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Browsing by Author "Cheney, Margaret, advisor"

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    Compound-Gaussian-regularized inverse problems: theory, algorithms, and neural networks
    (Colorado State University. Libraries, 2024) Lyons, Carter, author; Cheney, Margaret, advisor; Raj, Raghu G., advisor; Azimi, Mahmood, committee member; King, Emily, committee member; Mueller, Jennifer, committee member
    Linear inverse problems are frequently encountered in a variety of applications including compressive sensing, radar, sonar, medical, and tomographic imaging. Model-based and data-driven methods are two prevalent classes of approaches used to solve linear inverse problems. Model-based methods incorporate certain assumptions, such as the image prior distribution, into an iterative estimation algorithm, often, as an example, solving a regularized least squares problem. Instead, data-driven methods learn the inverse reconstruction mapping directly by training a neural network structure on actual signal and signal measurement pairs. Alternatively, algorithm unrolling, a recent approach to inverse problems, combines model-based and data-driven methods through the implementation of an iterative estimation algorithm as a deep neural network (DNN). This approach offers a vehicle to embed domain-level and algorithmic insights into the design of neural networks such that the network layers are interpretable. The performance, in reconstructed signal quality, of unrolled DNNs often exceeds that of corresponding iterative algorithms and standard DNNs while doing so in a computationally efficient fashion. In this work, we leverage algorithm unrolling to combine a powerful statistical prior, the compound Gaussian (CG) prior, with the powerful representational ability of machine learning and DNN approaches. Specifically, first we construct a novel iterative CG-regularized least squares algorithm for signal reconstruction and provide a computational theory for this algorithm. Second, using algorithm unrolling, the newly developed CG-based least squares iterative algorithm is transformed into an original DNN in a manner to facilitate the learning of the optimization landscape geometry. Third, a generalization on the newly constructed CG regularized least squares iterative algorithm is developed, theoretically analyzed, and unrolled to yield a novel state-of-the-art DNN that provides a partial learning of the prior distribution constrained to the CG class of distributions. Fourth, techniques in statistical learning theory are employed for deriving original generalization error bounds on both unrolled DNNs to substantiate theoretical guarantees of each neural network when estimating signals from linear measurements after training. Finally, ample numerical experimentation is conducted for every new CG-based iterative and DNN approach proposed in this paper. Simulation results show our methods outperform previous state-of-the-art iterative signal estimation algorithms and deep-learning-based methods, especially with limited training datasets.
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    General model-based decomposition framework for polarimetric SAR images
    (Colorado State University. Libraries, 2017) Dauphin, Stephen, author; Cheney, Margaret, advisor; Kirby, Michael, committee member; Pinaud, Olivier, committee member; Morton, Jade, committee member
    Polarimetric synthetic aperture radars emit a signal and measure the magnitude, phase, and polarization of the return. Polarimetric decompositions are used to extract physically meaningful attributes of the scatterers. Of these, model-based decompositions intend to model the measured data with canonical scatter-types. Many advances have been made to this field of model-based decomposition and this work is surveyed by the first portion of this dissertation. A general model-based decomposition framework (GMBDF) is established that can decompose polarimetric data with different scatter-types and evaluate how well those scatter-types model the data by comparing a residual term. The GMBDF solves for all the scatter-type parameters simultaneously that are within a given decomposition by minimizing the residual term. A decomposition with a lower residual term contains better scatter-type models for the given data. An example is worked through that compares two decompositions with different surface scatter-type models. As an application of the polarimetric decomposition analysis, a novel terrain classification algorithm of polSAR images is proposed. In the algorithm, the results of state-of-the-art polarimetric decompositions are processed for an image. Pixels are then selected to represent different terrain classes. Distributions of the parameters of these selected pixels are determined for each class. Each pixel in the image is given a score according to how well its parameters fit the parameter distributions of each class. Based on this score, the pixel is either assigned to a predefined terrain class or labeled unclassified.
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    Joint shape and motion estimation from echo-based sensor data
    (Colorado State University. Libraries, 2018) Pine, Samuel J., author; Cheney, Margaret, advisor; Bates, Daniel, committee member; Fosdick, Bailey, committee member; Peterson, Christopher, committee member
    Given a set of time-series data collected from echo-based ranging sensors, we study the problem of jointly estimating the shape and motion of the target under observation when the sensor positions are also unknown. Using an approach first described by Stuff et al., we model the target as a point configuration in Euclidean space and estimate geometric invariants of the configuration. The geometric invariants allow us to estimate the target shape, from which we can estimate the motion of the target relative to the sensor position. This work will unify the various geometric- invariant based shape and motion estimation literature under a common framework, and extend that framework to include results for passive, bistatic sensor systems.
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    Resource allocation for space domain awareness and synthetic aperture radar
    (Colorado State University. Libraries, 2022) Owens-Fahrner, Naomi, author; Cheney, Margaret, advisor; Mueller, Jennifer, committee member; Shipman, Patrick, committee member; Chandrasekar, Venkatachalam, committee member
    In this thesis, we will address two resource allocation problems. For each of these problems, the objective will be to make use of the resources in an optimal way. We will consider the Space Domain Awareness (SDA) sensor tasking problem as well as the Synthetic Aperture Radar (SAR) flight path planning problem. We will first present a new objective function for the problem of Space Domain Awareness resource allocation (SDARA) as well as a novel algorithm to maximize this new objective function. This SDARA problem aims to maximize the total number of targets seen while minimizing resource costs. These resources, namely the optical sensors, are assumed to be heterogeneous and have different associated tasking costs. The novel algorithm, called the "block greedy" algorithm, provides an approximate regional maximum of this objective function in a tractable amount of time. The block greedy algorithm is a hybrid of the weapon-target-assignment and greedy algorithms. This algorithm will be shown to outperform common algorithms used in solving the SDARA problem. Second, we will present an approach to create an optimal SAR flight path by varying the vehicle's heading, pitch, and antenna steering angles. An optimal flight path is one in which the scene coverage and resolution are maximized. We will utilize the data-collection manifold as a tool to measure scene resolution. We will then add a scene coverage consideration to build an objective function in which we can plan an optimal flight path for an aircraft. After this, we will consider many extensions and applications of using this objective function. These include adding a signal-to-noise ratio (SNR) consideration to SAR flight path planning. Additionally, we will extend this objective function to include multiple unmanned aerial vehicle (UAVs) for optimal flight paths for a SAR system. We will use our objective function to optimally plan flight paths for multiple UAVs.
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    Synthetic aperture source localization
    (Colorado State University. Libraries, 2018) Waddington, Chad, author; Cheney, Margaret, advisor; Pinaud, Oliver, committee member; Mueller, Jennifer, committee member; Given, James, committee member; Yang, Liuqing, committee member
    The detection and localization of sources of electromagnetic (EM) radiation has many applications in both civilian and defense communities. The goal of source localization is to identify the geographic position of an emitter of some radiation from measurements of the elds that the source produces. Although the problem has been studied intensively for many decades much work remains to be done. Many state-of-the-art methods require large numbers of sensors and perform poorly or require additional sensors when target emitters transmit highly correlated waveforms. Some methods also require a preprocessing step which attempts to identify regions of the data which come from emitters in the scene before processing the localization algorithm. Additionally, it has been proven that pure Angle of Arrival (AOA) techniques based on current methods are always suboptimal when multiple emitters are present. We present a new source localization technique which employs a cross correlation measure of the Time Dierence of Arrival (TDOA) for signals recorded at two separate platforms, at least one of which is in motion. This data is then backprojected through a Synthetic Aperture Radar (SAR)-like process to form an image of the locations of the emitters in a target scene. This method has the advantage of not requiring any a priori knowledge of the number of emitters in the scene. Nor does it rest on an ability to identify regions of the data which come from individual emitters, though if this capability is present it may improve image quality. Additionally we demonstrate that this method is capable of localizing emitters which transmit highly correlated waveforms, though complications arise when several such emitters are present in the scene. We discuss these complications and strategies to mitigate them. Finally we conclude with an overview of our method's performance for various levels of additive noise and lay out a path for advancing study of this new method through future work.