@article {ghadermarzy2013ncs,
	title = {Non-convex compressed sensing using partial support information},
	journal = {Journal of Sampling Theory in Signal and Image Processing},
	volume = {13},
	number = {3},
	year = {2014},
	pages = {249-270},
	abstract = {In this paper we address the recovery conditions of weighted $\ell_p$ minimization for signal reconstruction from compressed sensing measurements when partial support in- formation is available. We show that weighted $\ell_p$ minimization with 0 < p < 1 is stable and robust under weaker sufficient conditions compared to weighted $\ell_1$ minimization. Moreover, the sufficient recovery conditions of weighted $\ell_p$ are weaker than those of regular $\ell_p$ minimization if at least 50\% of the support estimate is accurate. We also review some algorithms which exist to solve the non-convex $\ell_p$ problem and illustrate our results with numerical experiments.},
	keywords = {compressed sensing, nonconvex optimization, sparse reconstruction, weighted $\ell_p$},
	url = {http://arxiv.org/abs/1311.3773},
	author = {Navid Ghadermarzy and Hassan Mansour and Ozgur Yilmaz}
}
@conference {ghadermarzy2014SEGsti,
	title = {Seismic trace interpolation with approximate message passing},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2014},
	note = {(SEG)},
	month = {10},
	pages = {3621-3626},
	abstract = {Approximate message passing (AMP) is a computationally effective algorithm for recovering high dimensional signals from a few compressed measurements. In this paper we use AMP to solve the seismic trace interpolation problem. We also show that we can exploit the fast AMP algorithm to improve the recovery results of seismic trace interpolation in curvelet domain, both in terms of convergence speed and recovery performance by using AMP in Fourier domain as a preprocessor for the L1 recovery in Curvelet domain.},
	keywords = {AMP, interpolation, SEG},
	doi = {http://dx.doi.org/10.1190/segam2014-0577.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2014/ghadermarzy2014SEGsti/ghadermarzy2014SEGsti.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2014/ghadermarzy2014SEGsti/ghadermarzy2014SEGsti_pres.pdf},
	author = {Navid Ghadermarzy and Ozgur Yilmaz and Felix J. Herrmann}
}
@presentation {tu2014SINBADsis,
	title = {Sparse inversion simplified},
	year = {2014},
	publisher = {SINBAD},
	abstract = {Implementation of the SPGl1 solver in low-level computer languages such as C or Fortran may sound daunting to many. This talk is tailored for you if you would like to reap benefits from using sparse constraints to regularize your inversion problem, and at the same time want some easy-to-implement algorithm to solve it. We discuss in this talk the linearized Bregman projection method that embraces both ingredients, and show promising applications in fast least-squares imaging and seismic data interpolation problems.},
	keywords = {Presentation, SINBAD, SINBADFALL2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Fall/tu2014SINBADsis/tu2014SINBADsis.pdf},
	author = {Ning Tu and Navid Ghadermarzy and Rajiv Kumar and Felix J. Herrmann}
}
@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 {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}
}
@mastersthesis {ghadermarzy2013THups,
	title = {Using prior support information in compressed sensing},
	year = {2013},
	note = {(MSc)},
	month = {08},
	school = {The University of British Columbia},
	type = {masters},
	address = {Vancouver},
	abstract = {Compressed sensing is a data acquisition technique that entails recovering estimates of sparse and compressible signals from $n$ linear measurements, significantly fewer than the signal ambient dimension $N$. In this thesis we show how we can reduce the required number of measurements even further if we incorporate prior information about the signal into the reconstruction algorithm. Specifically, we study certain weighted nonconvex $\ell_p$ minimization algorithms and a weighted approximate message passing algorithm. In Chapter 1 we describe compressed sensing as a practicable signal acquisition method in application and introduce the generic sparse approximation problem. Then we review some of the algorithms used in compressed sensing literature and briefly introduce the method we used to incorporate prior support information into these problems. In Chapter 2 we derive sufficient conditions for stable and robust recovery using weighted $\ell_p$ minimization and show that these conditions are better than those for recovery by regular $\ell_p$ and weighted $\ell_1$. We present extensive numerical experiments, both on synthetic examples and on audio, and seismic signals. In Chapter 3 we derive weighted AMP algorithm which iteratively solves the weighted $\ell_1$ minimization. We also introduce a reweighting scheme for weighted AMP algorithms which enhances the recovery performance of weighted AMP. We also apply these algorithms on synthetic experiments and on real audio signals.},
	keywords = {compressed sensing, MSc, thesis, weighted $\ell_1$},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2013/ghadermarzy2013THups.pdf},
	author = {Navid Ghadermarzy}
}
@presentation {ghadermarzy2012SINBADncc,
	title = {Non-convex compressed sensing using partial support information},
	year = {2012},
	publisher = {SINBAD},
	abstract = {In this talk, we will address the recovery conditions of weighted $\ell_p$ minimization for signal reconstruction from compressed sensing measurements when (possibly inaccurate) partial support information is available. First we will motivate the use of (weighted) $\ell_p$ minimization with $p<1$ and point out its advantages over weighted $\ell_1$ minimization when there is prior information on the support of the signal that is possibly partial and inaccurate. Then we will provide theoretical guarantees of sufficient recovery conditions for weighted $\ell_p$ minimization, which are better than those for (unweighted) $\ell_p$ minimization as well as those for weighted $\ell_1$. In the last part of the talk, we will illustrate our results with some numerical experiments stylized applications.},
	keywords = {Presentation, SINBAD, SINBADFALL2012, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2012/Fall/ghadermarzy2012SINBADncc/ghadermarzy2012SINBADncc_pres.pdf},
	author = {Navid Ghadermarzy}
}
