phdthesis.bib

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@PHDTHESIS{orozco2024THgmf,
  author = {Rafael Orozco},
  title = {GENERATIVE MODELS FOR UNCERTAINTY QUANTIFICATION OF MEDICAL AND SEISMIC IMAGING},
  school = {Georgia Institute of Technology},
  year = {2024},
  month = {12},
  address = {Atlanta},
  abstract = {This thesis investigates the intersection of machine learning-based generative models
with physics-based methods to address imaging problems, with an emphasis on accelerat-
ing computations while incorporating uncertainty quantification. Throughout the chapters,
a key conclusion emerges: machine learning methods, though powerful, are insufficient
when used in isolation. They must be combined with the trusted domain knowledge con-
tained in numerical physics simulations to achieve robust results. The methods presented
bridge two of the most impactful areas in modern computer science: numerical simula-
tions methods rooted in linear algebra and the transformative potential of deep learning,
particularly as exemplified by recent advancements in generative modeling.

The focus of this work is on scenarios where the underlying physics is computation-
ally expensive, requiring frugal use of simulations. This is particularly relevant in high-
dimensional, ill-posed inverse problems, such as those encountered in the applications
shown in this thesis: medical imaging and seismic exploration, where the forward oper-
ator is governed by complex partial differential equations (PDEs).

To address these challenges, this thesis introduces techniques that blend practical ma-
chine learning approaches with theoretical insights, particularly through the use of physics-
based summary statistics. These statistics enable efficient extraction of meaningful in-
formation from physics simulations, reducing computational overhead while preserving
the critical elements of the physical model. Theoretical foundations underpin the design
choices, ensuring that the methods are both efficient and ameliorate the potential bias that
would arise from using physics-based summary statistics instead of raw observations.

As an engineering-focused work, the thesis places a strong emphasis on practicality
and robustness. The proposed methods are stress-tested through validation experiments, on
increasingly complex scenarios with a clear pathway toward deployment in the real-world.
This applied perspective reflects the ultimate goal of leveraging these methods to create
tangible, impactful changes in domains such as healthcare and geophysics. By bridging
the gap between advanced machine learning and trusted physics-based methods, this work
contributes to the development of innovative tools that balance computational efficiency,
uncertainty quantification, and practical applicability.},
  
  keywords = {PhD, inverse problems, medical imaging, generative models, Bayesian inference, time-lapse, ccs, gcs, normalizing flows, conditional normalizing flows, variational inference, WISE, WISER, monitoring, FWI, RTM, CIG, uncertainty quantification, scientific machine learning},
  note = {(PhD)},
  url = {https://slim.gatech.edu/Publications/Public/Thesis/2024/orozco2024THgmf/Thesis_Orozco_pdf.pdf},
  presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2024/orozco2024THgmf/defense-real}
}

@PHDTHESIS{yin2024THsgi,
  author = {Ziyi Yin},
  title = {Solving geophysical inverse problems with scientific machine learning},
  school = {Georgia Institute of Technology},
  year = {2024},
  month = {06},
  address = {Atlanta},
  abstract = {Solving inverse problems involves estimating unknown parameters of interest from indirect measurements. Specifically, geophysical inverse problems seek to determine various Earth properties critical for geophysical exploration, carbon control, monitoring, and earthquake detection. These problems pose unique challenges: the parameters of interest are often high-dimensional, and the mapping from parameters to observables is computationally demanding. Moreover, these problems are typically non-convex and ill-posed, meaning that multiple sets of model parameters can adequately fit the observations, and inversion algorithms depend on accurate initial model parameters.

This thesis introduces several innovative methods to tackle these challenges using scientific machine learning techniques. It discusses algorithms and software frameworks that utilize surrogate and generative models to achieve scalable and reliable inversion. It also examines the integration of conditional generative models with physics for Bayesian variational inference and uncertainty quantification. These methods have been applied to two critical inverse problems in geophysical applications: monitoring geological carbon storage and full-waveform inversion, both of which are plagued by the aforementioned computational challenges.

The thesis consists of six papers. The first two papers present a scalable, interoperable, and differentiable programming framework for learned multiphysics inversion, showcased through realistic synthetic case studies in geological carbon storage monitoring. The third paper introduces a computationally efficient and reliable algorithm that employs surrogate models, particularly Fourier neural operators, to accelerate inversion. The reliability of this algorithm is ensured by using normalizing flows as learned constraints to safeguard the accuracy of the surrogate models throughout the inversion process. The subsequent paper explores a joint inversion approach and an explainable deep neural classifier for time-lapse seismic imaging and carbon dioxide leakage detection during geological carbon storage. The final two papers introduce amortized and semi-amortized variational inference approaches that employ information-preserving physics-informed summary statistics and refinements to provide computationally feasible and reliable uncertainty quantification in high-dimensional full-waveform inversion problems. They also assess the impact of the inherent uncertainty in these ill-posed inversion problems on subsequent imaging tasks.},
  keywords = {PhD, inverse problems, generative models, Bayesian inference, time-lapse, JRM, ccs, gcs, end-to-end, Fourier neural operators, normalizing flows, conditional normalizing flows, variational inference, WISE, WISER, monitoring, FWI, RTM, CIG, uncertainty quantification, scientific machine learning},
  note = {(PhD)},
  url = {https://slim.gatech.edu/Publications/Public/Thesis/2024/yin2024THsgi/yin2024THsgi.pdf},
  presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2024/yin2024THsgi/yin2024THsgi_pres.pdf}
}

@PHDTHESIS{zhang2023THlsw,
  author = {Yijun Zhang},
  title = {Large scale wavefield reconstruction via weighted matrix factorization and seismic survey design},
  school = {Georgia Institute of Technology},
  year = {2023},
  month = {06},
  address = {Atlanta},
  abstract = {Seismic data acquisition plays a crucial role in identifying potential oil and gas reservoirs during the early phases of exploration. However, obtaining finely sampled seismic data can be costly and physically impossible. Recent developments in Compressive Sensing have resulted in seismic data being increasingly collected at random along spatial coordinates. Although random sampling improves acquisition efficiency, it shifts the burden from seismic acquisition to data processing. Wavefield recovery is one of the required processes for reconstructing fully seismic data from coarsely subsampled data. Among the various techniques proposed for wavefield reconstruction, matrix completion methods are computationally efficient and straightforward to implement. These methods exploit the low-rank structure of fully seismic data. However, matrix completion performs well at low-to-mid frequencies and degrades at higher frequencies due to the failure of low-rank structure to accurately approximate higher frequencies. To address this issue, this thesis proposed a recursively weighted matrix completion method. Although effective, this method is computationally expensive, and a more efficient method for handling 2D seismic data was also proposed. Compared to 2D seismic data, 3D seismic data can detect reflections outside of the 2D plane but poses a computational challenge due to its large scale. To overcome this challenge, this thesis proposed a parallel weighted reconstruction method to improve the reconstruction of 3D seismic data. Land seismic data presents a greater challenge due to contamination by ground roll, which consists of surface waves with a high spatial frequency content and large amplitude. To address this issue, a practical workflow was proposed in this thesis to improve the recovery of land seismic data. Although matrix completion is an efficient technique for reconstructing fully seismic data, the optimal acquisition design is still being investigated. Recent studies have shown that the spectral gap can be used to predict and characterize the quality of wavefield reconstruction via matrix completion for a given subsampling mask. Based on these findings, a simulation-free seismic survey design for both 2D and 3D seismic data was proposed in this thesis to obtain an improved subsampling survey by minimizing the spectral gap ratio. Furthermore, this concept was extended to the design of a time-lapse seismic survey, which is essential for reservoir management and monitoring geological carbon storage but is difficult and expensive to acquire. To improve the reconstruction of the time-lapse wavefield, a joint recovery model was proposed that leverages the benefits of the non-replicated baseline and monitor subsampled seismic data. A time-lapse seismic survey design that incorporates the joint recovery model with spectral gap was proposed to generate sparse, non-replicated time-lapse acquisition geometries that favor wavefield recovery.},
  keywords = {PhD, time-lapse, JRM, acquisition, survey design, wavefield reconstruction, spectral gap, matrix factorization, 5D reconstruction, compressed sensing, frequency-domain, parallel, signal processing},
  note = {(PhD)},
  url = {https://slim.gatech.edu/Publications/Public/Thesis/2023/zhang2023THlsw/zhang2023THlsw.pdf},
  presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2023/zhang2023THlsw/zhang2023THlsw_pres.pdf},
  url2 = {https://slim.gatech.edu/Publications/Public/Thesis/2023/zhang2023THlsw}
}

@PHDTHESIS{siahkoohi2022THdgmf,
  author = {Ali Siahkoohi},
  title = {Deep generative models for solving geophysical inverse problems},
  school = {Georgia Institute of Technology},
  year = {2022},
  month = {07},
  address = {Atlanta},
  abstract = {My thesis presents several novel methods to facilitate solving large-scale
inverse problems by utilizing recent advances in machine learning, and
particularly deep generative modeling. Inverse problems involve reliably
estimating unknown parameters of a physical model from indirect observed data
that are noisy. Solving inverse problems presents primarily two challenges.
The first challenge is to capture and incorporate prior knowledge into
ill-posed inverse problems whose solutions cannot be uniquely identified. The
second challenge is the computational complexity of solving inverse problems,
particularly the cost of quantifying uncertainty. The main goal of this
thesis is to address these issues by developing practical data-driven methods
that are scalable to geophysical applications in which access to high-quality
training data is often limited.

There are six papers included in this thesis. A majority of these papers
focus on addressing computational challenges associated with Bayesian
inference and uncertainty quantification, while others focus on developing
regularization techniques to improve inverse problem solution quality and
accelerate the solution process. These papers demonstrate the applicability
of the proposed methods to seismic imaging, a large-scale geophysical inverse
problem with a computationally expensive forward operator for which
sufficiently capturing the variability in the Earth's heterogeneous
subsurface through a training dataset is challenging.

The first two papers present computationally feasible methods of applying a
class of methods commonly referred to as deep priors to seismic imaging and
uncertainty quantification. I also present a systematic Bayesian approach to
translate uncertainty in seismic imaging to uncertainty in downstream tasks
performed on the image. The next two papers aim to address the reliability
concerns surrounding data-driven methods for solving Bayesian inverse
problems by leveraging variational inference formulations that offer the
benefits of fully-learned posteriors while being directly informed by physics
and data. The last two papers are concerned with correcting forward modeling
errors where the first proposes an adversarially learned postprocessing step
to attenuate numerical dispersion artifacts in wave-equation simulations due
to coarse finite-difference discretizations, while the second trains a
Fourier neural operator surrogate forward model in order to accelerate the
qualification of uncertainty due to errors in the forward model
parameterization.},
  keywords = {PhD, Geophysics, Inverse Problems, Generative models, Bayesian Inference, Deep Learning},
  note = {(PhD)},
  url = {https://slim.gatech.edu/Publications/Public/Thesis/2022/siahkoohi2022THdgmf/siahkoohi2022THdgmf.pdf},
  presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2022/siahkoohi2022THdgmf/siahkoohi2022THdgmf_pres.pdf}
}

@PHDTHESIS{sharan2020THlsh,
  author = {Shashin Sharan},
  title = {Large scale high-frequency seismic wavefield reconstruction, acquisition via rank minimization and sparsity-promoting source estimation},
  school = {Georgia Institute of Technology},
  year = {2020},
  month = {11},
  address = {Atlanta},
  abstract = {Seismic data reconstruction on a dense periodic grid from seismic
data acquired on a coarse grid is a common approach followed by most of the
oil & gas companies. This approach allows them to save on operationally
challenging and expensive dense seismic data acquisition. Dense seismic data
is one of the key requirements for generating high-resolution images of
earth's subsurface for exploration and production decisions. Based on the
Compressive Sensing (CS) paradigm, low-rank matrix factorization based
seismic data reconstruction methods are computationally cheaper and scalable
to large datasets in comparison to sparsity-promotion based methods. The
sparsity-promotion based methods are based on transformation in certain
transform domains that can be computationally expensive for large datasets.
Although, low-rank matrix factorization based methods perform well at lower
frequencies, their performance degrades at higher frequencies due to increase
in rank of approximating matrix. One of the contributions of this thesis is a
recursively weighted matrix factorization approach to improve the quality of
reconstructed data at higher frequencies. This recursively weighted approach
exploits the similarity between adjacent frequency slices. Although,
recursively weighted method improves the data reconstruction quality at
higher frequencies, it can be computationally expensive for large scale
seismic datasets. This is because of the interdependence of frequencies
preventing simultaneous reconstruction of frequencies. Another contribution
of this thesis is a computationally efficient recursively weighted framework
for large scale dataset by parallelizing data reconstruction over rows of
low-rank factors of each frequency slices. To reduce the cost and turnaround
time of seismic data acquisition simultaneous source acquisition is adapted
by the oil and gas industry in last few years. Another contribution of this
thesis is a low-rank based method for simultaneous separation and
reconstruction of seismic data on a dense periodic grid from large scale
seismic data acquired with simultaneous source acquisition. Next part of this
thesis focuses on accurate detection of fractures created by hydraulic
fracturing in unconventional reservoirs for economical production of oil and
gas. Fracturing of rocks during hydraulic fracturing gives rise to
microseismic events, which are localized along these fractures. In this work,
a sparsity-promoting microseismic source estimation framework is proposed to
detect closely spaced microseismic sources along with estimation of their
associated source-time functions from noisy microseismic data recorded by
receivers along the earth's surface or along monitor wells. Detecting closely
spaced microseismic events helps in delineating fractures and estimation of
source-time function is useful in estimating fracture's origin in time. Also,
source-time functions can be potentially useful for estimating the
source-mechanism. Also, this method does not make any prior assumption on
number of microseismic sources or shape of their source-time functions.
Therefore, this method is useful for detecting microseismic sources with
different source signatures and frequency content. Last part of this thesis
focuses on sparsity-promoting photoacoustic imaging to detect photoabsorbers
along with estimating the associated source-time functions. Traditional
photoacoustic imaging can only estimate the locations of photoacoustic
absorbers. Also, traditional methods require dense transducer coverage
whereas sparsity-promotion based method can work with reduced transducer
sampling reducing the overall data storage cost.},
  keywords = {PhD, Sparsity-promoting, Low-Rank, Wavefield Reconstruction, Compressed Sensing},
  note = {(PhD)},
  url = {https://slim.gatech.edu/Publications/Public/Thesis/2020/sharan2020THlsh/sharan2020THlsh.pdf},
  presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2020/sharan2020THlsh/sharan2020THlsh_pres.pdf}
}

@PHDTHESIS{louboutin2020THmfi,
  author = {Mathias Louboutin},
  title = {Modeling for inversion in exploration geophysics},
  school = {Georgia Institute of Technology},
  year = {2020},
  month = {03},
  address = {Atlanta},
  abstract = {Seismic inversion, and more generally geophysical exploration, aims at better
understanding the earth's subsurface, which is one of today's most important
challenges. Firstly, it contains natural resources that are critical to our
technologies such as water, minerals and oil and gas. Secondly, monitoring
the subsurface in the context of CO2 sequestration, earthquake detection and
global seismology are of major interests with regard to safety and the
environment hazards. However, the technologies to monitor the subsurface or
find resources are scientifically extremely challenging. Seismic inversion
can be formulated as a mathematical optimization problem that minimizes the
difference between field recorded data and numerically modeled synthetic
data. The process of solving this optimization problem then requires to
numerically model, thousands of times, wave-propagation in large
three-dimensional representations of part of the earth subsurface. The
mathematical and computational complexity of this problem, therefore, calls
for software design that abstracts these requirements and facilitates
algorithm and software development.

My thesis addresses some of the challenges that arise from these problems;
mainly the computational cost and access to the right software for research
and development. In the first part, I will discuss a performance metric that
improves the current runtime-only benchmarks in exploration geophysics. This
metric, the roofline model, first provides insight at the hardware level of
the performance of a given implementation relative to the maximum achievable
performance. Second, this study demonstrates that the choice of numerical
discretization has a major impact on the achievable performance depending on
the hardware at hand and shows that a flexible framework with respect to the
discretization parameters is necessary. In the second part, I will introduce
and describe Devito, a symbolic finite-difference DSL that provides a
high-level interface to the definition of partial differential equations
(PDE) such as the wave equation. Devito, from the symbolic definition of
PDEs, then generates and compiles highly optimized C code on-the-fly to
compute the solution of the PDE. The combination of the high-level
abstractions and the just-in-time compiler enable research for geophysical
exploration and PDE-constrainted optimization based on the paradigm of
separation of concerns. This allows researchers to concentrate on their
respective field of study while having access to computationally performant
solvers with a flexible and easy to use interface to successfully implement
complex representations of the physics. The second part of my thesis will be
split into two sub-parts; first describing the symbolic application
programming interface (API), before describing and benchmarking the
just-in-time compiler. I will end my thesis with concluding remarks, the
latest developments and a brief description of projects that were enabled by
Devito.},
  keywords = {PhD, Finite-differences, HPC, performance, Imaging, Modeling, Inversion, FWI, RTM},
  note = {(PhD)},
  url = {https://slim.gatech.edu/Publications/Public/Thesis/2020/louboutin2020THmfi/louboutin2020THmfi.pdf},
  presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2020/louboutin2020THmfi/louboutin2020THmfi_pres.pdf}
}

@PHDTHESIS{witte2020THsal,
  author = {Philipp A. Witte},
  title = {Software and algorithms for large-scale seismic inverse problems},
  school = {Georgia Institute of Technology},
  year = {2020},
  month = {02},
  address = {Atlanta},
  abstract = {Seismic imaging and parameter estimation are an import class of inverse
problems with practical relevance in resource exploration, carbon control and
monitoring systems for geohazards. The goal of seismic inverse problems is to
image subsurface geological structures and estimate physical rock properties
such as wave speed or density. Mathematically, this can be achieved by
solving an optimization problem in which we minimize the mismatch between
numerically modeled data and observed data from a seismic survey. As wave
propagation through a medium is described by wave equations, seismic inverse
problems involve solving a large number of partial differential equations
(PDEs) during numerical optimization using finite difference modeling, making
them computationally expensive. Additionally, seismic inverse problems are
typically ill-posed, non-convex or ill-conditioned, thus making them
challenging from a mathematical standpoint as well. Similar to the field of
deep learning, this calls for software that is not only optimized for
performance, but also enables geophysical domain specialists to experiment
with algorithms in high-level programming languages and using different
computing environments, such as high-performance computing (HPC) clusters or
the cloud. Furthermore, they call for the adaption of dimensionality
reduction techniques and stochastic algorithms to address computational cost
from the algorithmic side.

This thesis makes three distinct contributions to address computational
challenges encountered in seismic inverse problems and to facilitate
algorithmic development in this field. Part one introduces a large-scale
framework for seismic modeling and inversion based on the paradigm of
separation of concerns, which combines a user interface based on domain
specific abstractions with a Python package for automatic code generation to
solve the underlying PDEs. The modular code structure makes it possible to
manage the complexity of a seismic inversion code, while matrix-free linear
operators and data containers enable the implementation of algorithms in a
fashion that closely resembles the underlying mathematical notation. The
second contribution of this thesis is an algorithm for seismic imaging, that
addresses its high computational cost and large memory imprint through a
combination of on-the-fly Fourier transforms, stochastic sampling techniques
and sparsity-promoting optimization. The algorithm combines the best of both
time- and frequency-domain inversion, as the memory imprint is independent of
the number of modeled time steps, while time-to-frequency conversions avoid
the need to solve Helmholtz equations, which involve inverting
ill-conditioned matrices. Part three of this thesis introduces a novel
approach for adapting the cloud for high-performance computing applications
like seismic imaging, which does not rely on a fixed cluster of permanently
running virtual machines. Instead, computational resources are automatically
started and terminated by the cloud environment during runtime and the
workflow takes advantage of cloud-native technologies such as event-driven
computations and containerized batch processing. The performance and cost
analysis shows that this approach is able to address current shortcomings of
the cloud such as inferior resilience, while at the same time reducing
operating cost up to an order of magnitude. As such, the workflow provides a
strategy for cost effectively running large-scale seismic imaging problems in
the cloud and is a viable alternative to conventional HPC clusters.},
  keywords = {PhD, seismic, imaging, RTM, FWI, AWS, software, algorithms},
  note = {(PhD)},
  url = {https://slim.gatech.edu/Publications/Public/Thesis/2020/witte2020THsal/witte2020THsal.pdf},
  presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2020/witte2020THsal/witte2020THsal_pres.pdf}
}

@PHDTHESIS{yang2020THsiw,
  author = {Mengmeng Yang},
  title = {Seismic imaging with extended image volumes and source estimation},
  school = {Georgia Institute of Technology},
  year = {2020},
  month = {03},
  address = {Atlanta},
  abstract = {Seismic imaging is an important tool for the exploration and production of
oil & gas, carbon sequestration, and the mitigation of geohazards. Through
the process of seismic migration, images of subsurface geological structures
are created from data collected at the surface. These images reflect changes
in the physical rock properties such as wave speed and density. While
significant progress has been made in the development of 3D imaging
technology for complex geological areas, several challenges remain, some of
which are addressed in this thesis. The first main contribution of this
thesis is in the area of creating so-called subsurface-offset gathers, which
play an increasingly important role in seismic imaging because they provide a
multitude of information ranging from the reflection mechanism itself to
information of the dips of specific reflectors and the accuracy of the
background velocity model. Unfortunately, the formation and manipulation of
these gathers
come with exceedingly high computational and storage costs because extended
image volumes are quadratic in the image size. These high costs are avoided
by using techniques from modern randomized linear algebra that allow for
compression of extended image volumes
into low-rank factorized form—i.e., the image volume is approximately
written as an outer product of a tall and a wide matrix. It is demonstrated
that this factorization provides access to different types of sub-surface
offset gathers, including common-image (point)
gathers, without the need to explicitly form this outer product. As a result,
challenging steep dip imaging situations, where conventional horizontal
offset gathers no longer focus, can be handled. Moreover, extended image
volumes for one background velocity model can directly be mapped to those of
another background velocity model. As a result, factorization costs are
incurred only once when examining imaging scenarios for different background
velocity models. The second main contribution of this thesis is on the
development of computationally efficient sparsity-promoting imaging
techniques and on-the-fly source estimation. In this work, an adaptive
technique is proposed where the unknown time signature of the sources is
estimated during imaging. Without accurate knowledge of these source
signatures, seismic images can be wrongly positioned and can have the wrong
amplitudes hampering subsequent geophysical and geological interpretations.
With the presented technique, this problem is mitigated. Finally, a
contribution is made to address the detrimental effects of surface-related
multiples. If not handled correctly, these multiples give rise to unwanted
artifacts in the image. A new technique is introduced to address this issue
in realistic settings where there is a strong density contrast at the ocean
bottom. As a result, the surface-related multiples are mapped to the
reflectors. Because bounce points at the surface can be considered as
sources, this mapping of the multiples rather than removal increases the
subsurface illumination.},
  keywords = {PhD, Extended image volumes, low rank, randomized linear algebra,
sparsity-promoting inversion, multiples, source estimation},
  note = {(PhD)},
  url = {https://slim.gatech.edu/Publications/Public/Thesis/2020/yang2020THsiw/yang2020THsiw.pdf},
  presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2020/yang2020THsiw/yang2020THsiw_pres.pdf}
}


%-----2019-----%

@PHDTHESIS{peters2019THiso,
  author = {Bas Peters},
  title = {Intersections and sums of sets for the regularization of inverse problems},
  school = {The University of British Columbia},
  year = {2019},
  month = {05},
  address = {Vancouver},
  abstract = {Inverse problems in the imaging sciences encompass a variety of
applications. The primary problem of interest is the identification of
physical parameters from observed data that come from experiments
governed by partial-differential-equations. The secondary type of
imaging problems attempts to reconstruct images and video that are
corrupted by, for example, noise, subsampling, blur, or saturation.

The quality of the solution of an inverse problem is sensitive to issues such
as
noise and missing entries in the data. The non-convex seismic full-waveform
inversion problem suffers from parasitic local minima that lead to wrong
solutions that may look realistic even for noiseless data. To meet some of
these
challenges, I propose solution strategies that constrain the model parameters
at
every iteration to help guide the inversion.

To arrive at this goal, I present new practical workflows, algorithms, and
software, that avoid manual tuning-parameters and that allow us to
incorporate
multiple pieces of prior knowledge. Opposed to penalty methods, I avoid
balancing the influence of multiple pieces of prior knowledge by working with
intersections of constraint sets. I explore and present advantages of
constraints for imaging. Because the resulting problems are often non-trivial
to
solve, especially on large 3D grids, I introduce faster algorithms, dedicated
to
computing projections onto intersections of multiple sets.

To connect prior knowledge more directly to problem formulations, I also
combine
ideas from additive models, such as cartoon-texture decomposition and robust
principal component analysis, with intersections of multiple constraint sets
for
the regularization of inverse problems. The result is an extension of the
concept of a Minkowski set.

Examples from non-unique physical parameter estimation problems show that
constraints in combination with projection methods provide control over the
model properties at every iteration. This can lead to improved results when
the
constraints are carefully relaxed.},
  keywords = {PhD, sets, regularization, FWI, optimization},
  note = {(PhD)},
  url = {https://slim.gatech.edu/Publications/Public/Thesis/2019/peters2019THiso/peters2019THiso.pdf},
  presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2019/peters2019THiso/peters2019THiso_pres.pdf}
}
%-----2018-----%

@PHDTHESIS{fang2018THsea,
  author = {Zhilong Fang},
  title = {Source estimation and uncertainty quantification for wave-equation based seismic imaging and inversion},
  school = {The University of British Columbia},
  year = {2018},
  month = {04},
  address = {Vancouver},
  abstract = {In  modern  seismic  exploration, wave-equation-based inversion and imaging approaches  are  widely employed for their potential  of  creating  high-resolution subsurface images from seismic data by using the wave equation
to describe  the  underlying  physical model of  wave  propagation. Despite
their successful practical applications, some key issues remain unsolved, including local minima, unknown sources, and the largely missing uncertainty
analyses  for  the  inversion. This  thesis  aims  to  address  the  following two
aspects:  to perform the inversion without prior knowledge of sources, and
to quantify uncertainties in the inversion. The unknown source can hinder the success of wave-equation-based ap-
proaches.  A simple time shift in the source can lead to misplaced reflectors
in  linearized  inversions  or  large  disturbances  in  nonlinear  problems. Unfortunately, accurate sources are typically unknown in real problems.  The first major contribution of this thesis is, given the fact that the wave equation linearly depends on the sources, I have proposed on-the-fly source estimation techniques for the following wave-equation-based approaches: (1)
time-domain  sparsity-promoting  least-squares  reverse-time  migration;  and
(2) wavefield-reconstruction  inversion. Considering the linear dependence
of the wave equation on the sources, I project out the sources by solving a
linear least-squares problem, which enables us to conduct successful wave-
equation-based inversions without prior knowledge of the sources.
Wave-equation-based  approaches  also  produce  uncertainties in the resulting velocity model due to the  noisy  data, which would influence the
subsequent exploration and financial decisions. The difficulties related to
practical uncertainty quantification lie in: (1) expensive computation related
to wave-equation solves, and (2) the nonlinear parameter-to-data map. The
second major contribution of this thesis is the proposal of a computationally
feasible Bayesian framework to analyze uncertainties in the resulting velocity models. Through relaxing the wave-equation constraints, I obtain a less
nonlinear parameter-to-data map and a posterior distribution that can be adequately approximated by a Gaussian distribution. I derive an implicit
formulation to construct the covariance matrix of the Gaussian distribution,
which allows us to sample the Gaussian distribution in a computationally
efficient manner. I demonstrate that the proposed Bayesian framework can
provide adequately accurate uncertainty analyses for intermediate to large-
scale problems with an acceptable computational cost.},
  keywords = {PhD, WRI, LS-RTM, source estimation, UQ, FWI},
  note = {(PhD)},
  url = {https://slim.gatech.edu/Publications/Public/Thesis/2018/fang2018THsea/fang2018THsea.pdf},
  presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2018/fang2018THsea/fang2018THsea_pres.pdf}
}

%-----2017-----%

@PHDTHESIS{dasilva2017THlso,
  author = {Curt Da Silva},
  title = {Large-scale optimization algorithms for missing data completion and inverse problems},
  school = {The University of British Columbia},
  year = {2017},
  month = {09},
  address = {Vancouver},
  abstract = {Inverse problems are an important class of problems
                  found in many areas of science and engineering. In
                  these problems, one aims to estimate unknown
                  parameters of a physical system through indirect
                  multi-experiment measurements. Inverse problems
                  arise in a number of fields including seismology,
                  medical imaging, and astronomy, among others. An
                  important aspect of inverse problems is the quality
                  of the acquired data itself. Real-world data
                  acquisition restrictions, such as time and budget
                  constraints, often results in measured data with
                  missing entries. Many inversion algorithms assume
                  that the input data is fully sampled and relatively
                  noise free and produce poor results when these
                  assumptions are violated. Given the multidimensional
                  nature of real-world data, we propose a new low-rank
                  optimization method on the smooth manifold of
                  Hierarchical Tucker tensors. Tensors that exhibit
                  this low-rank structure can be recovered from
                  solving this non-convex program in an efficient
                  manner. We successfully interpolate realistically
                  sized seismic data volumes using this approach. If
                  our low-rank tensor is corrupted with non-Gaussian
                  noise, the resulting optimization program can be
                  formulated as a convex-composite problem. This class
                  of problems involves minimizing a non-smooth but
                  convex objective composed with a nonlinear smooth
                  mapping. In this thesis, we develop a level set
                  method for solving composite-convex problems and
                  prove that the resulting subproblems converge
                  linearly. We demonstrate that this method is
                  competitive when applied to examples in noisy tensor
                  completion, analysis-based compressed sensing, audio
                  declipping, total-variation deblurring and
                  denoising, and one-bit compressed sensing. With
                  respect to solving the inverse problem itself, we
                  introduce a new software design framework that
                  manages the cognitive complexity of the various
                  components involved. Our framework is modular by
                  design, which enables us to easily integrate and
                  replace components such as linear solvers, finite
                  difference stencils, preconditioners, and
                  parallelization schemes. As a result, a researcher
                  using this framework can formulate her algorithms
                  with respect to high-level components such as
                  objective functions and hessian operators. We
                  showcase the ease with which one can prototype such
                  algorithms in a 2D test problem and, with little
                  code modification, apply the same method to
                  large-scale 3D problems.},
  keywords = {PhD, optimization, convex composite, tensor completion, low-rank, tensor, interpolation, software design},
  note = {(PhD)},
  url = {https://slim.gatech.edu/Publications/Public/Thesis/2017/dasilva2017THlso/dasilva2017THlso.pdf},
  presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2017/dasilva2017THlso/dasilva2017THlso_pres.pdf}
}


@PHDTHESIS{kumar2017THels,
  author = {Rajiv Kumar},
  title = {Enabling large-scale seismic data acquisition, processing and waveform-inversion via rank-minimization},
  school = {The University of British Columbia},
  year = {2017},
  month = {08},
  address = {Vancouver},
  abstract = {In this thesis, I adapt ideas from the field of
                  compressed sensing to mitigate the computational and
                  memory bottleneck of seismic processing workflows
                  such as missing-trace interpolation, source
                  separation and wave-equation based inversion for
                  large-scale 3- and 5-D seismic data. For
                  interpolation and source separation using
                  rank-minimization, I propose three main ingredients,
                  namely a rank-revealing transform domain, a
                  subsampling scheme that increases the rank in the
                  transform domain, and a practical large-scale
                  data-consistent rank-minimization framework, which
                  avoids the need for expensive computation of
                  singular value decompositions. We also devise a
                  wave-equation based factorization approach that
                  removes computational bottlenecks and provides
                  access to the kinematics and amplitudes of
                  full-subsurface offset extended images via actions
                  of full extended image volumes on probing vectors,
                  which I use to perform the amplitude-versus- angle
                  analyses and automatic wave-equation migration
                  velocity analyses on complex geological
                  environments. After a brief overview of matrix
                  completion techniques in Chapter 1, we propose a
                  singular value decomposition (SVD)-free
                  factorization based rank-minimization approach for
                  large-scale matrix completion problems. Then, I
                  extend this framework to deal with large-scale
                  seismic data interpolation problems, where I show
                  that the standard approach of partitioning the
                  seismic data into windows is not required, which use
                  the fact that events tend to become linear in these
                  windows, while exploiting the low-rank structure of
                  seismic data. Carefully selected synthetic and
                  realistic seismic data examples validate the
                  efficacy of the interpolation framework. Next, I
                  extend the SVD-free rank-minimization approach to
                  remove the seismic cross-talk in simultaneous source
                  acquisition. Experimental results verify that source
                  separation using the SVD-free rank-minimization
                  approaches are comparable to the sparsity-promotion
                  based techniques; however, separation via
                  rank-minimization is significantly faster and memory
                  efficient. We further introduce a matrix-vector
                  formulation to form full-subsurface extended image
                  volumes, which removes the storage and computational
                  bottleneck found in the convention methods. I
                  demonstrate that the proposed matrix-vector
                  formulation is used to form different image gathers
                  with which amplitude-versus-angle and wave-equation
                  migration velocity analyses is performed, without
                  requiring prior information on the geologic
                  dips. Finally, I conclude the thesis by outlining
                  potential future research directions and extensions
                  of the thesis work.},
  keywords = {PhD, acquisition, processing, waveform inversion, rank minimization, extended image volumes, migration velocity analysis},
  note = {(PhD)},
  url = {https://slim.gatech.edu/Publications/Public/Thesis/2017/kumar2017THels/kumar2017THels.pdf},
  presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2017/kumar2017THels/kumar2017THels_pres.pdf}
}


@PHDTHESIS{wason2017THsss,
  author = {Haneet Wason},
  title = {Simultaneous-source seismic data acquisition and processing with compressive sensing},
  school = {The University of British Columbia},
  year = {2017},
  month = {08},
  address = {Vancouver},
  abstract = {The work in this thesis adapts ideas from the field of
                  compressive sensing (CS) that lead to new insights
                  into acquiring and processing seismic data, where we
                  can fundamentally rethink how we design seismic
                  acquisition surveys and process acquired data to
                  minimize acquisition- and processing-related
                  costs. Current efforts towards dense source/receiver
                  sampling and full azimuthal coverage to produce
                  high-resolution images of the subsurface have led to
                  the deployment of multiple sources across survey
                  areas. A step ahead from multisource acquisition is
                  simultaneous-source acquisition, where multiple
                  sources fire shots at near-simultaneous/random times
                  resulting in overlapping shot records, in comparison
                  to no overlaps during conventional sequential-source
                  acquisition. Adoption of simultaneous-source
                  techniques has helped to improve survey efficiency
                  and data density. The engine that drives
                  simultaneous-source technology is
                  simultaneous-source separation --- a methodology
                  that aims to recover conventional sequential-source
                  data from simultaneous-source data. This is
                  essential because many seismic processing techniques
                  rely on dense and periodic (or regular)
                  source/receiver sampling. We address the challenge
                  of source separation through a combination of
                  tailored simultaneous-source acquisition design and
                  sparsity-promoting recovery via convex optimization
                  using l1 objectives. We use CS metrics to
                  investigate the relationship between marine
                  simultaneous-source acquisition design and data
                  reconstruction fidelity, and consequently assert the
                  importance of randomness in the acquisition system
                  in combination with an appropriate choice for a
                  sparsifying transform (i.e., curvelet transform) in
                  the reconstruction algorithm. We also address the
                  challenge of minimizing the cost of expensive,
                  dense, periodically-sampled and replicated
                  time-lapse surveying and data processing by adapting
                  ideas from distributed compressive sensing. We show
                  that compressive randomized time-lapse surveys need
                  not be replicated to attain acceptable levels of
                  data repeatability, as long as we know the shot
                  positions (post acquisition) to a sufficient degree
                  of accuracy. We conclude by comparing
                  sparsity-promoting and rank-minimization recovery
                  techniques for marine simultaneous-source
                  separation, and demonstrate that recoveries are
                  comparable; however, the latter approach readily
                  scales to large-scale seismic data and is
                  computationally faster.},
  keywords = {PhD, acquisition, marine, simultaneous source, source separation, compressive sensing, optimization},
  note = {(PhD)},
  url = {https://slim.gatech.edu/Publications/Public/Thesis/2017/wason2017THsss/wason2017THsss.pdf},
  presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2017/wason2017THsss/wason2017THsss_pres.pdf}
}


@PHDTHESIS{oghenekohwo2017THetl,
  author = {Felix Oghenekohwo},
  title = {Economic time-lapse seismic acquisition and imaging---{Reaping} the benefits of randomized sampling with distributed compressive sensing},
  school = {The University of British Columbia},
  year = {2017},
  month = {08},
  address = {Vancouver},
  abstract = {This thesis presents a novel viewpoint on the implicit
                  opportunities randomized surveys bring to time-lapse
                  seismic - which is a proven surveillance tool for
                  hydrocarbon reservoir monitoring. Time-lapse (4D)
                  seismic combines acquisition and processing of at
                  least two seismic datasets (or vintages) in order to
                  extract information related to changes in a
                  reservoir within a specified time interval. The
                  current paradigm places stringent requirements on
                  replicating the 4D surveys, which is an expensive
                  task often requiring uneconomical dense sampling of
                  seismic wavefields. To mitigate the challenges of
                  dense sampling, several advances in seismic
                  acquisition have been made in recent years including
                  the use of multiple sources firing at near
                  simultaneous random times, and the adaptation of
                  Compressive Sensing (CS) principles to design
                  practical acquisition engines that improve sampling
                  efficiency for seismic data acquisition. However,
                  little is known regarding the implications of these
                  developments for time-lapse studies. By conducting
                  multiple experiments modelling surveys adhering to
                  the principles of CS for 4D seismic, I propose a
                  model that demonstrates the feasibility of
                  randomized acquisitions for time-lapse seismic. The
                  proposed joint recovery model (JRM), which derives
                  from distributed CS, exploits the common information
                  in time-lapse data during recovery of dense
                  wavefields from measured subsampled data, providing
                  highly repeatable and high-fidelity vintages. I show
                  that we obtain better vintages when randomized
                  surveys are not replicated, in contrast to standard
                  practice, paving the way for an opportunity to relax
                  the rigorous requirement to replicate surveys
                  precisely. We assert that the vintages obtained
                  using our proposed model are of sufficient quality
                  to serve as inputs to processes that extract
                  time-lapse attributes from which subsurface changes
                  are deduced. Additionally, I show that recovery with
                  the JRM is robust with respect to errors due to
                  differences between actual and recorded postplot
                  information. Finally, I present an opportunity to
                  adapt our model to problems related to time-lapse
                  seismic imaging where the main finding is that we
                  can better delineate time-lapse changes by adapting
                  the joint recovery model to wave-equation based
                  inversion methods.},
  keywords = {PhD, time lapse, acquisition, joint recovery, thesis, compressive sensing, distributed compressive sensing},
  note = {(PhD)},
  url = {https://slim.gatech.edu/Publications/Public/Thesis/2017/oghenekohwo2017THetl/oghenekohwo2017THetl.pdf},
  presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2017/oghenekohwo2017THetl/oghenekohwo2017THetl_pres.pdf}
}


%-----2015-----%

@PHDTHESIS{lin2015THpes,
  author = {Tim T.Y. Lin},
  title = {Primary estimation with sparsity-promoting bi-convex optimization},
  school = {The University of British Columbia},
  year = {2015},
  month = {10},
  address = {Vancouver},
  abstract = {This thesis establishes a novel inversion methodology
                  for the surface-related primaries from a given
                  recorded seismic wavefield, called the Robust
                  Estimation of Primaries by Sparse Inversion (Robust
                  EPSI, or REPSI). Surface-related multiples are a
                  major source of coherent noise in seismic data, and
                  inferring fine geological structures from
                  active-source seismic recordings typically first
                  necessitates its removal or mitigation. For this
                  task, current practice calls for data-driven
                  approaches which produce only approximate multiple
                  models that must be non-linearly subtracted from the
                  data, often distorting weak primary events in the
                  process. A recently proposed method called
                  Estimation of Primaries by Sparse Inversion (EPSI)
                  avoids this adaptive subtraction by directly
                  inverting for a discrete representation of the
                  underlying multiple-free subsurface impulse response
                  as a set of band-limited spikes. However, in its
                  original form, the EPSI algorithm exhibits a few
                  notable shortcomings that impede adoption. Although
                  it was shown that the correct impulse response can
                  be obtained through a sparsest solution criteria,
                  the current EPSI algorithm is not designed to take
                  advantage of this finding, but instead approximates
                  a sparse solution in an ad-hoc manner that requires
                  practitioners to decide on a multitude of inversion
                  parameters. The Robust EPSI method introduced in
                  this thesis reformulates the original EPSI problem
                  as a formal bi-convex optimization problem that
                  makes obtaining the sparsest solution an explicit
                  goal, while also reliably admit satisfactory
                  solutions using contemporary self-tuning gradient
                  methods commonly seen in large-scale machine
                  learning communities. I show that the Robust EPSI
                  algorithm is able to operate successfully on a
                  variety of datasets with minimal user input, while
                  also producing a more accurate model of the
                  subsurface impulse response when compared to the
                  original algorithm. Furthermore, this thesis makes
                  several contributions that improves the capability
                  and practicality of EPSI: a novel scattering-based
                  multiple prediction model that allows Robust EPSI to
                  deal with wider near-offset receiver gaps than
                  previously demonstrated for EPSI, as well as a
                  multigrid-inspired continuation strategy that
                  significantly reduces the computation time needed to
                  solve EPSI-type problems. These additions are
                  enabled by and built upon the formalism of the
                  Robust EPSI as developed in this thesis.},
  keywords = {PhD, inversion, EPSI, biconvex, multiples, sparsity, optimization},
  note = {(PhD)},
  url = {https://slim.gatech.edu/Publications/Public/Thesis/2015/lin2015THpes/lin2015THpes.pdf},
  presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2015/lin2015THpes/lin2015THpes_pres.pdf}
}


@PHDTHESIS{tu2015THfis,
  author = {Ning Tu},
  title = {Fast imaging with surface-related multiples},
  school = {The University of British Columbia},
  year = {2015},
  month = {08},
  address = {Vancouver},
  abstract = {Surface-related multiples, which are waves that bounce
                  more than once between the water surface and the
                  subsurface reflectors, constitute a significant part
                  of the data acquired in marine seismic surveys. If
                  left untreated, they can lead to misplaced phantom
                  reflectors in the image, and result in erroneous
                  interpretations of the subsurface structure. As a
                  result, these multiples are removed before the
                  imaging procedure in conventional seismic data
                  processing. However, because they interact more with
                  the subsurface medium, they may carry extra
                  information that is not present in the primaries.
                  Therefore instead of removing these multiples, a
                  more desirable alternative is to make active use of
                  them. We derive from the well-established
                  "Surface-Related Multiple Elimination" relation, and
                  arrive at a linearized expression of the
                  wave-equation based modelling that incorporates the
                  surface- related multiples.  We then present a
                  computationally efficient approach to iteratively
                  invert this expression to obtain an image of the
                  subsurface from data that contain multiples. We
                  achieve the computational efficiency inside each
                  iteration by (i) using the wave-equation solver to
                  implicitly carry out the expensive multiple
                  prediction; and (ii) reducing the number of
                  wave-equation solves during data simulation by
                  subsampling the monochromatic source experiments. We
                  show that, compared with directly applying the
                  cross-correlation/deconvolutional imaging
                  conditions, the presented approach can suppress the
                  coherent imaging artifacts from multiples more
                  effectively. We also show that, by curvelet-domain
                  sparsity promoting and occasionally drawing new data
                  samples during the inversion, the proposed inversion
                  method gains improved robustness to velocity errors
                  in the background model, as well as modelling errors
                  incurred during linearization of the
                  wave-equation. To combine the information encoded in
                  both the primaries and the multiples, we then
                  propose a highly accurate source estimation method
                  to jointly invert the total upgoing wavefield. We
                  show with field data examples that we can reap
                  benefits from both the relative noise-free primaries
                  and the extra illumination coverage of the
                  multiples. We also demonstrate that the inclusion of
                  multiples help mitigate the amplitude ambiguity
                  during source estimation. We conclude the thesis
                  with an outlook for future research directions, as
                  well as potential extensions of the proposed work.},
  keywords = {inversion, seismic imaging, multiples, least-squares},
  note = {(PhD)},
  url = {https://slim.gatech.edu/Publications/Public/Thesis/2015/tu2015THfis/tu2015THfis.pdf},
  presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2015/tu2015THfis/tu2015THfis_pres.pdf}
}


@PHDTHESIS{li2015THsps,
  author = {Xiang Li},
  title = {Sparsity promoting seismic imaging and full-waveform inversion},
  school = {The University of British Columbia},
  year = {2015},
  month = {07},
  address = {Vancouver},
  abstract = {This thesis will address the large computational costs
                  of solving least-squares migration and full-waveform
                  inversion problems. Least-squares seismic imaging
                  and full-waveform inversion are seismic inversion
                  techniques that require iterative minimizations of
                  large least-squares misfit functions. Each iteration
                  requires an evaluation of the Jacobian operator and
                  its adjoint, both of which require two wave-equation
                  solves for all sources, creating prohibitive
                  computational costs. In order to reduce costs, we
                  utilize randomized dimensionality reduction
                  techniques, reducing the number of sources used
                  during inversion. The randomized dimensionality
                  reduction techniques create subsampling related
                  artifacts, which we mitigate by using
                  curvelet-domain sparsity-promoting inversion
                  techniques. Our method conducts least-squares
                  imaging at the approximate cost of one reverse-time
                  migration with all sources, and computes the
                  Gauss-Newton full-waveform inversion update at
                  roughly the cost of one gradient update with all
                  sources. Finally, during our research of the
                  full-waveform inversion problem, we discovered that
                  we can utilize our method as an alternative approach
                  to add sparse constraints on the entire velocity
                  model by imposing sparsity constraints on each model
                  update separately, rather than regularizing the
                  total velocity model as typically practiced. We also
                  observed this alternative approach yields a faster
                  decay of the residual and model error as a function
                  of iterations. We provided empirical arguments why
                  and when imposing sparsity on the updates can lead
                  to improved full-waveform inversion results.},
  keywords = {full-waveform inversion, Gauss-Newton method, sparsity promoting, least-squares imaging, seismic imaging},
  note = {(PhD)},
  url = {https://slim.gatech.edu/Publications/Public/Thesis/2015/li2015THsps/li2015THsps.pdf},
  presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2015/li2015THsps/li2015THsps_pres.pdf}
}


%-----2010-----%

@PHDTHESIS{moghaddam10phd,
  author = {Peyman P. Moghaddam},
  title = {Curvelet-based migration amplitude recovery},
  school = {The University of British Columbia},
  year = {2010},
  month = {05},
  address = {Vancouver},
  abstract = {Migration can accurately locate reflectors in the earth
                  but in most cases fails to correctly resolve their
                  amplitude. This might lead to mis-interpretation of
                  the nature of reflector. In this thesis, I
                  introduced a method to accurately recover the
                  amplitude of the seismic reflector. This method
                  relies on a new transform-based recovery that
                  exploits the expression of seismic images by the
                  recently developed curvelet transform. The elements
                  of this transform, called curvelets, are
                  multi-dimensional, multi-scale, and
                  multi-directional. They also remain approximately
                  invariant under the imaging operator. I exploit
                  these properties of the curvelets to introduce a
                  method called Curvelet Match Filtering (CMF) for
                  recovering the seismic amplitude in presence of
                  noise in both migrated image and data. I detail the
                  method and illustrate its performance on synthetic
                  dataset. I also extend CMF formulation to other
                  geophysical applications and present results on
                  multiple removal. In addition of that, I investigate
                  preconditioning of the migration which results to
                  rapid convergence rate of the iterative method using
                  migration.},
  note = {(PhD)},
  url = {https://slim.gatech.edu/Publications/Public/Thesis/2010/moghaddam10phd.pdf}
}


%-----2008-----%

@PHDTHESIS{hennenfent08phd,
  author = {Gilles Hennenfent},
  title = {Sampling and reconstruction of seismic wavefields in the curvelet domain},
  school = {The University of British Columbia},
  year = {2008},
  month = {05},
  address = {Vancouver},
  abstract = {Wavefield reconstruction is a crucial step in the
                  seismic processing flow. For instance, unsuccessful
                  interpolation leads to erroneous multiple
                  predictions that adversely affect the performance of
                  multiple elimination, and to imaging artifacts. We
                  present a new non-parametric transform-based
                  reconstruction method that exploits the compression
                  of seismic data by the recently developed curvelet
                  transform. The elements of this transform, called
                  curvelets, are multi-dimensional, multi-scale, and
                  multi-directional. They locally resemble wavefronts
                  present in the data, which leads to a compressible
                  representation for seismic data. This compression
                  enables us to formulate a new curvelet-based seismic
                  data recovery algorithm through sparsity-promoting
                  inversion (CRSI). The concept of sparsity-promoting
                  inversion is in itself not new to
                  geophysics. However, the recent insights from the
                  field of {\textquoteleft}{\textquoteleft}compressed
                  sensing{\textquoteright}{\textquoteright} are new
                  since they clearly identify the three main
                  ingredients that go into a successful formulation of
                  a reconstruction problem, namely a sparsifying
                  transform, a sub-Nyquist sampling strategy that
                  subdues coherent aliases in the sparsifying domain,
                  and a data-consistent sparsity-promoting
                  program. After a brief overview of the curvelet
                  transform and our seismic-oriented extension to the
                  fast discrete curvelet transform, we detail the CRSI
                  formulation and illustrate its performance on
                  synthetic and real datasets. Then, we introduce a
                  sub-Nyquist sampling scheme, termed jittered
                  undersampling, and show that, for the same amount of
                  data acquired, jittered data are best interpolated
                  using CRSI compared to regular or random
                  undersampled data. We also discuss the large-scale
                  one-norm solver involved in CRSI. Finally, we extend
                  CRSI formulation to other geophysical applications
                  and present results on multiple removal and
                  migration-amplitude recovery.},
  keywords = {curvelet transform, reconstruction, SLIM},
  note = {(PhD)},
  url = {https://slim.gatech.edu/Publications/Public/Thesis/2008/hennenfent08phd.pdf}
}