) to high-level vision (reconstruction, segmentation, recognition). We also discuss the techniques developed to process events, including learning-based techniques, as well as specialized processors for these novel sensors, such as spiking neural networks. Additionally, we highlight the challenges that remain to be tackled and the opportunities that lie ahead in the search for a more efficient, bio-inspired way for machines to perceive and interact with the world

Digital Image Processing

This book presents several recent advances that are related or fall under the umbrella of 'digital image processing', with the purpose of providing an insight into the possibilities offered by digital image processing algorithms in various fields. The presented mathematical algorithms are accompanied by graphical representations and illustrative examples for an enhanced readability. The chapters are written in a manner that allows even a reader with basic experience and knowledge in the digital image processing field to properly understand the presented algorithms. Concurrently, the structure of the information in this book is such that fellow scientists will be able to use it to push the development of the presented subjects even further