@article {zhang2023otl,
	title = {Optimized time-lapse acquisition design via spectral gap ratio minimization},
	journal = {Geophysics},
	volume = {88},
	number = {4},
	year = {2023},
	note = {(Geophysics)},
	month = {07},
	pages = {A19-A23},
	abstract = {Modern-day reservoir management and monitoring of geological carbon storage increasingly call for costly time-lapse seismic data collection. In this letter, we show how techniques from graph theory can be used to optimize acquisition geometries for low-cost sparse 4D seismic. Based on midpoint-offset domain connectivity arguments, the proposed algorithm automatically produces sparse non-replicated time-lapse acquisition geometries that favor wavefield recovery.},
	keywords = {Acquisition, JRM, matrix factorization, spectral gap, survey design, time-lapse, wavefield reconstruction},
	doi = {10.1190/geo2023-0024.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2023/zhang2023otl/Spectral_Gap_Paper.html},
	author = {Yijun Zhang and Ziyi Yin and Oscar Lopez and Ali Siahkoohi and Mathias Louboutin and Rajiv Kumar and Felix J. Herrmann}
}
@article {lopez2015IEEEogl,
	title = {Off-the-grid low-rank matrix recovery and seismic data reconstruction},
	journal = {IEEE Journal of Selected Topics in Signal Processing},
	volume = {10},
	number = {4},
	year = {2016},
	note = {(IEEE Journal of Selected Topics in Signal Processing)},
	month = {06},
	pages = {658-671},
	abstract = {Matrix sensing problems capitalize on the knowledge that a data matrix of interest exhibits low rank properties. This low dimensional structure often arises because the data matrix is obtained by sampling a smooth function on a regular (or structured) grid. However, in many practical situations the measurements are taken on an irregular grid (that is accurately known). This results in an "unstructured data matrix" that is less fit for the low rank model in comparison to its regular counterpart and therefore subject to degraded reconstruction via rank penalization techniques. In this paper, we propose and analyze a modified low-rank matrix recovery work-flow that admits unstructured observations. By incorporating a regularization operator which accurately maps structured data to unstructured data, into the nuclear-norm minimization problem, we are able to compensate for data irregularity. Furthermore, by construction our formulation yields output that is supported on a structured grid. We establish recovery error bounds for our methodology and offer matrix sensing and matrix completion numerical experiments including applications to seismic trace interpolation to demonstrate the potential of the approach.},
	keywords = {data regularization, matrix completion, matrix sensing, nonuniform discrete Fourier transform, nuclear-norm relaxation, seismic data, seismic trace interpolation},
	doi = {10.1109/JSTSP.2016.2555482},
	url = {https://slim.gatech.edu/Publications/Public/Journals/IEEESignalProcessingMagazine/2016/lopez2015IEEEogl/lopez2015IEEEogl.pdf},
	url2 = {http://ieeexplore.ieee.org/xpl/login.jsp?tp=\&arnumber=7454674},
	author = {Oscar Lopez and Rajiv Kumar and Ozgur Yilmaz and Felix J. Herrmann}
}
@article {dasilva2014htuck,
	title = {Optimization on the Hierarchical Tucker manifold - applications to tensor completion},
	journal = {Linear Algebra and its Applications},
	volume = {481},
	year = {2015},
	note = {(Linear Algebra and its Applications)},
	month = {09},
	pages = {131-173},
	abstract = {In this work, we develop an optimization framework for problems whose solutions are well-approximated by Hierarchical Tucker (HT) tensors, an efficient structured tensor format based on recursive subspace factorizations. By exploiting the smooth manifold structure of these tensors, we construct standard optimization algorithms such as Steepest Descent and Conjugate Gradient for completing tensors from missing entries. Our algorithmic framework is fast and scalable to large problem sizes as we do not require SVDs on the ambient tensor space, as required by other methods. Moreover, we exploit the structure of the Gramian matrices associated with the HT format to regularize our problem, reducing overfitting for high subsampling ratios. We also find that the organization of the tensor can have a major impact on completion from realistic seismic acquisition geometries. These samplings are far from idealized randomized samplings that are usually considered in the literature but are realizable in practical scenarios. Using these algorithms, we successfully interpolate large-scale seismic data sets and demonstrate the competitive computational scaling of our algorithms as the problem sizes grow.},
	keywords = {differential geometry, Gauss{\textendash}Newton, hierarchical tucker tensors, low-rank tensor, Riemannian manifold optimization, tensor completion},
	doi = {10.1016/j.laa.2015.04.015},
	url = {https://slim.gatech.edu/Publications/Public/Journals/LinearAlgebraAndItsApplications/2015/dasilva2014htuck/dasilva2014htuck.pdf},
	url2 = {http://www.sciencedirect.com/science/article/pii/S0024379515002530},
	author = {Curt Da Silva and Felix J. Herrmann}
}
@article {tang2008CITEocs,
	title = {Optimized Compressed Sensing for Curvelet-based Seismic Data Reconstruction},
	journal = {CiteSeer},
	year = {2008},
	abstract = {Compressed sensing (CS) or compressive sampling provides a new sampling theory to reduce data acquisition, which says that compressible signals can be exactly reconstructed from highly incomplete sets of measurements. Very recently, the CS has been applied for seismic exploration and started to compact the traditional data acquisition. In this paper, we present an optimized sampling strategy for the CS data acquisition, which leads to better performance by the curvelet sparsity-promoting inversion in comparison with random sampling and jittered sampling scheme. One of motivation is to reduce the mutual coherence between measurement sampling schemes and curvelet sparse transform in the CS framework. The basic idea of our optimization is to directly redistribute the energy in frequency domain making original spectrum easily discriminated from the random noise induced by random undersampling, while offering control on the maximum gap size. Numerical experiments on synthetic and real seismic data show good performances of the proposed optimized CS for seismic data reconstruction.},
	keywords = {curvelet transform, Optimized Compressive Sensing},
	url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.7994},
	url2 = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.154.7994\&rep=rep1\&type=pdf},
	author = {Wen Tang and Jianwei Ma and Felix J. Herrmann}
}
