@article {daskalakis2019SIAMJISasr,
	title = {Accelerating Sparse Recovery by Reducing Chatter},
	journal = {SIAM Journal on Imaging Sciences},
	volume = {13},
	number = {3},
	year = {2020},
	note = {(SIAM Journal on Imaging Sciences)},
	month = {07},
	pages = {1211{\textendash}1239},
	abstract = {Compressive Sensing has driven a resurgence of sparse recovery algorithms with l_1-norm minimization. While these minimizations are relatively well understood for small underdetermined, possibly inconsistent systems, their behavior for large over-determined and inconsistent systems has received much less attention. Specifically, we focus on large systems where computational restrictions call for algorithms that use randomized subsets of rows that are touched a limited number of times. In that regime, l_1-norm minimization algorithms exhibit unwanted fluctuations near the desired solution, and the Linear Bregman iterations are no exception. We explain this observed lack of performance in terms of chatter, a well-known phenomena observed in non-smooth dynamical systems, where intermediate solutions wander between different states stifling convergence. By identifying chatter as the culprit, we modify the Bregman iterations with chatter reducing adaptive element-wise step lengths in combination with potential support detection via threshold crossing. We demonstrate the performance of our algorithm on carefully selected stylized examples and a realistic seismic imaging problem involving millions of unknowns and matrix-free matrix-vector products that involve expensive wave-equation solves.},
	keywords = {chatter, inconsistent linear systems, Kacmarz, linearized Bregman dynamical systems, non-smooth dynamics, sparsity promotion},
	doi = {10.1137/19M129111X},
	url = {https://slim.gatech.edu/Publications/Public/Journals/SIAMJournalOnImagingSciences/2020/daskalakis2019SIAMJISasr/daskalakis2019SIAMJISasr.pdf},
	author = {Emmanouil Daskalakis and Felix J. Herrmann and Rachel Kuske}
}
@conference {rizzuti2019SIAMGStwri,
	title = {A dual formulation for time-domain wavefield reconstruction inversion},
	booktitle = {SIAM Conference on Mathematical and Computational Issues in the Geosciences},
	year = {2019},
	note = {(SIAM GS)},
	month = {03},
	abstract = {Wavefield reconstruction inversion (WRI) is based on the combination of data misfit and PDE-residual penalty terms, and it aims at the reconstruction of the optimal property model and field pair. A full-space optimization would require the storage of field variables for every frequency or time sample (and every source). Remedies via variable projection are well studied, but they entail the solution of a modified wave equation, which is costly both in frequency and time domain. Here, we explore an efficient alternative to WRI, where properties are complemented, instead, by elements of the dual data space. The starting point of our proposal is the denoising reformulation of WRI: the PDE compliance is optimized under the constraint of a given data fit. Since the field variable can be eliminated from the associated saddle-point problem, we obtain a new objective functional of only properties and Lagrange multipliers. Its evaluation, and gradient computation, involves the solution of the original wave equation, which is amenable to time-domain discretization. The optimization scheme of choice can now leverage on affordable storage of the iterates.},
	keywords = {WRI},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SIAMGS/2019/rizzuti2019SIAMGStwri/rizzuti2019SIAMGStwri.pdf},
	author = {Gabrio Rizzuti and Mathias Louboutin and Rongrong Wang and Emmanouil Daskalakis and Felix J. Herrmann}
}
@conference {rizzuti2019SEGadf,
	title = {A dual formulation for time-domain wavefield reconstruction inversion},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2019},
	note = {(SEG, San Antonio)},
	month = {09},
	pages = {1480-1485},
	abstract = {We illustrate a dual formulation for full-waveform inversion potentially apt to large 3-D problems. It is based on the optimization of the wave equation compliance, under the constraint of data misfit not exceeding a prescribed noise level. In the Lagrangian formulation, model and wavefield state variables are complemented with multipliers having the same dimension of data ("dual data" variables). Analogously to classical wavefield reconstruction inversion, the wavefield unknowns can be projected out in closed form, by solving a version of the augmented wave equation. This leads to a saddle-point problem whose variables are only model and dual data. As such, this formulation represents a model extension, and is potentially robust against local minima. The classical downsides of model extension methods and wavefield reconstruction inversion are here effectively mitigated: storage of the dual variables is affordable, the augmented wave equation is amenable to time-marching finite-difference schemes, and no continuation strategy for penalty parameters is needed, with the prospect of 3-D applications.},
	keywords = {3D, Full-waveform inversion, SEG, Time-domain},
	doi = {10.1190/segam2019-3216760.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2019/rizzuti2019SEGadf/rizzuti2019SEGadf.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2019/rizzuti2019SEGadf/rizzuti2019SEGadf_pres.pdf},
	software = {https://github.com/slimgroup/Software.rizzuti2019SEGadf},
	author = {Gabrio Rizzuti and Mathias Louboutin and Rongrong Wang and Emmanouil Daskalakis and Felix J. Herrmann}
}
@conference {daskalakis2017SEGdds,
	title = {Developments in the direction of solving extremly large problems in Geophysics},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2017},
	note = {(SEG, Houston)},
	month = {09},
	pages = {4375-4378},
	abstract = {Often in exploration Geophysics we are forced to work with extremely large problems. Acquisitions via dense grids of receivers translate into very large mathematical systems. Usually, depending on the acquisition, the size of the matrix of the system to be solved, can be measured in the millions. The proper way to address this problem is by subsampling. Even though subsampling can reduce the computational efforts required, it can not address stability problems caused by preconditioning and/or instrumental response errors. In this abstract, we introduce a modification of the linearized Bregman solver for these large problems that resolves stability issues.},
	keywords = {cycling, least-squares migration, linearized Bregman, SEG, weighted increment},
	doi = {10.1190/segam2017-17795188.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2017/daskalakis2017SEGdds/daskalakis2017SEGdds.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2017/daskalakis2017SEGdds/daskalakis2017SEGdds_pres.pdf},
	author = {Emmanouil Daskalakis and Rachel Kuske and Felix J. Herrmann}
}
@conference {yang2017SEGfsp,
	title = {Fast sparsity-promoting least-squares migration with multiples in time domain},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2017},
	note = {(SEG, Houston)},
	month = {09},
	pages = {4828-4832},
	abstract = {Based on the latest developments of research in inversion technology with optimization, researchers have made significant progress in the implementation of least-squares reverse-time migration (LS-RTM) of primaries. In Marine data however, these applications rely on the success of a pre-imaging separation of primaries and multiples, which can be modeled as a multi-dimensional convolution between the vertical derivative of the surface-free Green{\textquoteright}s function and the down-going receiver wavefield. Instead of imaging the primaries and multiples separately, we implement the LS-RTM of the total down-going wavefield by combining areal source injection and linearized Born modelling, where strong surface related multiples are generated from a strong density variation at the ocean bottom. The advantage including surface related multiples in LS-RTM is the extra illumination we obtain from these multiples without incurring additional computational costs related to carrying out multi-dimensional convolutions part of conventional multiple prediction procedures. Even though we are able to avert these computational costs, our approach shares the large costs of LSRTM. We reduce these costs by combining randomized source subsampling with our sparsity-promoting imaging technology, which produces artifact-free, high-resolution images, with the surface-related multiples migrated properly.},
	keywords = {least-squares RTM, multiples, SEG, sparsity, time domain},
	doi = {10.1190/segam2017-17741608.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2017/yang2017SEGfsp/yang2017SEGfsp.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2017/yang2017SEGfsp/yang2017SEGfsp_pres.pdf},
	author = {Mengmeng Yang and Emmanouil Daskalakis and Felix J. Herrmann}
}
@presentation {yang2017SINBADFiwm,
	title = {Imaging with multiples in shallow water},
	year = {2017},
	publisher = {SINBAD},
	abstract = {Based on the latest developments of research in inversion technology with optimization, researchers have made significant progress in the implementation of least-squares reverse-time migration (LS-RTM) of primaries. In Marine data however, these applications rely on the success of a pre-imaging separation of primaries and multiples, which can be modeled as a multi-dimensional convolution between the vertical derivative of the surface-free Green{\textquoteright}s function and the down-going receiver wavefield. Instead of imaging the primaries and multiples separately, we implement the LS-RTM of the total down-going wavefield by combining areal source injection and linearized Born modelling, where strong surface related multiples are generated from a strong density variation at the ocean bottom. The advantage including surface related multiples in LS-RTM is the extra illumination we obtain from these multiples without incurring additional computational costs related to carrying out multi-dimensional convolutions part of conventional multiple prediction procedures. Even though we are able to avert these computational costs, our approach shares the large costs of LS-RTM. We reduce these costs by combining randomized source subsampling with our sparsity-promoting imaging technology, which produces artifact-free, high-resolution images, with the surface-related multiples migrated properly.},
	keywords = {Presentation, SINBAD, SINBADFALL2017, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2017/Fall/yang2017SINBADFiwm/yang2017SINBADFiwm.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2017/Fall/yang2017SINBADFiwm/yang2017SINBADFiwm.mov},
	author = {Mengmeng Yang and Emmanouil Daskalakis and Felix J. Herrmann}
}
@presentation {wang2017SINBADFnra,
	title = {Noise robust and time-domain formulations of Wavefield Reconstruction Inversion},
	year = {2017},
	publisher = {SINBAD},
	abstract = {We propose a wave-equation-based subsurface inversion method that in many cases is more robust than conventional Full-Waveform Inversion. The new formulation is written in a denoising form that allows the synthetic data to match the observed ones up to a small error. Compared to regular Full-Waveform Inversion, our method treats the noise arising from the data meassuring/recording process and that from the synthetic modelling process separately. Compared to Wavefields Reconstruction Inversion, the new formulation mitigates the difficulty of choosing the penalty parameter λ. To solve the proposed optimization problem, we develop an efficient frequency domain algorithm that alternatively updates the model and the data. Numerical experiments confirm strong stability of the proposed method by comparisons between the results of our algorithm with that from both plain FWI and a weighted formulation of the FWI. We also discuss a new memory efficient time-domain formulation for Wavefield Reconstruction Inversion based on duality.},
	keywords = {Presentation, SINBAD, SINBADFALL2017, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2017/Fall/wang2017SINBADFnra/wang2017SINBADFnra.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2017/Fall/wang2017SINBADFnra/wang2017SINBADFnra.mov},
	author = {Rongrong Wang and Mathias Louboutin and Bas Peters and Emmanouil Daskalakis and Felix J. Herrmann}
}
@presentation {daskalakis2017SINBADFsof,
	title = {Stochastic Optimization from the perspective of dynamical systems},
	year = {2017},
	publisher = {SINBAD},
	abstract = {We present improvements to a family of methods (Linearized Bregman, Kaczmarz and Stochastic Gradient Descent) that are often use in optimization problems. We explain the link of those methods with dynamical systems and we draw ideas for improving their performance. We use a simple idea to improve the stability and the performance of our family of optimization methods especially for ill-posed, inconsistent large-scale problems. Finally we present an application at a least squares migration problem, which highlight the importance of the suggested improvements on large scale Geophysical problems.},
	keywords = {Presentation, SINBAD, SINBADFALL2017, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2017/Fall/daskalakis2017SINBADFsof/daskalakis2017SINBADFsof.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2017/Fall/daskalakis2017SINBADFsof/daskalakis2017SINBADFsof.m4v},
	author = {Emmanouil Daskalakis and Rachel Kuske and Mengmeng Yang and Felix J. Herrmann}
}
