@mastersthesis {peters2019THiso,
	title = {Intersections and sums of sets for the regularization of inverse problems},
	year = {2019},
	note = {(PhD)},
	month = {05},
	school = {The University of British Columbia},
	type = {phd},
	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 = {FWI, Optimization, PhD, regularization, Sets},
	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},
	author = {Bas Peters}
}
@mastersthesis {petrenko2014THaih,
	title = {Accelerating an iterative Helmholtz solver using reconfigurable hardware},
	year = {2014},
	note = {(MSc)},
	month = {04},
	school = {The University of British Columbia},
	type = {masters},
	address = {Vancouver},
	abstract = {An implementation of seismic wave simulation on a platform consisting of a conventional host processor and a reconfigurable hardware accelerator is presented. This research is important in the field of exploration for oil and gas resources, where a 3D model of the subsurface of the Earth is frequently required. By comparing seismic data collected in a real-world survey with synthetic data generated by simulated waves, it is possible to deduce such a model. However this requires many time-consuming simulations with different Earth models to find the one that best fits the measured data. Speeding up the wave simulations would allow more models to be tried, yielding a more accurate estimate of the subsurface. The reconfigurable hardware accelerator employed in this work is a field programmable gate array (FPGA). FPGAs are computer chips that consist of electronic building blocks that the user can configure and reconfigure to represent their algorithm in hardware. Whereas a traditional processor can be viewed as a pipeline for processing instructions, an FPGA is a pipeline for processing data. The chief advantage of the FPGA is that all the instructions in the algorithm are already hardwired onto the chip. This means that execution time depends only on the amount of data to be processed, and not on the complexity of the algorithm. The main contribution is an implementation of the well-known Kaczmarz row projection algorithm on the FPGA, using techniques of dataflow programming. This kernel is used as the preconditioning step of CGMN, a modified version of the conjugate gradients method that is used to solve the time-harmonic acoustic isotropic constant density wave equation. Using one FPGA-based accelerator, the current implementation allows seismic wave simulations to be performed over twice as fast, compared to running on one Intel Xeon E5-2670 core. I also discuss the effect of modifications of the algorithm necessitated by the hardware on the convergence properties of CGMN. Finally, a specific plan for future work is set-out in order to fully exploit the accelerator platform, and the work is set in its larger context.},
	keywords = {CG, CGMN, FPGA, Helmholtz, Kaczmarz, linear solver, Maxeler, MSc, thesis, wave equation},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2014/petrenko2014THaih/petrenko2014THaih.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2014/petrenko2014THaih/petrenko2014THaih_pres.pdf},
	author = {Art Petrenko}
}
