@article{Benichoux2013,
author = {Benichoux, Alexis},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/bvg13\_revised.pdf:pdf},
journal = {\ldots on Acoustics, Speech, \ldots},
title = {{A fundamental pitfall in blind deconvolution with sparse and shift-invariant priors}},
url = {http://hal.archives-ouvertes.fr/hal-00800770/},
year = {2013}
}
@article{DAspremont2007,
abstract = {Given multivariate time series, we study the problem of forming portfolios with maximum mean reversion while constraining the number of assets in these portfolios. We show that it can be formulated as a sparse canonical correlation analysis and study various algorithms to solve the corresponding sparse generalized eigenvalue problems. After discussing penalized parameter estimation procedures, we study the sparsity versus predictability tradeoff and the impact of predictability in various markets.},
archivePrefix = {arXiv},
arxivId = {0708.3048},
author = {D'Aspremont, Alexandre},
eprint = {0708.3048},
file = {:D$\backslash$:/Dropbox/docs/math/chapter/refs/0708.3048v2.pdf:pdf},
keywords = {convergence trading,covari-,mean reversion,momentum trading,sparse estimation},
month = aug,
pages = {1--24},
title = {{Identifying Small Mean Reverting Portfolios}},
url = {http://arxiv.org/abs/0708.3048},
year = {2007}
}
@article{Dey,
author = {Dey, Ayon K and Lines, Laurence R},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/seismic\_deconv\_refs.pdf:pdf},
number = {1994},
pages = {1--28},
title = {{Seismic source wavelet estimation and the random reflectivity assumption}},
volume = {10}
}
@article{Eckstein1992,
author = {Eckstein, Jonathan and Bertsekas, Dimitri P.},
doi = {10.1007/BF01581204},
file = {:D$\backslash$:/Dropbox/docs/old\_desktop/papers/convex/Eckstein\_Bertsekas.pdf:pdf},
journal = {Mathematical Programming},
keywords = {decomposition,monotone operators,proximal point algorithm},
month = apr,
number = {1-3},
pages = {293--318},
title = {{On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators}},
url = {http://link.springer.com/10.1007/BF01581204},
volume = {55},
year = {1992}
}
@article{Efrat,
author = {Efrat, Netalee and Glasner, Daniel and Apartsin, Alexander and Nadler, Boaz and Levin, Anat},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/SupresEfratEtal-iccv2013.pdf:pdf},
title = {{Accurate Blur Models vs . Image Priors in Single Image Super-Resolution}}
}
@article{Esser2014,
author = {Esser, E.E. and Herrmann, F.J.H.},
file = {:D$\backslash$:/Dropbox/docs/math/slim/papers/esser2014EAGEacp.pdf:pdf},
title = {{Application of a Convex Phase Retrieval Method to Blind Seismic Deconvolution}},
url = {http://www.earthdoc.org/publication/publicationdetails/?publication=76459},
year = {2014}
}
@article{EvansK.F.,
author = {{Evans, K.F.}, Cornwell T.J.},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/1985A+A\_\_\_143\_\_\_77C.pdf:pdf},
title = {{A simple maximum entropy deconvolution method}}
}
@article{Gholami2012,
author = {Gholami, Ali and Sacchi, Mauricio D.},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/gholami\_sacchi.pdf:pdf},
issn = {0196-2892},
journal = {IEEE Transactions on Geoscience and Remote Sensing},
month = oct,
number = {10},
pages = {4105--4116},
title = {{A Fast and Automatic Sparse Deconvolution in the Presence of Outliers}},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6185658},
volume = {50},
year = {2012}
}
@article{Gray1979,
author = {Gray, WC},
file = {:D$\backslash$:/Dropbox/docs/math/slim/papers/14\_19.pdf:pdf},
title = {{Variable norm deconvolution}},
url = {http://sepwww.stanford.edu/theses/sep19/19\_00.pdf},
year = {1979}
}
@article{Ji2012,
author = {Ji, Hui and Li, Jia and Shen, Zuowei and Wang, Kang},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/sharp\_wavelet.pdf:pdf},
issn = {10635203},
journal = {Applied and Computational Harmonic Analysis},
month = mar,
number = {2},
pages = {295--304},
publisher = {Elsevier Inc.},
title = {{Image deconvolution using a characterization of sharp images in wavelet domain}},
url = {http://linkinghub.elsevier.com/retrieve/pii/S1063520311001059},
volume = {32},
year = {2012}
}
@article{Lines1977,
author = {Lines, LR and Ulrych, TJ},
file = {:D$\backslash$:/Dropbox/docs/math/slim/papers/seismic\_deconv\_lines\_ulrych.pdf:pdf},
journal = {Geophysical Prospecting},
title = {{The Old and the New in Seismic Deconvolution and Wavelet ESTIMATION*}},
url = {http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2478.1977.tb01185.x/full},
year = {1977}
}
@article{Oymak2012,
abstract = {The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank matrices, among others. In various applications in signal processing and machine learning, the model of interest is known to be structured in $\backslash$emph\{several\} ways at the same time, for example, a matrix that is simultaneously sparse and low-rank. An important application is the sparse phase retrieval problem, where the goal is to recover a sparse signal from phaseless measurements. In machine learning, the problem comes up when combining several regularizers that each promote a certain desired structure. Often penalties (norms) that promote each individual structure are known and yield an order-wise optimal number of measurements (e.g., \$\backslash ell\_1\$ norm for sparsity, nuclear norm for matrix rank), so it is reasonable to minimize a combination of such norms. We show that, surprisingly, if we use multi-objective optimization with the individual norms, then we can do no better, order-wise, than an algorithm that exploits only one of the several structures. This result suggests that to fully exploit the multiple structures, we need an entirely new convex relaxation, i.e., not one that is a function of the convex relaxations used for each structure. We then specialize our results to the case of sparse and low-rank matrices. We show that a nonconvex formulation of the problem can recover the model from very few measurements, on the order of the degrees of freedom of the matrix, whereas the convex problem obtained from a combination of the \$\backslash ell\_1\$ and nuclear norms requires many more measurements. This proves an order-wise gap between the performance of the convex and nonconvex recovery problems in this case.},
archivePrefix = {arXiv},
arxivId = {1212.3753},
author = {Oymak, Samet and Jalali, Amin and Fazel, Maryam and Eldar, Yonina C and Hassibi, Babak},
eprint = {1212.3753},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/sparse\_AND\_lowrank.pdf:pdf},
journal = {arXiv.org},
keywords = {compressed sensing,convex relaxation,performance bounds,regularization},
month = dec,
pages = {30},
publisher = {Cornell University Library},
title = {{Simultaneously Structured Models with Application to Sparse and Low-rank Matrices}},
url = {http://arxiv.org/abs/1212.3753$\backslash$npapers2://publication/uuid/DD9963F1-0C91-435A-9A84-DC1FB206BE38},
volume = {cs.IT},
year = {2012}
}
@article{Wiggins1978,
author = {Wiggins, RA},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/1-s2.0-0016714278900054-main.pdf:pdf},
journal = {Geoexploration},
pages = {21--35},
title = {{Minimum entropy deconvolution}},
url = {http://www.sciencedirect.com/science/article/pii/0016714278900054},
volume = {16},
year = {1978}
}
@article{Ahmed2012,
abstract = {We consider the problem of recovering two unknown vectors, \$\backslash w\$ and \$\backslash x\$, of length \$L\$ from their circular convolution. We make the structural assumption that the two vectors are members of known subspaces, one with dimension \$N\$ and the other with dimension \$K\$. Although the observed convolution is nonlinear in both \$\backslash w\$ and \$\backslash x\$, it is linear in the rank-1 matrix formed by their outer product \$\backslash w\backslash x\^{}*\$. This observation allows us to recast the deconvolution problem as low-rank matrix recovery problem from linear measurements, whose natural convex relaxation is a nuclear norm minimization program. We prove the effectiveness of this relaxation by showing that for "generic" signals, the program can deconvolve \$\backslash w\$ and \$\backslash x\$ exactly when the maximum of \$N\$ and \$K\$ is almost on the order of \$L\$. That is, we show that if \$\backslash x\$ is drawn from a random subspace of dimension \$N\$, and \$\backslash w\$ is a vector in a subspace of dimension \$K\$ whose basis vectors are "spread out" in the frequency domain, then nuclear norm minimization recovers \$\backslash w\backslash x\^{}*\$ without error. We discuss this result in the context of blind channel estimation in communications. If we have a message of length \$N\$ which we code using a random \$L\backslash times N\$ coding matrix, and the encoded message travels through an unknown linear time-invariant channel of maximum length \$K\$, then the receiver can recover both the channel response and the message when \$L\backslash gtrsim N+K\$, to within constant and log factors.},
archivePrefix = {arXiv},
arxivId = {1211.5608},
author = {Ahmed, Ali and Recht, Benjamin and Romberg, Justin},
eprint = {1211.5608},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/blind\_deconv\_SDP.pdf:pdf},
journal = {arXiv preprint arXiv:1211.5608},
month = nov,
pages = {40},
title = {{Blind deconvolution using convex programming}},
url = {http://arxiv.org/abs/1211.5608},
year = {2012}
}
@book{Bertsekas1982a,
author = {Bertsekas, Dimitri P.},
publisher = {Academic Press, Inc.},
title = {{Constrained Optimization and Lagrange Multiplier Methods}},
year = {1982}
}
@article{Choudhary,
author = {Choudhary, Sunav and Mitra, Urbashi},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/SBD\_id-3.pdf:pdf},
title = {{Sparse Blind Deconvolution : What Cannot Be Done}}
}
@book{CLaerbout1979,
author = {Claerbout, J.},
booktitle = {IEEE Transactions on Acoustics, Speech, and Signal Processing},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/claerbout.pdf:pdf},
month = oct,
number = {5},
pages = {564--565},
title = {{Fundamentals of geophysical data processing}},
volume = {27},
year = {1979}
}
@article{Donoho1981,
author = {Donoho, D},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/MED.pdf:pdf},
journal = {Applied time series analysis II},
title = {{On minimum entropy deconvolution}},
url = {http://scholar.google.com/scholar?hl=en\&btnG=Search\&q=intitle:on+minimum+entropy+deconvolution\#0},
year = {1981}
}
@article{Groenestijn2009,
author = {van Groenestijn, GJ and Verschuur, DJ},
file = {:D$\backslash$:/Dropbox/docs/math/slim/papers/vanGroenestijn\_2009.pdf:pdf},
journal = {Geophysics},
number = {3},
title = {{Estimating primaries by sparse inversion and application to near-offset data reconstruction}},
url = {http://library.seg.org/doi/abs/10.1190/1.3111115},
volume = {74},
year = {2009}
}
@techreport{Kabal2011,
author = {Kabal, Peter},
booktitle = {MMSP Lab Technical Report, Dept. Electrical \& Computer Engineering, McGill University},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/KabalR2011a.pdf:pdf},
institution = {MMSP Lab Technical Report, Dept. Electrical \& Computer Engineering, McGill University},
number = {March},
title = {{Minimum-Phase \& All-Pass Filters}},
url = {http://www-mmsp.ece.mcgill.ca/documents/reports/2011/KabalR2011a.pdf},
year = {2011}
}
@article{Santosa1986,
author = {Santosa, Fadil and Symes, William W.},
journal = {SIAM Journal on Scientific and Statistical Computing},
month = oct,
number = {4},
pages = {1307--1330},
title = {{Linear Inversion of Band-Limited Reflection Seismograms}},
url = {http://epubs.siam.org/doi/abs/10.1137/0907087},
volume = {7},
year = {1986}
}
@book{Ulrych2006,
author = {Ulrych, T.J. and Sacchi, M.D.},
pages = {436},
publisher = {Elsevier Science},
title = {{Information-Based Inversion and Processing with Applications, Volume 36 (Handbook of Geophysical Exploration: Seismic Exploration)}},
url = {http://www.amazon.com/Information-Based-Processing-Applications-Geophysical-Exploration/dp/008044721X},
year = {2006}
}
@article{Verschuur1992,
author = {Verschuur, D. J. and Berkhout, a. J. and Wapenaar, C. P. a.},
file = {:D$\backslash$:/Dropbox/docs/math/slim/papers/geo\_92b.pdf:pdf},
journal = {Geophysics},
month = sep,
number = {9},
pages = {1166--1177},
title = {{Adaptive surface related multiple elimination}},
url = {http://library.seg.org/doi/abs/10.1190/1.1443330},
volume = {57},
year = {1992}
}
@article{Candes2013,
abstract = {Suppose we wish to recover a signal x in C\^{}n from m intensity measurements of the form |<x,z\_i>|\^{}2, i = 1, 2,..., m; that is, from data in which phase information is missing. We prove that if the vectors z\_i are sampled independently and uniformly at random on the unit sphere, then the signal x can be recovered exactly (up to a global phase factor) by solving a convenient semidefinite program---a trace-norm minimization problem; this holds with large probability provided that m is on the order of n log n, and without any assumption about the signal whatsoever. This novel result demonstrates that in some instances, the combinatorial phase retrieval problem can be solved by convex programming techniques. Finally, we also prove that our methodology is robust vis a vis additive noise.},
archivePrefix = {arXiv},
arxivId = {http://arxiv.org/abs/1109.4499},
author = {Cand\`{e}s, Emmanuel J. and Strohmer, Thomas and Voroninski, Vladislav},
eprint = {/arxiv.org/abs/1109.4499},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/ExactPR-3.pdf:pdf},
journal = {Communications on Pure and Applied Mathematics},
month = aug,
number = {8},
pages = {1241--1274},
primaryClass = {http:},
title = {{PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming}},
url = {http://doi.wiley.com/10.1002/cpa.21432},
volume = {66},
year = {2013}
}
@article{Netrapalli2013,
archivePrefix = {arXiv},
arxivId = {arXiv:1306.0160v1},
author = {Netrapalli, Praneeth and Jain, P and Sanghavi, Sujay},
eprint = {arXiv:1306.0160v1},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/phase\_retrieval\_altmin.pdf:pdf},
journal = {Advances in Neural Information \ldots},
pages = {1--22},
title = {{Phase retrieval using alternating minimization}},
url = {http://papers.nips.cc/paper/5041-phase-retrieval-using-alternating-minimization},
year = {2013}
}
@article{Larue,
author = {Larue, Anthony and Baan, Mirko Van Der and Mars, I and Jutten, Christian},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/seg05\_abstract.pdf:pdf},
title = {{Sparsity or whiteness : what criterion to use for blind deconvolution of seismic data ? Deconvolution algorithm}}
}
@inproceedings{Lin2014,
author = {Lin, T.T.Y. and Herrmann, F.J.},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/lin2014EAGEmas.pdf:pdf},
title = {{Multilevel Acceleration Strategy for the Robust Estimation of Primaries by Sparse Inversion}},
url = {http://www.earthdoc.org/publication/publicationdetails/?publication=75544},
year = {2014}
}
@article{Demanet2012,
abstract = {We address the problem of recovering an n-vector from m linear measurements lacking sign or phase information. We show that lifting and semidefinite relaxation suffice by themselves for stable recovery in the setting of m = O(n log n) random sensing vectors, with high probability. The recovery method is optimizationless in the sense that trace minimization in the PhaseLift procedure is unnecessary. That is, PhaseLift reduces to a feasibility problem. The optimizationless perspective allows for a Douglas-Rachford numerical algorithm that is unavailable for PhaseLift. This method exhibits linear convergence with a favorable convergence rate and without any parameter tuning.},
archivePrefix = {arXiv},
arxivId = {1208.1803},
author = {Demanet, Laurent and Hand, Paul},
eprint = {1208.1803},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/demanet.pdf:pdf},
journal = {arXiv preprint arXiv:1208.1803},
keywords = {15a83,65k05,90c22,ams classifications,douglas-rachford,feasibility,lifting,matrix completion,phase retrieval,phaselift,semidefinite relaxation},
month = aug,
pages = {1--20},
title = {{Stable optimizationless recovery from phaseless linear measurements}},
url = {http://arxiv.org/abs/1208.1803},
year = {2012}
}
@article{Lemarechal1999,
author = {Lemar\'{e}chal, C and Oustry, F},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/SDPlifting.pdf:pdf},
title = {{Semidefinite relaxations and Lagrangian duality with application to combinatorial optimization}},
url = {http://hal.archives-ouvertes.fr/docs/00/07/29/58/PDF/RR-3710.pdf},
year = {1999}
}
@article{Claerbout1973,
author = {Claerbout, JF and Muir, Francis},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/826.full.pdf:pdf},
journal = {Geophysics},
title = {{Robust modeling with erratic data}},
url = {http://library.seg.org/doi/abs/10.1190/1.1440378},
volume = {38},
year = {1973}
}
@article{Combettes2007,
author = {Combettes, PL and Pesquet, JC},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/jstsp1.pdf:pdf},
journal = {Selected Topics in Signal \ldots},
number = {4},
pages = {1--12},
title = {{A Douglas–Rachford splitting approach to nonsmooth convex variational signal recovery}},
url = {http://ieeexplore.ieee.org/xpls/abs\_all.jsp?arnumber=4407760},
volume = {1},
year = {2007}
}
@article{Damera-Venkata2000,
author = {Damera-Venkata, N and Evans, B.L. and McCaslin, S.R.},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/ComplexMinPhase.pdf:pdf},
issn = {1053587X},
journal = {IEEE Transactions on Signal Processing},
month = may,
number = {5},
pages = {1491--1495},
title = {{Design of optimal minimum-phase digital FIR filters using discrete Hilbert transforms}},
url = {http://ieeexplore.ieee.org/xpls/abs\_all.jsp?arnumber=840000 http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=840000},
volume = {48},
year = {2000}
}
@article{DAspremont2007a,
author = {D'Aspremont, A and Ghaoui, L El and Jordan, MI and Lanckriet, GRG},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/SIAMSparsePCA.pdf:pdf},
journal = {SIAM review},
keywords = {62h25,90c22,90c27,ams subject classifications,definite relaxation,eve transform,factor analysis,karhunen-lo,moreau-yosida regularization,principal component analysis,semi-,semidefinite programming},
pages = {1--15},
title = {{A direct formulation for sparse PCA using semidefinite programming}},
url = {http://epubs.siam.org/doi/abs/10.1137/050645506},
year = {2007}
}
@article{Donoho1992,
author = {Donoho, David},
file = {:D$\backslash$:/Dropbox/docs/math/slim/papers/0523074.pdf:pdf},
journal = {SIAM J. Math. Anal},
keywords = {diffraction-limited imaging,entire functions of exponential,interpolation,inverse problems,nonlinear recovery,nyquist rate,rayleigh criterion,spectroscopy,superresolution,type},
number = {5},
pages = {1309--1331},
title = {superresoution via sparsity constraints},
volume = {23},
year = {1992}
}
@article{Dossal2005,
author = {Dossal, C and Mallat, S},
file = {:D$\backslash$:/Dropbox/docs/math/slim/papers/SparseSpike.pdf:pdf},
journal = {In Proceedings of Signal Processing with Adaptive Sparse Structured Representations},
number = {4},
pages = {123 -- 126},
title = {{Sparse spike deconvolution with minimum scale}},
url = {http://www.cmap.polytechnique.fr/~mallat/papiers/SparseSpike.pdf},
year = {2005}
}
@article{Esser2013,
author = {Esser, Ernie and Lou, Yifei and Xin, Jack},
file = {:D$\backslash$:/Dropbox/docs/math/slim/ernweb/90540.pdf:pdf},
journal = {SIAM Journal on Imaging Sciences},
keywords = {basis pursuit,difference of convex programming,differential optical absorption spec-,hyperspectral imaging,nonnegative least squares,scaled gradient projec-,structured sparsity,tion,unmixing},
month = jan,
number = {4},
pages = {2010--2046},
title = {{A Method for Finding Structured Sparse Solutions to Nonnegative Least Squares Problems with Applications}},
url = {http://epubs.siam.org/doi/abs/10.1137/13090540X},
volume = {6},
year = {2013}
}
@article{Hamdi1998,
author = {Hamdi, Abdelouahed},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/MMnonconvex.pdf:pdf},
keywords = {65k05,90c30,ams subject classification,augmented lagrangian,nonconvex programming,proximal regularization},
pages = {1--22},
title = {{Convergence Results on Proximal Method of Multipliers In Nonconvex Programming ∗}},
year = {1998}
}
@article{Krishnan2011,
author = {Krishnan, Dilip and Tay, Terence and Fergus, Rob},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/krishnan\_tay\_fergus.pdf:pdf},
journal = {Cvpr 2011},
month = jun,
pages = {233--240},
publisher = {Ieee},
title = {{Blind deconvolution using a normalized sparsity measure}},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5995521},
year = {2011}
}
@article{Lamoureux2007,
author = {Lamoureux, MP and Margrave, GF},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/analytic\_min\_phase.pdf:pdf},
journal = {CREWES Research Report},
number = {1},
pages = {1--12},
title = {{An analytic approach to minimum phase signals}},
url = {www.crewes.org/ForOurSponsors/ResearchReports/2007/2007-35.pdf‎},
volume = {19},
year = {2007}
}
@article{Long2014,
author = {Long, X and Solna, K and Xin, J},
file = {:D$\backslash$:/Dropbox/docs/math/slim/papers/cam14-55-3.pdf:pdf},
journal = {UCLA CAM Reports [14-55]},
keywords = {1,2 norms,91g10,91g60,91g70,ams subject classifications,around a,convergence trade is a,convergence trading,from the,introduction,l 1 and l,mean reversion,of the prices of,phenomenon that the difference,sparse estimation,trade designed to benefit,two assets may fluctuate},
pages = {1--29},
title = {{Two l1 based nonconvex methods for constructing sparse mean reverting portfolios}},
url = {ftp://ftp.math.ucla.edu/pub/camreport/cam14-55.pdf},
year = {2014}
}
@article{Repetti2014,
archivePrefix = {arXiv},
arxivId = {arXiv:1407.5465v2},
author = {Repetti, Audrey and Pham, MQ and Duval, Laurent},
eprint = {arXiv:1407.5465v2},
file = {:D$\backslash$:/Dropbox/docs/math/slim/papers/1407.5465v2.pdf:pdf},
pages = {1--11},
title = {{Euclid in a Taxicab: Sparse Blind Deconvolution with Smoothed l1/l2 Regularization}},
url = {http://ieeexplore.ieee.org/xpls/abs\_all.jsp?arnumber=6920070},
year = {2014}
}
@misc{Schmidt2012,
author = {Schmidt, Mark},
title = {{minFunc}},
url = {http://www.cs.ubc.ca/~schmidtm/Software/minFunc.html},
note = {http://www.cs.ubc.ca/~schmidtm/Software/minFunc.html},
year = {2012}
}
@article{White1974,
author = {White, RE and O'Brien, PNS},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/primary\_seismic\_pulse.pdf:pdf},
journal = {Geophysical Prospecting},
title = {{Estimation of the primary seismic pulse}},
url = {http://www.earthdoc.org/publication/publicationdetails/?publication=34819},
year = {1974}
}
@article{Yin2014,
author = {Yin, Penghang and Lou, Yifei and He, Qi and Xin, Jack},
file = {:D$\backslash$:/Dropbox/docs/math/slim/papers/cam14-01.pdf:pdf},
journal = {math.ucla.edu},
keywords = {1,2 minimization,49m29,65k10,90c26,algorithm,ams subject classifications,compressed sensing,cs,difference of convex functions,growing field of research,has been a rapidly,introduction,non-convex,simulate annealing,sparsity,ℓ 1},
pages = {1--25},
title = {{Minimization of L1-L2 for Compressed Sensing}},
url = {ftp://ftp.math.ucla.edu/pub/camreport/cam14-01.pdf},
year = {2014}
}
@article{Yin2014a,
abstract = {Phase retrieval aims to recover a signal \$x \backslash in \backslash mathbb\{C\}\^{}\{n\}\$ from its amplitude measurements \$|<x, a\_i > |\^{}2\$, \$i=1,2,...,m\$, where \$a\_i\$'s are over-complete basis vectors, with \$m\$ at least \$3n -2\$ to ensure a unique solution up to a constant phase factor. The quadratic measurement becomes linear in terms of the rank-one matrix \$X = x x\^{}*\$. Phase retrieval is then a rank-one minimization problem subject to linear constraint for which a convex relaxation based on trace-norm minimization (PhaseLift) has been extensively studied recently. At \$m=O(n)\$, PhaseLift recovers with high probability the rank-one solution. In this paper, we present a precise proxy of rank-one condition via the difference of trace and Frobenius norms which we call PhaseLiftOff. The associated least squares minimization with this penalty as regularization is equivalent to the rank-one least squares problem under a mild condition on the measurement noise. Stable recovery error estimates are valid at \$m=O(n)\$ with high probability. Computation of PhaseLiftOff minimization is carried out by a convergent difference of convex functions algorithm. In our numerical example, \$a\_i\$'s are Gaussian distributed. Numerical results show that PhaseLiftOff outperforms PhaseLift and its nonconvex variant (log-determinant regularization), and successfully recovers signals near the theoretical lower limit on the number of measurements without the noise.},
archivePrefix = {arXiv},
arxivId = {1406.6761},
author = {Yin, Penghang and Xin, Jack},
eprint = {1406.6761},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/1406.6761v3.pdf:pdf},
month = jun,
pages = {1--21},
title = {{PhaseLiftOff: an Accurate and Stable Phase Retrieval Method Based on Difference of Trace and Frobenius Norms}},
url = {http://arxiv.org/abs/1406.6761},
year = {2014}
}
@article{You,
author = {You, Seungil and Peng, Q},
file = {:D$\backslash$:/Dropbox/docs/math/SLIM/papers/opf\_proxy.pdf:pdf},
journal = {cds.caltech.edu},
title = {{A Non-convex Alternating Direction Method of Multipliers Heuristic for Optimal Power Flow}},
url = {http://www.cds.caltech.edu/~syou/pubs/opf\_proxy.pdf}
}