Fetching the paper…
Reading the bibliography…
In this paper, we show that, under the assumption that $\|\e\|_2\leq \epsilon$, every $k-$sparse signal $\x\in \mathbb{R}^n$ can be stably ($\epsilon\neq0$) or exactly recovered ($\epsilon=0$) from $\y=\A\x+\e$ via $l_p-$mnimization with $p\in(0, \bar{p}]$, where \beqnn \bar{p}= \begin{cases} \frac{50}{31}(1-\delta_{2k}), &\delta_{2k}\in[\frac{\sqrt{2}}{2}, 0.7183)\cr 0.4541, &\delta_{2k}\in[0.7183,0.7729)\cr 2(1-\delta_{2k}), &\delta_{2k}\in[0.7729,1) \end{cases}, \eeqnn even if the restricted isometry constant of $\A$ satisfies $\delta_{2k}\in[\frac{\sqrt{2}}{2}, 1)$.
E. J. Candés and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory , vol. 51, no. 12, pp. 4203–4215, 2005
2005
Earlier work this paper cites.
J. J. Fuchs., “Recovery of exact sparse representations in the presence of bounded noise,” IEEE Trans. Inf. Theory , vol. 51, no. 10, pp. 3601–3608, 2005
2005
Earlier work this paper cites.
D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory , vol. 52, no. 4, pp. 1289–1306, 2006
2006
Earlier work this paper cites.
D. L. Donoho, M. Elad, and V. N. Temlyakov, “Stable recovery of sparse overcomplete representations in the presence of noise,” IEEE Trans. Inf. Theory , vol. 52, pp. 6–18, 2006
2006
Earlier work this paper cites.
E. J. Candés, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure Appl. Math , vol. 59, pp. 1207–1223, 2006
2006
Earlier work this paper cites.
E. J. Candés and T. Tao, “The dantzig selector: Statistical estimation when p p is much larger than n n ,” Ann. Statist , vol. 35, pp. 2313–2351, 2007
2007
Earlier work this paper cites.
R. Chartrand, “Exact reconstruction of sparse signals via nonconvex minimization,” IEEE Signal Processing Letters , vol. 14, no. 10, pp. 707–710, 2007
2007
Earlier work this paper cites.
E. J. Candés, “The restricted isometry property and its implications for compressed sensing,” C. R. Acad. Sci. Paris, Ser. I , vol. 346, no. 11, pp. 589–592, 2008
2008
Cited alongside, same era.
A. Cohen, W. Dahmen, and R. DeVore, “Compressed sensing and best k k -term approximation,” J. Amer. Math. Soc. , vol. 22, pp. 211–231, 2009
2009
Cited alongside, same era.
S. Foucart and M.-J. Lai, “Sparsest solutions of underdetermined linear systems via l q − l_{q}- minimization for 0 < q ≤ 1 0<q\leq 1 ,” Appl. Comput. Harmon. Anal. , vol. 26, no. 3, pp. 395–407, 2009
2009
Cited alongside, same era.
M. E. Davies and R. Gribonval, “Restricted isometry constants where l p l^{p} sparse recovery can fail for 0 < p ≤ 1 0<p\leq 1 ,” IEEE Trans. Inf. Theory , vol. 55, no. 5, pp. 2203–2214, 2009
2009
Cited alongside, same era.
Q. Mo and S. Li, “New bounds on the restricted isometry constant δ 2 k \delta_{2k} ,” Appl. Comput. Harmon. Anal. , vol. 31, pp. 460–468, 2011
2011
Later among the works it cites.
M.-J. Lai and L. Y. Liu, “A new estimate of restricted isometry constants for sparse solutions,” Online http://www.math.uga.edu/ mjlai/papers/LaiLiu11.pdf , 2011
2011
Later among the works it cites.
Q. Sun, “Recovery of sparsest signals via l p l_{p} -minimization,” Appl. Comput. Harmon. Anal. , vol. 32, no. 3, pp. 329–341, 2012
2012
Later among the works it cites.
T. Cai and A. Zhang, “Sharp RIP bound for sparse signal and low-rank matrix recovery,” Appl. Comput. Harmon. Anal. , vol. 35, pp. 74–93, 2013
2013
Later among the works it cites.
R. Wu and D.-R. Chen, “The improved bounds of restricted isometry constant for recovery via l p l_{p} -minimization,” IEEE Trans. Inf. Theory , vol. 59, no. 9, pp. 6142–6147, 2013
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2010
Cited alongside, same era.
I. Daubechies, R. Devore, M. Fornasier, and S. Gunturk, “Iteratively reweighted least squares minimization for sparse recovery,” Comm. Pure Appl. Math , vol. 63, no. 1, pp. 1–38, 2010
2010
Cited alongside, same era.
2010
Cited alongside, same era.
T. Cai and A. Zhang, “Sparse representation of a polytope and recovery of sparse signals and low-rank matrices,” IEEE Trans. Inf. Theory , vol. 60, no. 1, pp. 122–132
Cited in the paper.
2013
Later among the works it cites.
S. Bahmani and B. Raj, “A unifying analysis of projected gradient descent for l p l_{p} -constrained least squares,” Appl. Comput. Harmon. Anal. , vol. 34, no. 11, pp. 366–378, 2013
2013
Later among the works it cites.