@presentation {yilmaz2014SINBADadc,
	title = {Analog-to-digital conversion in compressive sampling},
	year = {2014},
	publisher = {SINBAD},
	abstract = {Compressive sampling theory is now established as an effective method for dimension reduction when the underlying signals (e.g., seismic data) are sparse with respect to some suitable basis or frame (e.g., curvelets in the case of seismic). One important problem directly related to the acquisition of analog signals is how to perform analog-to-digital conversion. This is directly related to two important issues: (i) how accurately one can acquire a signal using compressive sampling (in terms of bit depth), and (ii) how {\textquoteleft}{\textquoteleft}compressed{\textquoteright}{\textquoteright} is compressive sampling (in terms of the total number of bits one ends up using after acquiring the signal). We will present recent results that provide answers to these questions. Specifically, we provide an analog-to-digital conversion method that achieves nearly optimal compression using cheap analog devices with a large margin for imperfections.},
	keywords = {Presentation, SINBAD, SINBADFALL2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Fall/yilmaz2014SINBADadc/yilmaz2014SINBADadc.pdf},
	author = {Ozgur Yilmaz}
}
@presentation {ghadermarzy2014SINBADwrr,
	title = {Wavefield reconstruction via randomized sampling},
	year = {2014},
	publisher = {SINBAD},
	abstract = {Regular sampling along the time axis is a common approach for seismic imaging. However, seismic data are often spatially undersampled due to economical reasons as well as ground surface limitations. Operational conditions might result in noisy traces or even gaps in coverage and irregular sampling which often leads to image artifacts. Seismic trace interpolation aims to interpolate missing traces in an otherwise regularly sampled seismic data to a complete regular grid. In this talk, we explain some techniques, with low computational complexity, that can be used to improve the results. In particular, we talk about weighting, switching to midpoint-offset domain from frequency-space domain, and uniform versus jittered undersampling. We illustrate the advantages of these modifications using a real seismic line from the Gulf of Suez.},
	keywords = {Presentation, SINBAD, SINBADFALL2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Fall/ghadermarzy2014SINBADwrr/ghadermarzy2014SINBADwrr.pdf},
	author = {Navid Ghadermarzy and Ozgur Yilmaz and Felix J. Herrmann}
}
@presentation {hargreaves2013SINBADbfo,
	title = {The bridge from orthogonal to redundant transforms and weighted $\ell_1$ optimization},
	year = {2013},
	publisher = {SINBAD},
	abstract = {Traditional arguments in synthesis $\ell_1$ -optimization require our forward operator to be orthogonal, though we use redundant transforms in practice. These traditional arguments do not translate to redundant transforms, and other arguments require impractical conditions on our effective measurement matrix. Recent theory in one-norm analysis, namely the optimal dual $\ell_1$ analysis of Shidong et al, have provided point-wise reconstruction error estimates for synthesis using an equivalence relationship where we can use weaker assumptions. This exposes an important model assumption indicating why analysis might outperform synthesis, for which careful consideration in seismic is necessary, and the need for models such as the cosparse model. In this talk we will discuss these ideas, provide evidence which indicates this theory should generalize to uniform error estimates(and thus not signal dependent), and how redundancy, support information, and weighting play important roles.},
	keywords = {Presentation, SINBAD, SINBADFALL2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Fall/hargreaves2013SINBADbfo/hargreaves2013SINBADbfo.pdf},
	author = {Brock Hargreaves and Ozgur Yilmaz and Felix J. Herrmann}
}
@presentation {yeung2013SINBADcsr,
	title = {Compressed sensing, recovery of signals using random Turbo matrices},
	year = {2013},
	publisher = {SINBAD},
	abstract = {Compressed sensing is an emerging technique that allows us to recover an image using far fewer number of measurements than classical sampling techniques. Designing the measurement matrices with certain properties are critical to this task. Gaussian matrices are most commonly used. We discover a new class of random matrices that can outperform the Gaussian matrices when we are in a situation of taking an outrageously small number of samples.},
	keywords = {Presentation, SINBAD, SINBADFALL2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Fall/yeung2013SINBADcsr/yeung2013SINBADcsr.pdf},
	author = {Enrico Au-Yeung and Ozgur Yilmaz and Felix J. Herrmann}
}
@presentation {ghadermarzy2013SINBADups,
	title = {Using prior support information in approximate message passing algorithms},
	year = {2013},
	publisher = {SINBAD},
	abstract = {Consider the standard compressed sensing problem. We want to recover sparse compressible aorsignal from few linear measurements. In this talk we investigate recovery performance when we have prior information about the support, i.e., the indices of the non-zero entries, of the signal to be recovered. First we briefly review the results of "weighted $\ell_p$ minimization algorithm with p = 1 and 0 < p < 1". Then we derive a weighted approximate message passing (AMP) algorithm which incorporates prior support information into the AMP algorithm. We empirically show that this algorithm recovers sparse signals significantly faster than weighted $\ell_1$ minimization. We also introduce a reweighting scheme for AMP and weighted AMP which, we observe, substantially improves the recovery conditions of these algorithms. We illustrate our results with extensive numerical experiments on synthetic data and seismic data reconstruction.},
	keywords = {Presentation, SINBAD, SINBADFALL2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Fall/ghadermarzy2013SINBADups/ghadermarzy2013SINBADups.pdf},
	author = {Navid Ghadermarzy and Ozgur Yilmaz and Felix J. Herrmann}
}
@presentation {au-yeung2012SINBADcs,
	title = {Compressed sensing, random Fourier matrix and jitter sampling},
	year = {2012},
	publisher = {SINBAD},
	abstract = {Compressed sensing is an emerging signal processing technique that allows signals to be sampled well below the Nyquist rate, when the signal has a sparse representation in an orthonormal basis. By using a random Fourier matrix or a Gaussian matrix as our measurement matrix, we can reconstruct a signal from far fewer measurements than required by Shannon sampling theorem. In this talk, we will discuss the role of uniform versus jitter sampling, both in a theoretical and practical viewpoint.},
	keywords = {Presentation, SINBAD, SINBADFALL2012, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2012/Fall/au-yeung2012SINBADcs/au-yeung2012SINBADcs_pres.pdf},
	author = {Enrico Au-Yeung and Hassan Mansour and Ozgur Yilmaz}
}
@presentation {yilmaz2012SINBADwms,
	title = {Weighted methods in sparse recovery},
	year = {2012},
	publisher = {SINBAD},
	abstract = {In the recent years we have successfully employed "weighted" algorithms to recover sparse signals from few linear, non-adaptive measurements. The general principle here is to use prior knowledge about the signal to be recovered, e.g., approximate locations of large-in-magnitude transform coefficients, if such information is available. An example for this is the use of weighted 1-norm minimization to improve wavefield reconstruction from randomized (sub)sampling. We will review these results and outline some new directions we have explored during the last year, such as weighted non-convex sparse recovery (see Ghadermarzy{\textquoteright}s talk), weighted analysis-based recovery (see Hargreaves{\textquoteright}s talk), and a weighted randomized Kaczmarz algorithm for solving large overdetermined systems of equations that are known to admit a (nearly) sparse solution. Various examples in seismic will be shown.},
	keywords = {Presentation, SINBAD, SINBADFALL2012, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2012/Fall/yilmaz2012SINBADwms/yilmaz2012SINBADwms_pres.pdf},
	author = {Ozgur Yilmaz}
}
@presentation {yilmaz2011SINBADcsp,
	title = {Compressed sensing with prior information},
	year = {2011},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2011, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2011/Fall/yilmaz2011SINBADcsp/yilmaz2011SINBADcsp_pres.pdf},
	author = {Ozgur Yilmaz}
}
@presentation {yilmaz2010SINBADsac,
	title = {Sparse approximations and compressive sensing: an overview},
	year = {2010},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2010, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2010/Fall/yilmaz2010SINBADsac/yilmaz2010SINBADsac_pres.pdf},
	author = {Ozgur Yilmaz}
}
@conference {wang2008SINBADrri,
	title = {Recent results in curvelet-based primary-multiple separation},
	booktitle = {SINBAD 2008},
	year = {2008},
	abstract = {We present a nonlinear curvelet-based sparsity-promoting formulation for the primary-multiple separation problem. We show that these coherent signal components can be separated robustly by explicitly exploiting the locality of curvelets in phase space (space-spatial frequency plane) and their ability to compress data volumes that contain wavefronts. This work is an extension of earlier results and the presented algorithms are shown to be stable under noise and moderately erroneous multiple predictions.},
	keywords = {Presentation, SINBAD, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2008/wang2008SINBADrri/wang2008SINBADrri.pdf},
	author = {Deli Wang and Rayan Saab and Ozgur Yilmaz and Felix J. Herrmann}
}
@conference {yilmaz2008SINBADsse,
	title = {Stable sparse expansions via non-convex optimization},
	booktitle = {SINBAD 2008},
	year = {2008},
	abstract = {We present theoretical results pertaining to the ability of p-(quasi)norm minimization to recover sparse and compressible signals from incomplete and noisy measurements. In particular, we extend the results of Candes, Romberg and Tao for 1-norm to the p $\ll$ 1 case. Our results indicate that depending on the restricted isometry constants and the noise level, p-norm minimization with certain values of p $\ll$ 1 provides better theoretical guarantees in terms of stability and robustness compared to 1-norm minimization. This is especially true when the restricted isometry constants are relatively large, or equivalently, when the data is significantly undersampled.},
	keywords = {Presentation, SINBAD, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2008/yilmaz2008SINBADsse/yilmaz2008SINBADsse.pdf},
	author = {Ozgur Yilmaz}
}
