@article {silva2018alr,
	title = {Applications of low-rank compressed seismic data to full waveform inversion and extended image volumes},
	journal = {Geophysics},
	year = {2019},
	note = {Accepted on January 22, 2019.},
	abstract = {Conventional oil and gas fields are increasingly difficult to explore and image, resulting in the call for more complex wave-equation based inversion algorithms that require dense long-offset samplings. Consequently, there is an exponential growth in the size of data volumes and prohibitive demands on computational resources. In this work, we propose a method to compress and process seismic data directly in a low-rank tensor format, which drastically reduces the amount of storage required to represent the data. We first outline how seismic data exhibits low-rank structure in a particular transform-domain, which can be exploited to compress the dense data in one extremely storage-efficient tensor format when the data is fully sampled. In the more realistic case of missing data, we can use efficient interpolation techniques to approximate the fully sampled volume in compressed form. In either case, once we have our data represented in its compressed tensor form, we design an algorithm to extract source or receiver gathers directly from the compressed parameters. This extraction process can be done on-the-fly directly on the compressed data, in a full waveform inversion context, and does not require scanning through the entire dataset in order to form shot gathers. To the best of our knowledge, this work is one of the first major contributions to working with seismic data applications directly in the compressed domain without reconstructing the entire data volume. We use a stochastic inversion approach, which works with small subsets of source experiments at each iteration, further reducing the computational and memory costs of full waveform inversion. We also demonstrate how this data compression and extraction technique can be applied to forming full subsurface image gathers through probing techniques.},
	keywords = {common shot/receiver gather, extended image volume, full waveform inversion, low rank, tensor},
	doi = {10.1190/geo2018-0116.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2019/silva2018alr/silva2018alr.pdf},
	author = {Curt Da Silva and Yiming Zhang and Rajiv Kumar and Felix J. Herrmann}
}
@mastersthesis {dasilva2017THlso,
	title = {Large-scale optimization algorithms for missing data completion and inverse problems},
	year = {2017},
	note = {(PhD)},
	month = {09},
	school = {The University of British Columbia},
	type = {phd},
	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 = {convex composite, interpolation, low-rank, Optimization, PhD, software design, tensor, tensor completion},
	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},
	author = {Curt Da Silva}
}
