@techreport {kumar2015EAGElse,
	title = {Least-squares extended imaging with surface-related multiples},
	number = {TR-EOAS-2015-1},
	year = {2015},
	month = {01},
	institution = {UBC},
	abstract = {Common image gathers are used in building velocity models, inverting for anisotropy parameters, and analyzing reservoir attributes. Typically, only primary reflections are used to form image gathers as multiples can cause artifacts that interfere with the events of interest. However, it has been shown that multiples can actually provide extra illumination of the subsurface, especially for delineating the near-surface features. In this paper, we aim to form common image gathers directly from the data with surface related multiples by applying concepts that have been used to successfully deal with surface-related multiples in imaging. We achieve this by effectively inverting an extended migration operator. This results in extended images with better near-surface illumination that are free of artifacts that can hamper velocity analysis. In addition, being able to generate extended images directly from the total data avoids the need for (time-consuming) pre-processing. Synthetic examples on a layered model show that the proposed formulation is promising.},
	keywords = {image gathers, surface-related multiples},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2015/kumar2015EAGElse/kumar2015EAGElse.html},
	author = {Rajiv Kumar and Ning Tu and Tristan van Leeuwen and Felix J. Herrmann}
}
@techreport {esser2015tvwri,
	title = {Total variation regularization strategies in full waveform inversion for improving robustness to noise, limited data and poor initializations},
	number = {TR-EOAS-2015-5},
	year = {2015},
	month = {06},
	institution = {UBC},
	abstract = {We propose an extended full waveform inversion formulation that includes convex constraints on the model. In particular, we show how to simultaneously constrain the total variation of the slowness squared while enforcing bound constraints to keep it within a physically realistic range. Synthetic experiments show that including total variation regularization can improve the recovery of a high velocity perturbation to a smooth background model, removing artifacts caused by noise and limited data. Total variation-like constraints can make the inversion results significantly more robust to a poor initial model, leading to reasonable results in some cases where unconstrained variants of the method completely fail. Numerical results are presented for portions of the SEG/EAGE salt model and the 2004 BP velocity benchmark. ***Disclaimer.*** *This technical report is ongoing work (and posted as is except for the addition of another author) of the late John "Ernie" Esser (May 19, 1980 - March 8, 2015), who passed away under tragic circumstances. We will work hard to finalize and submit this work to the peer-review literature.* Felix J. Herrmann},
	keywords = {cones constraints, hinge loss, total-variation, Wavefield Reconstruction Inversion},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2015/esser2015tvwri/esser2015tvwri.html},
	author = {Ernie Esser and Llu{\'\i}s Guasch and Tristan van Leeuwen and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
@techreport {herrmann2014pmpde,
	title = {A penalty method for PDE-constrained optimization},
	number = {WO 2014/172787},
	year = {2014},
	note = {(International publication date 30 October 2014. International publication number WO 2014/172787.)},
	month = {10},
	institution = {UBC},
	type = {Patent},
	abstract = {The invention is directed to a computer-implemented method for obtaining a physical model having physical model parameters wherein solutions to one or more partial-differential-equations (PDE{\textquoteright}s) are calculated ans wherein (i) an appropriate initial model is selected, (ii) setup a system of equations referred to as the data-augmented PDE for the field, comprising of the discretized PDE, the sampling operator, the source function and the observed data, and solve the data-augmented PDE in a suitable manner to obtain a field that both satisfies the PDE and fits the data to some degree, (iii) setup a system of equations by using the PDE, the source function and the field obtained in step (ii) and solve this system of equations in a suitable manner to obtain an update of the physical model parameters and repeat steps (ii)-(iii) until a predetermined stopping criterion is met.},
	keywords = {Optimization, patent, penalty method},
	url = {https://slim.gatech.edu/Publications/Public/Patents/2014/herrmann2014pmpde/herrmann2014pmpde_WO2014172787.pdf},
	url2 = {http://patentscope.wipo.int/search/en/WO2014172787},
	author = {Felix J. Herrmann and Tristan van Leeuwen}
}
@techreport {esser2014SEGsgp,
	title = {A scaled gradient projection method for total variation regularized full waveform inversion},
	number = {TR-EOAS-2014-2},
	year = {2014},
	month = {04},
	institution = {UBC},
	abstract = {We propose an extended full waveform inversion formulation that includes convex constraints on the model. In particular, we show how to simultaneously constrain the total variation of the slowness squared while enforcing bound constraints to keep it within a physically realistic range. Synthetic experiments show that including total variation regularization can improve the recovery of a high velocity perturbation to a smooth background model.},
	keywords = {convex constraints, full waveform inversion, total variation regularization},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2014/esser2014SEGsgp/esser2014SEGsgp.html},
	author = {Ernie Esser and Tristan van Leeuwen and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
@techreport {vanLeeuwen2013Penalty2,
	title = {A penalty method for PDE-constrained optimization},
	number = {TR-EOAS-2013-6},
	year = {2013},
	month = {04},
	institution = {UBC},
	abstract = {We present a method for solving PDE constrained optimization problems based on a penalty formulation. This method aims to combine advantages of both full-space and reduced methods by exploiting a large search-space (consisting of both control and state variables) while allowing for an efficient implementation that avoids storing and updating the state-variables. This leads to a method that has roughly the same per-iteration complexity as conventional reduced approaches while dening an objective that is less non-linear in the control variable by implicitly relaxing the constraint. We apply the method to a seismic inverse problem where it leads to a particularly ecient implementation when compared to a conventional reduced approach as it avoids the use of adjoint state-variables. Numerical examples illustrate the approach and suggest that the proposed formulation can indeed mitigate some of the well-known problems with local minima in the seismic inverse problem.},
	keywords = {Optimization, waveform inversion},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2013/vanLeeuwen2013Penalty2/vanLeeuwen2013Penalty2.pdf},
	author = {Tristan van Leeuwen and Felix J. Herrmann}
}
@techreport {petrenko2013SEGsaoc,
	title = {Software acceleration of CARP, an iterative linear solver and preconditioner},
	number = {TR-EOAS-2013-4},
	year = {2013},
	institution = {UBC},
	abstract = {We present the results of software optimization of a row-wise preconditioner (Component Averaged Row Projections) for the method of conjugate gradients, which is used to solve the diagonally banded Helmholtz system representing frequency domain, isotropic acoustic seismic wave simulation. We demonstrate that in our application, a preconditioner bound to one processor core and accessing memory contiguously reduces execution time by 7\% for matrices having on the order of 108 non-zeros. For reference we note that our C implementation is over 80 times faster than the corresponding code written for a high-level numerical analysis language.},
	keywords = {frequency-domain, Helmholtz equation, Kaczmarz, software, wave propagation},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2013/petrenko2013SEGsaoc/petrenko2013SEGsaoc.pdf},
	author = {Art Petrenko and Tristan van Leeuwen and Felix J. Herrmann}
}
@techreport {vanleeuwen2012CGMN,
	title = {Fourier analysis of the CGMN method for solving the Helmholtz equation},
	number = {TR-EOAS-2012-1},
	year = {2012},
	institution = {Department of Earth, Ocean and Atmospheric Sciences},
	address = {The University of British Columbia, Vancouver},
	abstract = {The Helmholtz equation arises in many applications, such as seismic and medical imaging. These application are characterized by the need to propagate many wavelengths through an inhomogeneous medium. The typical size of the problems in 3D applications precludes the use of direct factorization to solve the equation and hence iterative methods are used in practice. For higher wavenumbers, the system becomes increasingly indefinite and thus good preconditioners need to be constructed. In this note we consider an accelerated Kazcmarz method (CGMN) and present an expression for the resulting iteration matrix. This iteration matrix can be used to analyze the convergence of the CGMN method. In particular, we present a Fourier analysis for the method applied to the 1D Helmholtz equation. This analysis suggests an optimal choice of the relaxation parameter. Finally, we present some numerical experiments.},
	keywords = {Helmholtz equation, Modelling},
	url = {http://arxiv.org/abs/1210.2644},
	author = {Tristan van Leeuwen}
}
@techreport {vanleeuwen2012smii,
	title = {A parallel matrix-free framework for frequency-domain seismic modelling, imaging and inversion in Matlab},
	number = {TR-EOAS-2012-5},
	year = {2012},
	month = {07},
	abstract = {I present a parallel matrix-free framework for frequency-domain seismic modeling, imaging and inversion. The framework provides basic building blocks for designing and testing optimization-based formulations of both linear and non-linear seismic in- verse problems. By overloading standard linear-algebra operations, such as matrix-vector multiplications, standard optimization packages can be used to work with the code without any modification. This leads to a scalable testbed on which new methods can be rapidly prototyped and tested on medium-sized 2D problems. I present some numerical examples on both linear and non-linear seismic inverse problems.},
	keywords = {Matlab, object-oriented programming, Optimization, seismic imaging},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2012/vanleeuwen2012smii/vanleeuwen2012smii.pdf},
	author = {Tristan van Leeuwen}
}
@techreport {vanleeuwen2012SEGparallel,
	title = {A parallel, object-oriented framework for frequency-domain wavefield imaging and inversion.},
	number = {TR-EOAS-2012-2},
	year = {2012},
	month = {04},
	institution = {Department of Earth and Ocean Sciences},
	address = {University of British Columbia, Vancouver},
	abstract = {We present a parallel object-oriented matrix-free framework for frequency-domain seismic modeling, imaging and inversion. The key aspects of the framework are its modularity and level of abstraction, which allows us to write code that reflects the underlying mathematical structure and develop unit-tests that guarantee the fidelity of the code. By overloading standard linear-algebra operations, such as matrix-vector multiplications, we can use standard optimization packages to work with our code without any modification. This leads to a scalable testbed on which new methods can be rapidly prototyped and tested on medium-sized 2D problems. Although our current implementation uses (parallel) Matlab, all of these design principles can also be met by using lower-level languages which is important when we want to scale to realistic 3D problems. We present some numerical examples on synthetic data.},
	keywords = {Imaging, inversion, Modeling, SEG},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2012/vanleeuwen2012SEGparallel/vanleeuwen2012SEGparallel.pdf},
	author = {Tristan van Leeuwen and Felix J. Herrmann}
}
@techreport {vandenberg08gsv,
	title = {Group sparsity via linear-time projection},
	number = {TR-2008-09},
	year = {2008},
	month = {06},
	institution = {UBC - Department of Computer Science},
	abstract = {We present an efficient spectral projected-gradient algorithm for optimization subject to a group one-norm constraint. Our approach is based on a novel linear-time algorithm for Euclidean projection onto the one- and group one-norm constraints. Numerical experiments on large data sets suggest that the proposed method is substantially more efficient and scalable than existing methods.},
	keywords = {Optimization, SLIM},
	url = {http://www.optimization-online.org/DB_FILE/2008/07/2056.pdf},
	author = {Ewout van den Berg and Mark Schmidt and Michael P. Friedlander and K. Murphy}
}
@techreport {vandenberg07TRipr,
	title = {In pursuit of a root},
	number = {TR-EOAS-2007-19},
	year = {2007},
	month = {06},
	institution = {Department of Computer Science},
	address = {University of British Columbia, Vancouver},
	abstract = {The basis pursuit technique is used to find a minimum one-norm solution of an underdetermined least-squares problem. Basis pursuit denoise fits the least-squares problem only approximately, and a single parameter determines a curve that traces the trade-off between the least-squares fit and the one-norm of the solution. We show that the function that describes this curve is convex and continuously differentiable over all points of interest. The dual solution of a least-squares problem with an explicit one-norm constraint gives function and derivative information needed for a root-finding method. As a result, we can compute arbitrary points on this curve. Numerical experiments demonstrate that our method, which relies on only matrix-vector operations, scales well to large problems.},
	url = {http://www.optimization-online.org/DB_HTML/2007/06/1708.html},
	author = {Ewout van den Berg and Michael P. Friedlander}
}
