@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}
}
