Fetching the paper…
Reading the bibliography…
In many application areas we are faced with the following question: Can we recover a sparse vector $x_o \in \mathbb{R}^N$ from its undersampled set of noisy observations $y \in \mathbb{R}^n$, $y=A x_o+w$.
C. Stein, “Estimation of the mean of a multivariate normal distribution,” The Annals of Statistics , pp. 1135–1151, 1981
1981
Earlier work this paper cites.
M. Mézard and G. Parisi, “Replicas and optimization,” Journal de Physique Lettres , vol. 46, no. 17, pp. 771–778, 1985
1985
Earlier work this paper cites.
T. Tanaka, “A statistical-mechanics approach to large-system analysis of CDMA multiuser detectors,” IEEE Transactions on Information Theory , vol. 48, no. 11, pp. 2888–2910, 2002
2002
Earlier work this paper cites.
T. Castellani and A. Cavagna, “Spin-glass theory for pedestrians,” Journal of Statistical Mechanics: Theory and Experiment , vol. 2005, no. 05, p. P05012, 2005
2005
Earlier work this paper cites.
D. Guo and S. Verdú, “Randomly spread CDMA: Asymptotics via statistical physics,” IEEE Transactions on Information Theory , vol. 51, no. 6, pp. 1983–2010, 2005
2005
Earlier work this paper cites.
E. L. Lehmann and J. P. Romano, Testing statistical hypotheses . Wiley New York et al, 2005
2005
Earlier work this paper cites.
R. Baraniuk, “Compressive sensing,” IEEE signal processing magazine , vol. 24, no. 4, 2007
2007
Earlier work this paper cites.
R. Chartrand, “Exact reconstruction of sparse signals via nonconvex minimization,” Signal Processing Letters , vol. 14, no. 10, pp. 707–710, 2007
2007
Earlier work this paper cites.
J. Trzasko, A. Manduca, and E. Borisch, “Sparse MRI reconstruction via multiscale ℓ 0 \ell_{0} -continuation,” in Proc. of IEEE Workshop on Statistical Signal Processing , 2007, pp. 176–180
2007
Earlier work this paper cites.
R. Chartrand and V. Staneva, “Restricted isometry properties and nonconvex compressive sensing,” Inverse Problems , vol. 24, no. 3, p. 035020, 2008
2008
Earlier work this paper cites.
R. Saab, R. Chartrand, and O. Yilmaz, “Stable sparse approximations via nonconvex optimization,” in Proc. IEEE International Conference on Acoustics, Speech and Signal Processing , 2008, pp. 3885–3888
2008
Earlier work this paper cites.
E. J. Candes, M. B. Wakin, and S. P. Boyd, “Enhancing sparsity by reweighted ℓ 1 \ell_{1} minimization,” Journal of Fourier analysis and applications , vol. 14, no. 5-6, pp. 877–905, 2008
2008
Earlier work this paper cites.
S. Foucart and M.-J. Lai, “Sparsest solutions of underdetermined linear systems via ℓ q \ell_{q} -minimization for 0 < q < 1 0<q<1 ,” Applied and Computational Harmonic Analysis , vol. 26, no. 3, pp. 395–407, 2009
2009
Earlier work this paper cites.
Y. Kabashima, T. Wadayama, and T. Tanaka, “A typical reconstruction limit for compressed sensing based on lp-norm minimization,” Journal of Statistical Mechanics: Theory and Experiment , vol. 2009, no. 09, p. L09003, 2009
2009
Earlier work this paper cites.
S. Rangan, V. Goyal, and A. K. Fletcher, “Asymptotic analysis of map estimation via the replica method and compressed sensing,” in Proc. Advances in Neural Information Processing Systems , 2009, pp. 1545–1553
2009
Earlier work this paper cites.
M. E. Davies and R. Gribonval, “Restricted isometry constants where ℓ p \ell_{p} -sparse recovery can fail for 0 < p ≤ 1 0<p\leq 1 ,” IEEE Transactions on Information Theory , vol. 55, no. 5, pp. 2203–2214, 2009
2009
Cited alongside, same era.
D. L. Donoho, A. Maleki, and A. Montanari, “Message-passing algorithms for compressed sensing,” Proceedings of the National Academy of Sciences , vol. 106, no. 45, pp. 18 914–18 919, 2009
2009
Cited alongside, same era.
D. L. Donoho, A. Maleki, and A. Montanari, “Supporting information to: Message-passing algorithms for compressed sensing,” Proceedings of National Academy of Sciences , 2009
2009
Cited alongside, same era.
2009
Cited alongside, same era.
2011
Later among the works it cites.
M. Bayati and A. Montanari, “The dynamics of message passing on dense graphs, with applications to compressed sensing,” IEEE Transactions on Information Theory , vol. 57, no. 2, pp. 764–785, 2011
2011
Later among the works it cites.
Y. Wu and S. Verdú, “Mmse dimension,” Information Theory, IEEE Transactions on , vol. 57, no. 8, pp. 4857–4879, 2011
2011
Later among the works it cites.
Q. Sun, “Recovery of sparsest signals via ℓ q \ell_{q} -minimization,” Applied and Computational Harmonic Analysis , vol. 32, no. 3, pp. 329–341, 2012
2012
Later among the works it cites.
Y. Shen and S. Li, “Restricted p–isometry property and its application for nonconvex compressive sensing,” Advances in Computational Mathematics , vol. 37, no. 3, pp. 441–452, 2012
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
R. Saab and Ö. Yılmaz, “Sparse recovery by non-convex optimization–instance optimality,” Applied and Computational Harmonic Analysis , vol. 29, no. 1, pp. 30–48, 2010
2010
Cited alongside, same era.
A. Maleki, Approximate message passing algorithms for compressed sensing . Stanford University, 2010
2010
Cited alongside, same era.
P. Schniter, “Turbo reconstruction of structured sparse signals,” in Proc. of Annual Conference on Information Sciences and Systems , 2010, pp. 1–6
2010
Cited alongside, same era.
A. Maleki and D. L. Donoho, “Optimally tuned iterative reconstruction algorithms for compressed sensing,” IEEE Journal of Selected Topics in Signal Processing , vol. 4, no. 2, pp. 330–341, 2010
2010
Cited alongside, same era.
D. Ge, X. Jiang, and Y. Ye, “A note on the complexity of l p l_{p} -minimization,” Mathematical programming , vol. 129, no. 2, pp. 285–299, 2011
2011
Cited alongside, same era.
M.-J. Lai and J. Wang, “An unconstrained ℓ q \ell_{q} minimization with 0 ≤ q ≤ 1 0\leq q\leq 1 for sparse solution of underdetermined linear systems,” SIAM Journal on Optimization , vol. 21, no. 1, pp. 82–101, 2011
2011
Cited alongside, same era.
A. Aldroubi, X. Chen, and A. Powell, “Stability and robustness of lq minimization using null space property,” in Proc. of Sampling Theory and Its Applications , 2011
2011
Cited alongside, same era.
R. Mazumder, J. H. Friedman, and T. Hastie, “Sparsenet: Coordinate descent with nonconvex penalties,” Journal of the American Statistical Association , vol. 106, no. 495, 2011
2011
Cited alongside, same era.
2012
Later among the works it cites.
M. Bayati and A. Montanari, “The lasso risk for gaussian matrices,” IEEE Transactions on Information Theory , vol. 58, no. 4, pp. 1997–2017, 2012
2012
Later among the works it cites.
F. Krzakala, M. Mézard, F. Sausset, Y. Sun, and L. Zdeborová, “Statistical-physics-based reconstruction in compressed sensing,” Physical Review X , vol. 2, no. 2, p. 021005, 2012
2012
Later among the works it cites.
A. Maleki, L. Anitori, Z. Yang, and R. Baraniuk, “Asymptotic analysis of complex LASSO via complex approximate message passing (CAMP),” IEEE Transactions on Information Theory , vol. 59, no. 7, pp. 4290–4308, 2013
2013
Later among the works it cites.
M. Stojnic, “Lifting ℓ q \ell_{q} -optimization thresholds,” arXiv preprint arXiv:1306.3976 , 2013
2013
Later among the works it cites.
2013
Later among the works it cites.
2013
Later among the works it cites.
J. K. Pant, W.-S. Lu, and A. Antoniou, “New improved algorithms for compressive sensing based on p norm.” IEEE Transactions on Circuits and Systems , vol. 61, no. 3, pp. 198–202, 2014
2014
Later among the works it cites.
2014
Later among the works it cites.
2015
Closest in time.