A U-Net to Identify Deforested Areas in Satellite Imagery of the Amazon

Description
Deforestation in the Amazon rainforest has the potential to have devastating effects on ecosystems on both a local and global scale, making it one of the most environmentally threatening phenomena occurring today. In order to minimize deforestation in the Ama- zon and its…

Deforestation in the Amazon rainforest has the potential to have devastating effects on ecosystems on both a local and global scale, making it one of the most environmentally threatening phenomena occurring today. In order to minimize deforestation in the Ama- zon and its consequences, it is helpful to analyze its occurrence using machine learning architectures such as the U-Net. The U-Net is a type of Fully Convolutional Network that has shown significant capability in performing semantic segmentation. It is built upon a symmetric series of downsampling and upsampling layers that propagate feature infor- mation into higher spatial resolutions, allowing for the precise identification of features on the pixel scale. Such an architecture is well-suited for identifying features in satellite imagery. In this thesis, we construct and train a U-Net to identify deforested areas in satellite imagery of the Amazon through semantic segmentation.
Date Created
2024-05
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Texture Metrics for Arctic Sea Ice Elevation Modeling Using LiDAR and Optical Imagery

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Description
Recent satellite and remote sensing innovations have led to an eruption in the amount and variety of geospatial ice data available to the public, permitting in-depth study of high-definition ice imagery and digital elevation models (DEMs) for the goal of…

Recent satellite and remote sensing innovations have led to an eruption in the amount and variety of geospatial ice data available to the public, permitting in-depth study of high-definition ice imagery and digital elevation models (DEMs) for the goal of safe maritime navigation and climate monitoring. Few researchers have investigated texture in optical imagery as a predictive measure of Arctic sea ice thickness due to its cloud pollution, uniformity, and lack of distinct features that make it incompatible with standard feature descriptors. Thus, this paper implements three suitable ice texture metrics on 1640 Arctic sea ice image patches, namely (1) variance pooling, (2) gray-level co-occurrence matrices (GLCMs), and (3) textons, to assess the feasibly of a texture-based ice thickness regression model. Results indicate that of all texture metrics studied, only one GLCM statistic, namely homogeneity, bore any correlation (0.15) to ice freeboard.
Date Created
2024-05
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A U-Net to Identify Deforested Areas in Satellite Imagery of the Amazon

Description
Deforestation in the Amazon rainforest has the potential to have devastating effects on ecosystems on both a local and global scale, making it one of the most environmentally threatening phenomena occurring today. In order to minimize deforestation in the Amazon…

Deforestation in the Amazon rainforest has the potential to have devastating effects on ecosystems on both a local and global scale, making it one of the most environmentally threatening phenomena occurring today. In order to minimize deforestation in the Amazon and its consequences, it is helpful to analyze its occurrence using machine learning architectures such as the U-Net. The U-Net is a type of Fully Convolutional Network that has shown significant capability in performing semantic segmentation. It is built upon a symmetric series of downsampling and upsampling layers that propagate feature information into higher spatial resolutions, allowing for the precise identification of features on the pixel scale. Such an architecture is well-suited for identifying features in satellite imagery. In this thesis, we construct and train a U-Net to identify deforested areas in satellite imagery of the Amazon through semantic segmentation.
Date Created
2024-05
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Bayesian Inference for Markov Kernels Valued in Wasserstein Spaces

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Description
In this work, the author analyzes quantitative and structural aspects of Bayesian inference using Markov kernels, Wasserstein metrics, and Kantorovich monads. In particular, the author shows the following main results: first, that Markov kernels can be viewed as Borel measurable…

In this work, the author analyzes quantitative and structural aspects of Bayesian inference using Markov kernels, Wasserstein metrics, and Kantorovich monads. In particular, the author shows the following main results: first, that Markov kernels can be viewed as Borel measurable maps with values in a Wasserstein space; second, that the Disintegration Theorem can be interpreted as a literal equality of integrals using an original theory of integration for Markov kernels; third, that the Kantorovich monad can be defined for Wasserstein metrics of any order; and finally, that, under certain assumptions, a generalized Bayes’s Law for Markov kernels provably leads to convergence of the expected posterior distribution in the Wasserstein metric. These contributions provide a basis for studying further convergence, approximation, and stability properties of Bayesian inverse maps and inference processes using a unified theoretical framework that bridges between statistical inference, machine learning, and probabilistic programming semantics.
Date Created
2023
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Learning-based Estimation of Parameters for Spectral Windowed Regularization using Multiple Data Sets

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Description
During the inversion of discrete linear systems, noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during inversion. This is a process called regularization.…

During the inversion of discrete linear systems, noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during inversion. This is a process called regularization. The influence of the provided prior information is controlled by the introduction of non-negative regularization parameter(s). Many methods are available for both the selection of appropriate regularization parame- ters and the inversion of the discrete linear system. Generally, for a single problem there is just one regularization parameter. Here, a learning approach is considered to identify a single regularization parameter based on the use of multiple data sets de- scribed by a linear system with a common model matrix. The situation with multiple regularization parameters that weight different spectral components of the solution is considered as well. To obtain these multiple parameters, standard methods are modified for identifying the optimal regularization parameters. Modifications of the unbiased predictive risk estimation, generalized cross validation, and the discrepancy principle are derived for finding spectral windowing regularization parameters. These estimators are extended for finding the regularization parameters when multiple data sets with common system matrices are available. Statistical analysis of these estima- tors is conducted for real and complex transformations of data. It is demonstrated that spectral windowing regularization parameters can be learned from these new esti- mators applied for multiple data and with multiple windows. Numerical experiments evaluating these new methods demonstrate that these modified methods, which do not require the use of true data for learning regularization parameters, are effective and efficient, and perform comparably to a supervised learning method based on es- timating the parameters using true data. The theoretical developments are validated for one and two dimensional image deblurring. It is verified that the obtained estimates of spectral windowing regularization parameters can be used effectively on validation data sets that are separate from the training data, and do not require known data.
Date Created
2023
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Partition of Unity Methods for Solving Partial Differential Equations on Surfaces

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Description
Solving partial differential equations on surfaces has many applications including modeling chemical diffusion, pattern formation, geophysics and texture mapping. This dissertation presents two techniques for solving time dependent partial differential equations on various surfaces using the partition of unity method.…

Solving partial differential equations on surfaces has many applications including modeling chemical diffusion, pattern formation, geophysics and texture mapping. This dissertation presents two techniques for solving time dependent partial differential equations on various surfaces using the partition of unity method. A novel spectral cubed sphere method that utilizes the windowed Fourier technique is presented and used for both approximating functions on spherical domains and solving partial differential equations. The spectral cubed sphere method is applied to solve the transport equation as well as the diffusion equation on the unit sphere. The second approach is a partition of unity method with local radial basis function approximations. This technique is also used to explore the effect of the node distribution as it is well known that node choice plays an important role in the accuracy and stability of an approximation. A greedy algorithm is implemented to generate good interpolation nodes using the column pivoting QR factorization. The partition of unity radial basis function method is applied to solve the diffusion equation on the sphere as well as a system of reaction-diffusion equations on multiple surfaces including the surface of a red blood cell, a torus, and the Stanford bunny. Accuracy and stability of both methods are investigated.
Date Created
2021
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Recursive Bayesian Estimation on Projective Spaces: Theoretical Foundations and Practical Algorithms

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Description
This thesis develops geometrically and statistically rigorous foundations for multivariate analysis and bayesian inference posed on grassmannian manifolds. Requisite to the development of key elements of statistical theory in a geometric realm are closed-form, analytic expressions for many differential geometric…

This thesis develops geometrically and statistically rigorous foundations for multivariate analysis and bayesian inference posed on grassmannian manifolds. Requisite to the development of key elements of statistical theory in a geometric realm are closed-form, analytic expressions for many differential geometric objects, e.g., tangent vectors, metrics, geodesics, volume forms. The first part of this thesis is devoted to a mathematical exposition of these. In particular, it leverages the classical work of Alan James to derive the exterior calculus of differential forms on special grassmannians for invariant measures with respect to which integration is permissible. Motivated by various multi-­sensor remote sensing applications, the second part of this thesis describes the problem of recursively estimating the state of a dynamical system propagating on the Grassmann manifold. Fundamental to the bayesian treatment of this problem is the choice of a suitable probability distribution to a priori model the state. Using the Method of Maximum Entropy, a derivation of maximum-­entropy probability distributions on the state space that uses the developed geometric theory is characterized. Statistical analyses of these distributions, including parameter estimation, are also presented. These probability distributions and the statistical analysis thereof are original contributions. Using the bayesian framework, two recursive estimation algorithms, both of which rely on noisy measurements on (special cases of) the Grassmann manifold, are the devised and implemented numerically. The first is applied to an idealized scenario, the second to a more practically motivated scenario. The novelty of both of these algorithms lies in the use of thederived maximum­entropy probability measures as models for the priors. Numerical simulations demonstrate that, under mild assumptions, both estimation algorithms produce accurate and statistically meaningful outputs. This thesis aims to chart the interface between differential geometry and statistical signal processing. It is my deepest hope that the geometric-statistical approach underlying this work facilitates and encourages the development of new theories and new computational methods in geometry. Application of these, in turn, will bring new insights and bettersolutions to a number of extant and emerging problems in signal processing.
Date Created
2021
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Demodulation and Leading-Edge Detection for LiDAR Pulses

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Description

The idea for this thesis emerged from my senior design capstone project, A Wearable Threat Awareness System. A TFmini-S LiDAR sensor is used as one component of this system; the functionality of and signal processing behind this type of sensor…

The idea for this thesis emerged from my senior design capstone project, A Wearable Threat Awareness System. A TFmini-S LiDAR sensor is used as one component of this system; the functionality of and signal processing behind this type of sensor are elucidated in this document. Conceptual implementations of the optical and digital stages of the signal processing is described in some detail. Following an introduction in which some general background knowledge about LiDAR is set forth, the body of the thesis is organized into two main sections. The first section focuses on optical processing to demodulate the received signal backscattered from the target object. This section describes the key steps in demodulation and illustrates them with computer simulation. A series of graphs capture the mathematical form of the signal as it progresses through the optical processing stages, ultimately yielding the baseband envelope which is converted to digital form for estimation of the leading edge of the pulse waveform using a digital algorithm. The next section is on range estimation. It describes the digital algorithm designed to estimate the arrival time of the leading edge of the optical pulse signal. This enables the pulse’s time of flight to be estimated, thus determining the distance between the LiDAR and the target. Performance of this algorithm is assessed with four different levels of noise. A calculation of the error in the leading-edge detection in terms of distance is also included to provide more insight into the algorithm’s accuracy.

Date Created
2022-05
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The Role of Fourier Phase in Image Representation and Reconstruction

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Description

The Fourier representation of a signal or image is equivalent to its native representation in the sense that the signal or image can be reconstructed exactly from its Fourier transform. The Fourier transform is generally complex-valued, and each value of…

The Fourier representation of a signal or image is equivalent to its native representation in the sense that the signal or image can be reconstructed exactly from its Fourier transform. The Fourier transform is generally complex-valued, and each value of the Fourier spectrum thus possesses both magnitude and phase. Degradation of signals and images when Fourier phase information is lost or corrupted has been studied extensively in the signal processing research literature, as has reconstruction of signals and images using only Fourier magnitude information. This thesis focuses on the case of images, where it examines the visual effect of quantifiable levels of Fourier phase loss and, in particular, studies the merits of introducing varying degrees of phase information in a classical iterative algorithm for reconstructing an image from its Fourier magnitude.

Date Created
2021-05
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Model-Based Machine Learning for the Power Grid

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Description
The availability of data for monitoring and controlling the electrical grid has increased exponentially over the years in both resolution and quantity leaving a large data footprint. This dissertation is motivated by the need for equivalent representations of…

The availability of data for monitoring and controlling the electrical grid has increased exponentially over the years in both resolution and quantity leaving a large data footprint. This dissertation is motivated by the need for equivalent representations of grid data in lower-dimensional feature spaces so that machine learning algorithms can be employed for a variety of purposes. To achieve that, without sacrificing the interpretation of the results, the dissertation leverages the physics behind power systems, well-known laws that underlie this man-made infrastructure, and the nature of the underlying stochastic phenomena that define the system operating conditions as the backbone for modeling data from the grid.

The first part of the dissertation introduces a new framework of graph signal processing (GSP) for the power grid, Grid-GSP, and applies it to voltage phasor measurements that characterize the overall system state of the power grid. Concepts from GSP are used in conjunction with known power system models in order to highlight the low-dimensional structure in data and present generative models for voltage phasors measurements. Applications such as identification of graphical communities, network inference, interpolation of missing data, detection of false data injection attacks and data compression are explored wherein Grid-GSP based generative models are used.

The second part of the dissertation develops a model for a joint statistical description of solar photo-voltaic (PV) power and the outdoor temperature which can lead to better management of power generation resources so that electricity demand such as air conditioning and supply from solar power are always matched in the face of stochasticity. The low-rank structure inherent in solar PV power data is used for forecasting and to detect partial-shading type of faults in solar panels.
Date Created
2020
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