@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 {hargreaves2012SINBADavs,
	title = {Analysis versus synthesis in weighted sparse recovery},
	year = {2012},
	publisher = {SINBAD},
	abstract = {The synthesis model for compressive sensing has been the model of choice for many years and various weighting schemes have been shown to improve it{\textquoteright}s performance (see Yilmaz, Mansour, and Ghadermarzy talks). However, there is a counterpart model to synthesis, namely the analysis model, which has been less popular but recently attracted more attention (see Lin{\textquoteright}s talk). In this talk, weighting in the analysis model is discussed and applied to the seismic trace interpolation problem.},
	keywords = {Presentation, SINBAD, SINBADFALL2012, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2012/Fall/hargreaves2012SINBADavs/hargreaves2012SINBADavs_pres.pdf},
	author = {Brock Hargreaves}
}
