@presentation {lin2015SINBADFosd,
	title = {Our student-driven HPC environment},
	year = {2015},
	publisher = {SINBAD},
	abstract = {A major role of academic environments is to provide learning experiences for students to critically analyze and develop methods, both at a high-level of mathematical rigour, and at a low-enough level of implementation in order to yield experimental results on real datasets. Often these two goals are in conflict with each other, in terms of both learning time and attention. At SLIM, we strive to strike a balance between the two by abstracting away many of the low-level aspects of distributed HPC under a framework that matches syntactically with the mathematics of our field, while exposing enough control parameters for tuning performance characteristics. This talk will touch on the history of our efforts at SLIM, and culminate in an overview of our current method of interacting with the in-house compute cluster.},
	keywords = {Presentation, SINBAD, SINBADFALL2015, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2015/Fall/lin2015SINBADFosd/lin2015SINBADFosd.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
@presentation {esser2015SINBADFrsa,
	title = {Resolving scaling ambiguities with the L1/L2 norm in a blind deconvolution problem with feedback},
	year = {2015},
	publisher = {SINBAD},
	abstract = {Compared to more mundane blind deconvolution problems, blind deconvolution in seismic applications involves a feedback mechanism related to the free surface. The presence of this feedback mechanism gives us an unique opportunity to remove ambiguities that have plagued blind deconvolution for a long time. While beneficial, this feedback by itself is insufficient to remove the ambiguities even with L1 constraints. However, when paired with an L1/L2 constraint the feedback allows us to resolve the scaling ambiguity under relatively mild assumptions. Inspired by lifting approaches, we propose to split the sparse signal into positive and negative components and apply an \ell_1/\ell_2 constraint to the difference, thereby obtaining a constraint that is easy to implement. Numerical experiments demonstrate robustness to the initialization as well as to noise in the data.},
	keywords = {Presentation, SINBAD, SINBADFALL2015, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2015/Fall/esser2015SINBADFrsa/esser2015SINBADFrsa.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2015/Fall/esser2015SINBADFrsa/esser2015SINBADFrsa.mov},
	author = {Ernie Esser and Rongrong Wang and Tim T.Y. Lin and Felix J. Herrmann}
}
@conference {lin2015IIPFWIsws,
	title = {Software and workflows at SLIM/SINBAD},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	keywords = {FWI, SLIM, software},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/lin2015IIPFWIsws/lin2015IIPFWIsws_pres.pdf},
	author = {Tim T.Y. Lin and Curt Da Silva and Felix J. Herrmann}
}
@presentation {lin2014SINBADdag,
	title = {Dealing with acquisition gaps in Robust EPSI without interpolation using wavefield auto-convolution},
	year = {2014},
	publisher = {SINBAD},
	abstract = {Straightforward modifications to the Estimation of Primaries by Sparse Inversion (EPSI) problem allows us to mitigate acquisition holes without any reconstruction of the missing traces, neither prior to nor during the inversion process. This is achieved by simulating the missing multiple contributions with terms involving auto-convolutions of the primary wavefield. In this formulation we no longer need to treat the missing data as another unknown in the inversion process, which is important in eliminating a significant source of possible local minima from attempting to invent data using incorrect primary and multiple models. In this talk we investigate the necessary modifications to the Robust EPSI problem, as well as algorithms that account for the resulting non-linear modelling operator. We will also investigate the reconstruction limits of this approach in relation to acquisition geometry and subsurface characteristics.},
	keywords = {Presentation, SINBAD, SINBADFALL2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Fall/lin2014SINBADdag/lin2014SINBADdag.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
@presentation {tu2014SINBADfis2,
	title = {Fast imaging with source estimation},
	year = {2014},
	publisher = {SINBAD},
	abstract = {In seismic imaging, an inaccurate estimate of the source wavelet may result in degraded seismic images. While conventional reverse-time migration requires the knowledge of the source wavelet as prior information, we propose to include source estimation in the fast compressive imaging procedure. Using the proposed method, we can obtain seismic images that are comparable to those imaged with the true source wavelet, with computational costs that are comparable to conventional RTM images with all the data. We also extend the proposed method to image data with surface-related multiples, where these multiples help to mitigate the amplitude ambiguity in source estimation. We verify the proposed method using realistic synthetic examples.},
	keywords = {Presentation, SINBAD, SINBADFALL2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Fall/tu2014SINBADfis2/tu2014SINBADfis2.pdf},
	author = {Ning Tu and Aleksandr Y. Aravkin and Tristan van Leeuwen and Tim T.Y. Lin and Felix J. Herrmann}
}
@presentation {lin2014SINBADiit,
	title = {Implicit interpolation of trace gaps in REPSI using auto-convolution terms},
	year = {2014},
	publisher = {SINBAD},
	abstract = {It is possible to solve the Estimation of Primaries by Sparse Inversion problem from a sesimic record with large holes without any explicit data reconstruction, by instead simulating the missing multiple contributions with terms involving auto-convolutions of the primary wavefield. Exclusion of the unknown data as an inversion variable from the REPSI process is desireable, since it eliminates a significant source of local minima that arises from attempting to invert for the unobserved traces using primary and multiple models that may be far-away from the true solution. In this talk we investigate the necessary modifications to the REPSI algorithm to account for the resulting non-linear modeling operator, and demonstrate that just a few auto-convolution terms are enough to satisfactorily mitigate the effects of data gaps during the inversion process.},
	keywords = {Presentation, SINBAD, SINBADSPRING2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Spring/lin2014SINBADiit/lin2014SINBADiit.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
@presentation {esser2014SINBADlcs,
	title = {A lifted $\ell_1$/$\ell_2$ constraint for sparse blind deconvolution},
	year = {2014},
	publisher = {SINBAD},
	abstract = {We propose a modification to a sparsity constraint based on the ratio of l1 and l2 norms for solving blind seismic deconvolution problems in which the data consist of linear convolutions of different sparse reflectivities with the same source wavelet. No assumptions are made about the location of the support of either the wavelet or the sparse signals. Minimizing the ratio of l1 and l2 norms has been previously shown to promote sparsity in a variety of applications including blind deconvolution. Most existing implementations are heuristic or require smoothing the l1/l2 penalty. Lifted versions of l1/l2 constraints have also been proposed but are still challenging to implement. Inspired by the lifting approach, we propose to split the sparse signals into positive and negative components and apply an l1/l2 constraint to the difference, thereby obtaining a constraint that is easy to implement without smoothing the l1 or l2 norms. We show that a method of multipliers implementation of the resulting model can recover source wavelets that are not necessarily minimum phase and approximately reconstruct the sparse reflectivities. It appears to be robust to the initialization and to small amounts of noise in the data. We also discuss extensions to the Estimation of Primaries by Sparse Inversion (EPSI) convolution model.},
	keywords = {Presentation, SINBAD, SINBADFALL2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Fall/esser2014SINBADlcs/esser2014SINBADlcs.pdf},
	author = {Ernie Esser and Tim T.Y. Lin and Rongrong Wang and Felix J. Herrmann}
}
@presentation {lin2014SINBADmas,
	title = {Multilevel acceleration strategy for REPSI},
	year = {2014},
	publisher = {SINBAD},
	abstract = {This talk discusses a multilevel inversion strategy that aims to substantially reduce the computational costs of the Robust Estimation of Primaries by Sparse Inversion algorithm. The proposed method solves early iterations of REPSI at very coarse spatial sampling grids while gradually ramping-up the spatial sampling when more accuracy is desired. No changes to the the core implementation of the original algorithm are necessary while in addition only requiring trace decimation, low-pass filtering, and rudimentary interpolation techniques.},
	keywords = {Presentation, SINBAD, SINBADSPRING2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Spring/lin2014SINBADmas/lin2014SINBADmas.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
@presentation {lin2013SINBADbre,
	title = {Bootstrapping robust EPSI with coarsely sampled data},
	year = {2013},
	publisher = {SINBAD},
	abstract = {The EPSI method of surface multiple removal directly inverts for the free-surface operator, i.e., the multiple-free Greens function of the subsurface seismic response. One peculiar feature of this approach is the theoretical independence of the spectrum of the free-surface operator from the spectrum of the observed data. The SRME approach requires coarsely sampled data to be low-pass filtered sufficiently in order to avoid aliasing in multiple contribution gathers, which in turn limits the temporal resolution of the demultipled result. Conversely, such limitations in temporal resolution do not directly apply to the inversion solution of EPSI. This property can in turn be exploited both to significantly lower the cost of EPSI and to mitigate the effect of under sampled data in a controlled way.},
	keywords = {Presentation, SINBAD, SINBADFALL2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Fall/lin2013SINBADbre/lin2013SINBADbre.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
@presentation {lin2013SINBADcsd,
	title = {Cosparse seismic data interpolation},
	year = {2013},
	publisher = {SINBAD},
	abstract = {Over the years we have investigated seismic data interpolation and redatuming algorithms rely on on the assumption that seismic records and images permit sparse approximations under certain representations, such as Curvelet coefficients. Recent findings have suggested that for redundant representations (of which Curvelet is an example), the analysis operator that maps the physical signal to coefficients may also play a crucial role in recovering data from incomplete observations. This insight elevates the significance of a question that often goes unaddressed: is it better for the transform-domain sparsity to be achieved through explicit construction of sparse representations (e.g., by thresholding of small transform-domain coefficients), or by demanding that the algorithm return physical signals which produces sparse coefficients when hit with the forward transform? Recent results show that the two approaches give rise to different solutions when the transform is redundant, and that the latter approach imposes a whole new class of constraints. In particular, the number of zero-valued coefficients given by the analysis operator acting on the signal, referred to as its "cosparsity", have an analogous role to the sparsity of the signal in terms of the coefficients. From this framework, a new reconstruction algorithm is proposed which may allow better reconstruction from subsampled signaled than what the sparsity assumption alone would predict. In this work we apply the new framework and algorithm to the case of seismic data interpolation under the curvelet domain, and show that it admits better reconstruction than some existing L1 sparsity-based methods derived from compressive sensing for a range of subsampling factors. We will also investigate different analysis operators and their impact on both sparsity and cosparsity-based algorithms.},
	keywords = {Presentation, SINBAD, SINBADSPRING2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Spring/lin2013SINBADcsd/lin2013SINBADcsd.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
@presentation {lin2012SINBADics,
	title = {An introduction to cosparse signal reconstruction},
	year = {2012},
	publisher = {SINBAD},
	abstract = {Undersampling techniques in exploration seismology usually relies on the assumption that seismic records and images permit sparse approximations under certain representations, such as Curvelet coefficients. Recent findings have suggested that for redundant representations (of which Curvelet is an example), the analysis operator that maps the physical signal to coefficients may also play a crucial role in recovering data from incomplete observations. In particular, the number of zero-valued coefficients given by the analysis operator acting on the signal, referred to as its "cosparsity", have an analogous role to the sparsity of the signal in terms of the coefficients. The cosparsity of the signal permits recovery guarantees that are completely separate from sparsity-based models, and gives rise to distinct sets of reconstruction algorithms and performances compared to sparsity-based approaches. We present in this talk some initial findings on the viability of cosparse reconstruction for a variety of seismic applications that previously relied on sparse signal reconstruction, such as data interpolation and source separation.},
	keywords = {Presentation, SINBAD, SINBADFALL2012, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2012/Fall/lin2012SINBADics/lin2012SINBADics_pres.pdf},
	author = {Tim T.Y. Lin}
}
@presentation {Lin2012SINBADrdr,
	title = {Recent developments on the robust estimation of primaries by sparse inversion},
	year = {2012},
	publisher = {SINBAD},
	abstract = {Robust estimation of primaries by sparse inversion is a next-generation surface multiple removal technique with an objective to truly invert an operator that models the free-surface. Key to the success of this approach is the imposition of a sparsity constraint on the primary impulse response in the time domain. This is accomplished by carefully applying large-scale convex optimization techniques on an extended L1 minimization problem. One of the benefits of our approach is that many extensions to the algorithm can be devised under this optimization framework to improve the quality of the solution given fixed computational costs and mitigating various shortcomings in field data. This talk will first review the basic technique of Robust EPSI and follow with some highlights on recent further developments of the algorithm, including a discussion on the role of regularization by reciprocity and the interpolation of near-offset data, as well as investigations into optimality and robustness to data outliers.},
	keywords = {Presentation, SINBAD, SINBADFALL2012, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2012/Fall/Lin2012SINBADrdr/Lin2012SINBADrdr_pres.pdf},
	author = {Tim T.Y. Lin}
}
@presentation {herrmann2012SINBADhpc,
	title = {SLIM{\textquoteright}s perspective on HPC \& big data},
	year = {2012},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2012, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2012/Fall/herrmann2012SINBADhpc/herrmann2012SINBADhpc_pres.pdf},
	author = {Tim T.Y. Lin and Tristan van Leeuwen and Felix J. Herrmann}
}
@presentation {lin2011SINBADirEPSI,
	title = {Inside the robust EPSI formulation},
	year = {2011},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2011, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2011/Fall/lin2011SINBADirEPSI/lin2011SINBADirEPSI_pres.pdf},
	author = {Tim T.Y. Lin}
}
@presentation {lin2011SINBADrep,
	title = {Robust EPSI in a curvelet-like representation domain},
	year = {2011},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADSPRING2011, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2011/Spring/lin2011SINBADrep/lin2011SINBADrep_pres.pdf},
	author = {Tim T.Y. Lin}
}
@presentation {lin2011SINBADslim,
	title = {SLIM{\textquoteright}s software design principles},
	year = {2011},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2011, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2011/Fall/lin2011SINBADslim/lin2011SINBADslim_pres.pdf},
	author = {Tim T.Y. Lin}
}
@presentation {lin2010SINBADlib,
	title = {Leveraging informed blind deconvolution techniques for the estimation of primaries by sparse inversion},
	year = {2010},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2010, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2010/Fall/lin2010SINBADlib/lin2010SINBADlib_pres.pdf},
	author = {Tim T.Y. Lin}
}
@presentation {lin2010SINBADsre,
	title = {Software release: estimation of primaries by L1 inversion},
	year = {2010},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2010, SLIM},
	author = {Tim T.Y. Lin}
}
@presentation {lin2010SINBADsol,
	title = {Sparse optimization and the L1 norm},
	year = {2010},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2010, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2010/Fall/lin2010SINBADsol/lin2010SINBADsol_pres.pdf},
	author = {Tim T.Y. Lin}
}
@article {herrmann2009GEOPcsf,
	title = {Compressive simultaneous full-waveform simulation},
	journal = {Geophysics},
	volume = {74},
	number = {4},
	year = {2009},
	month = {07-08},
	pages = {A35-A40},
	abstract = {The fact that computational complexity of wavefield simulation is proportional to the size of the discretized model and acquisition geometry, and not to the complexity of the simulated wavefield, is a major impediment within seismic imaging. By turning simulation into a compressive sensing problem{\textendash}-where simulated data is recovered from a relatively small number of independent simultaneous sources{\textendash}-we remove this impediment by showing that compressively sampling a simulation is equivalent to compressively sampling the sources, followed by solving a reduced system. As in compressive sensing, this allows for a reduction in sampling rate and hence in simulation costs. We demonstrate this principle for the time-harmonic Helmholtz solver. The solution is computed by inverting the reduced system, followed by a recovery of the full wavefield with a sparsity promoting program. Depending on the wavefield{\textquoteright}s sparsity, this approach can lead to significant cost reductions, in particular when combined with the implicit preconditioned Helmholtz solver, which is known to converge even for decreasing mesh sizes and increasing angular frequencies. These properties make our scheme a viable alternative to explicit time-domain finite-differences.},
	keywords = {Compressive Sensing, full-waveform, Modelling, SLIM},
	doi = {10.1190/1.3115122},
	url = {http://library.seg.org/doi/abs/10.1190/1.3115122},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2009/herrmann2009GEOPcsf/herrmann2009GEOPcsf.pdf},
	author = {Felix J. Herrmann and Yogi A. Erlangga and Tim T.Y. Lin}
}
@mastersthesis {lin08THccl,
	title = {Compressed computation of large-scale wavefield extrapolation in inhomogeneous medium},
	year = {2008},
	month = {04},
	school = {University of British Columbia},
	type = {mastersmasters},
	abstract = {In this work an explicit algorithm for the extrapolation of one-way wavefields is proposed which combines recent developments in information theory and theoretical signal processing with the physics of wave propagation. Because of excessive memory requirements, explicit formulations for wave propagation have proven to be a challenge in 3-D. By using ideas from {\textquoteleft}{\textquoteleft}compressed sensing{\textquoteright}{\textquoteright}, we are able to formulate the (inverse) wavefield extrapolation problem on small subsets of the data volume, thereby reducing the size of the operators. Compressed sensing entails a new paradigm for signal recovery that provides conditions under which signals can be recovered from incomplete samplings by \emphnonlinear recovery methods that promote sparsity of the to-be-recovered signal. According to this theory, signals can successfully be recovered when the measurement basis is \emphincoherent with the representation in which the wavefield is sparse. In this new approach, the eigenfunctions of the Helmholtz operator are recognized as a basis that is incoherent with sparsity transforms that are known to compress seismic wavefields. By casting the wavefield extrapolation problem in this framework, wavefields can successfully be extrapolated in the modal domain, despite evanescent wave modes. The degree to which the wavefield can be recovered depends on the number of missing (evanescent) wave modes and on the complexity of the wavefield. A proof of principle for the {\textquoteleft}{\textquoteleft}compressed sensing{\textquoteright}{\textquoteright} method is given for inverse wavefield extrapolation in 2-D. The results show that our method is stable, has reduced dip limitations and handles evanescent waves in inverse extrapolation.},
	keywords = {BSc, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2008/lin08THccl.pdf},
	author = {Tim T.Y. Lin}
}
@conference {lin2008SINBADcwe,
	title = {Compressed wavefield extrapolation},
	booktitle = {SINBAD},
	year = {2008},
	keywords = {Presentation, SINBAD, SLIM},
	presentation = {https://slim.gatech.edu/sites/data/Papers/lin08cwe.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
@conference {herrmann2008SIAMcsm,
	title = {Compressive sampling meets seismic imaging},
	booktitle = {SIAM},
	year = {2008},
	abstract = {Compressive sensing has led to fundamental new insights in the recovery of compressible signals from sub-Nyquist samplings. It is shown how jittered subsampling can be used to create favorable recovery conditions. Applications include mitigation of incomplete acquisitions and wavefield computations. While the former is a direct adaptation of compressive sampling, the latter application represents a new way of compressing wavefield extrapolation operators. Operators are not diagonalized but are compressively sampled reducing the computational costs.},
	keywords = {Presentation, SIAM, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2008/herrmann2008SIAMcsm/herrmann2008SIAMcsm.pdf},
	author = {Felix J. Herrmann and Yogi A. Erlangga and Tim T.Y. Lin}
}
@conference {lin2008SEGiso,
	title = {Interpolating solutions of the Helmholtz equation with compressed sensing},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {27},
	year = {2008},
	month = {01},
	pages = {2122-2126},
	publisher = {SEG},
	organization = {SEG},
	abstract = {We present an algorithm which allows us to model wavefields with frequency-domain methods using a much smaller number of frequencies than that typically required by the classical sampling theory in order to obtain an alias-free result. The foundation of the algorithm is the recent results on the compressed sensing, which state that data can be successfully recovered from an incomplete measurement if the data is sufficiently sparse. Results from numerical experiment show that only 30\% of the total frequency spectrum is need to capture the full wavefield information when working in the hard 2D synthetic Marmousi model.},
	keywords = {Presentation, SEG, SLIM},
	doi = {10.1190/1.3059307},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2008/lin08SEGiso/lin08SEGiso.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2008/lin08SEGiso/lin08SEGiso.pdf},
	author = {Tim T.Y. Lin and Evgeniy Lebed and Yogi A. Erlangga and Felix J. Herrmann}
}
@conference {herrmann2008SINBADitc,
	title = {Introduction to compressive (wavefield) computation},
	booktitle = {SINBAD 2008},
	year = {2008},
	keywords = {Presentation, SINBAD, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2008/herrmann2008SINBADitc/herrmann2008SINBADitc.pdf},
	author = {Felix J. Herrmann and Yogi A. Erlangga and Tim T.Y. Lin and Cody R. Brown}
}
@article {lin2007GEOPcwe,
	title = {Compressed wavefield extrapolation},
	journal = {Geophysics},
	volume = {72},
	number = {5},
	year = {2007},
	month = {08},
	pages = {SM77-SM93},
	publisher = {SEG},
	abstract = {An explicit algorithm for the extrapolation of one-way wavefields is proposed that combines recent developments in information theory and theoretical signal processing with the physics of wave propagation. Because of excessive memory requirements, explicit formulations for wave propagation have proven to be a challenge in 3D. By using ideas from compressed sensing, we are able to formulate the (inverse) wavefield extrapolation problem on small subsets of the data volume, thereby reducing the size of the operators. Compressed sensing entails a new paradigm for signal recovery that provides conditions under which signals can be recovered from incomplete samplings by nonlinear recovery methods that promote sparsity of the to-be-recovered signal. According to this theory, signals can be successfully recovered when the measurement basis is incoherent with the representa-tion in which the wavefield is sparse. In this new approach, the eigenfunctions of the Helmholtz operator are recognized as a basis that is incoherent with curvelets that are known to compress seismic wavefields. By casting the wavefield extrapolation problem in this framework, wavefields can be successfully extrapolated in the modal domain, despite evanescent wave modes. The degree to which the wavefield can be recovered depends on the number of missing (evanescent) wavemodes and on the complexity of the wavefield. A proof of principle for the compressed sensing method is given for inverse wavefield extrapolation in 2D, together with a pathway to 3D during which the multiscale and multiangular properties of curvelets, in relation to the Helmholz operator, are exploited. The results show that our method is stable, has reduced dip limitations, and handles evanescent waves in inverse extrapolation. \copyright2007 Society of Exploration Geophysicists},
	keywords = {Modelling, SLIM, wave propagation},
	doi = {10.1190/1.2750716},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2007/lin07cwe/lin07cwe.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
@conference {lin2007SEGcwe1,
	title = {Compressed wavefield extrapolation with curvelets},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {26},
	year = {2007},
	pages = {1997-2001},
	abstract = {An explicit algorithm for the extrapolation of one-way wavefields is proposed which combines recent developments in information theory and theoretical signal processing with the physics of wave propagation. Because of excessive memory requirements, explicit formulations for wave propagation have proven to be a challenge in 3-D. By using ideas from {\textquoteleft}{\textquoteleft}compressed sensing{\textquoteright}{\textquoteright}, we are able to formulate the (inverse) wavefield extrapolation problem on small subsets of the data volume, thereby reducing the size of the operators. According to compressed sensing theory, signals can successfully be recovered from an imcomplete set of measurements when the measurement basis is incoherent with the representation in which the wavefield is sparse. In this new approach, the eigenfunctions of the Helmholtz operator are recognized as a basis that is incoherent with curvelets that are known to compress seismic wavefields. By casting the wavefield extrapolation problem in this framework, wavefields can successfully be extrapolated in the modal domain via a computationally cheaper operation. A proof of principle for the {\textquoteleft}{\textquoteleft}compressed sensing{\textquoteright}{\textquoteright} method is given for wavefield extrapolation in 2-D. The results show that our method is stable and produces identical results compared to the direct application of the full extrapolation operator. \copyright2007 Society of Exploration Geophysicists},
	keywords = {Presentation, SEG, SLIM},
	doi = {10.1190/1.2792882},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2007/lin07SEGcwe1/lin07SEGcwe1.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2007/lin07SEGcwe1/lin07SEGcwe1_pres.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
@conference {lin2006SINBADci,
	title = {Compressed imaging},
	booktitle = {SINBAD 2006},
	year = {2006},
	abstract = {In 1998 Grimbergen et. al. introduced a new method for computing wavefield propagation which improved on the previously employed local explicit operator method in that it exhibited no dip limitation, accurately handled laterally varying background ground velocity models, and is unconditionally stable. These desirable properties are mainly attributed to bringing the propagation problem into an eigenvector basis that diagonalizes the propagation operators. This modal-transform method, however, requires at each depth-level the solution of a large-scale sparse eigenvalue problem to compute the square-root of the Helmholtz operator. By using recent results from compressed sensing, we hope to reduce these computational costs that typically involve the synthesizes of the imaging operators and the cost of matrix-vector products. To reduce these costs, we compress the extrapolation operators by using only a fraction of the positive eigenvalues and temporal frequencies. This reduction not only leads to smaller matrices but also to reduced synthesis costs. These reductions go at the expense of solving a recovery problem from incomplete data. During the presentation, we show that wavefields can accurately be extrapolated with a compressed operators and competitive costs.},
	keywords = {Presentation, SINBAD, SLIM},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2006/lin2006SINBADci/lin2006SINBADci.pdf},
	author = {Tim T.Y. Lin}
}
