-
1
-
-
77955783919
-
An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems
-
doi:10.1109/TIP.2010.2076294
-
Afonso, M.V., Bioucas-Dias, J.M., Figueiredo, M.A.T.: An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems. IEEE Trans. Image Process. 19(11), (2010). doi:10.1109/TIP.2010.2076294
-
(2010)
IEEE Trans. Image Process
, vol.19
, Issue.11
-
-
Afonso, M.V.1
Bioucas-Dias, J.M.2
Figueiredo, M.A.T.3
-
2
-
-
33747151859
-
Interior gradient and proximal methods for convex and conic optimization
-
Auslender, A., Teboulle, M.: Interior gradient and proximal methods for convex and conic optimization. SIAM J. Optim. 16(3), 697-725 (2006)
-
(2006)
SIAM J. Optim.
, vol.16
, Issue.3
, pp. 697-725
-
-
Auslender, A.1
Teboulle, M.2
-
3
-
-
85014561619
-
A fast iterative shrinkage-thresholding algorithm for linear inverse problems
-
Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2(1), 183-202 (2009)
-
(2009)
SIAM J. Imaging Sci.
, vol.2
, Issue.1
, pp. 183-202
-
-
Beck, A.1
Teboulle, M.2
-
5
-
-
79551550744
-
NESTA: A fast and accurate first-order method for sparse recovery
-
Becker, S., Bobin, J., Candès, E.J.: NESTA: a fast and accurate first-order method for sparse recovery. SIAM J. Imaging Sci. 4(1), 1-39 (2011)
-
(2011)
SIAM J. Imaging Sci.
, vol.4
, Issue.1
, pp. 1-39
-
-
Becker, S.1
Bobin, J.2
Candès, E.J.3
-
6
-
-
84870449147
-
Templates for first-order conic solvers user guide
-
Preprint
-
Becker, S., Candès, E.J., Grant, M.: Templates for first-order conic solvers user guide. Technical report (2010). Preprint. http://tfocs.stanford.edu
-
(2010)
Technical report
-
-
Becker, S.1
Candès, E.J.2
Grant, M.3
-
7
-
-
65649137930
-
Probing the Pareto frontier for basis pursuit solutions
-
doi:10.1137/080714488
-
van den Berg, E., Friedlander, M.P.: Probing the Pareto frontier for basis pursuit solutions. SIAM J. Sci. Comput. 31(2), 890 (2009). doi:10.1137/080714488. http://link.aip.org/link/SJOCE3/v31/i2/ p890/s1&Agg=doi
-
(2009)
SIAM J. Sci. Comput.
, vol.31
, Issue.2
, pp. 890
-
-
van den Berg, E.1
Friedlander, M.P.2
-
8
-
-
0042594684
-
-
Athena Scientific, Cambridge
-
Bertsekas, D.P., Nedíc, A., Ozdaglar, A.E.: Convex Analysis and Optimization. Athena Scientific, Cambridge (2003)
-
(2003)
Convex Analysis and Optimization
-
-
Bertsekas, D.P.1
Nedíc, A.2
Ozdaglar, A.E.3
-
10
-
-
77951291046
-
A singular value thresholding algorithm for matrix completion
-
Cai, J.F., Candès, E.J., Shen, Z.: A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 20, 1956-1982 (2010)
-
(2010)
SIAM J. Optim.
, vol.20
, pp. 1956-1982
-
-
Cai, J.F.1
Candès, E.J.2
Shen, Z.3
-
12
-
-
0036836408
-
New multiscale transforms, minimum total-variation synthesis: Applications to edge-preserving image reconstruction
-
Candès, E.J., Guo, F.: New multiscale transforms, minimum total-variation synthesis: applications to edge-preserving image reconstruction. Signal Process. 82(11), 1519-1543 (2002)
-
(2002)
Signal Process.
, vol.82
, Issue.11
, pp. 1519-1543
-
-
Candès, E.J.1
Guo, F.2
-
14
-
-
71049116435
-
Exact matrix completion via convex optimization
-
Candès, E.J., Recht, B.: Exact matrix completion via convex optimization. Found. Comput. Math. 9(6), 717-772 (2009)
-
(2009)
Found. Comput. Math.
, vol.9
, Issue.6
, pp. 717-772
-
-
Candès, E.J.1
Recht, B.2
-
17
-
-
34548275795
-
The Dantzig selector: Statistical estimation when p is much larger than n
-
Candès, E.J., Tao, T.: The Dantzig selector: statistical estimation when p is much larger than n. Ann. Stat. 35(6), 2313-2351 (2007)
-
(2007)
Ann. Stat.
, vol.35
, Issue.6
, pp. 2313-2351
-
-
Candès, E.J.1
Tao, T.2
-
18
-
-
77951528523
-
The power of convex relaxation: Near-optimal matrix completion
-
Candès, E.J., Tao, T.: The power of convex relaxation: Near-optimal matrix completion. IEEE Trans. Inf. Theory 56(5), 2053-2080 (2010)
-
(2010)
IEEE Trans. Inf. Theory
, vol.56
, Issue.5
, pp. 2053-2080
-
-
Candès, E.J.1
Tao, T.2
-
19
-
-
57349174008
-
Enhancing sparsity by reweighted 1 minimization
-
Candès, E.J., Wakin, M.B., Boyd, S.P.: Enhancing sparsity by reweighted 1 minimization. J. Fourier Anal. Appl. 14(5-6), 877-905 (2008)
-
(2008)
J. Fourier Anal. Appl.
, vol.14
, Issue.5-6
, pp. 877-905
-
-
Candès, E.J.1
Wakin, M.B.2
Boyd, S.P.3
-
20
-
-
79953201848
-
A first-order primal-dual algorithm for convex problems with applications to imaging
-
Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40(1), 120-145 (2010)
-
(2010)
J. Math. Imaging Vis.
, vol.40
, Issue.1
, pp. 120-145
-
-
Chambolle, A.1
Pock, T.2
-
22
-
-
79955006538
-
Dualization of signal recovery problems
-
Combettes, P.L., D̃ung, D., Ṽu, B.C.: Dualization of signal recovery problems. Set-Valued Var. Anal. 18, 373-404 (2010)
-
(2010)
Set-Valued Var. Anal.
, vol.18
, pp. 373-404
-
-
Combettes, P.L.1
D̃ung, D.2
Ṽu, B.C.3
-
23
-
-
39449085530
-
A Douglas-Rachford splitting approach to nonsmooth convex variational signal recovery
-
Combettes, P.L., Pesquet, J.C.: A Douglas-Rachford splitting approach to nonsmooth convex variational signal recovery. IEEE J. Sel. Topics Signal Process. 1(4), 564-574 (2007)
-
(2007)
IEEE J. Sel. Topics Signal Process.
, vol.1
, Issue.4
, pp. 564-574
-
-
Combettes, P.L.1
Pesquet, J.C.2
-
24
-
-
30844438177
-
Signal recovery by proximal forward-backward splitting
-
Combettes, P.L., Wajs, V.R.: Signal recovery by proximal forward-backward splitting. SIAM Multiscale Model. Simul. 4(4), 1168-1200 (2005)
-
(2005)
SIAM Multiscale Model. Simul.
, vol.4
, Issue.4
, pp. 1168-1200
-
-
Combettes, P.L.1
Wajs, V.R.2
-
25
-
-
55349134896
-
Fast solution of 1 minimization problems when the solution may be sparse
-
Donoho, D.L., Tsaig, Y.: Fast solution of 1 minimization problems when the solution may be sparse. IEEE Trans. Inform. Theory 54(11), 4789-4812 (2008)
-
(2008)
IEEE Trans. Inform. Theory
, vol.54
, Issue.11
, pp. 4789-4812
-
-
Donoho, D.L.1
Tsaig, Y.2
-
26
-
-
3242708140
-
Least angle regression
-
Efron, B., Hastie, T., Johnstone, I., Tibshirani, R.: Least angle regression. Ann. Stat. 32(2), 407-499 (2004)
-
(2004)
Ann. Stat.
, vol.32
, Issue.2
, pp. 407-499
-
-
Efron, B.1
Hastie, T.2
Johnstone, I.3
Tibshirani, R.4
-
27
-
-
34249671661
-
Analysis versus synthesis in signal priors
-
Elad, M., Milanfar, P., Rubinstein, R.: Analysis versus synthesis in signal priors. Inverse Problems 23, 947-968 (2007)
-
(2007)
Inverse Problems
, vol.23
, pp. 947-968
-
-
Elad, M.1
Milanfar, P.2
Rubinstein, R.3
-
28
-
-
39449126969
-
Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems
-
Figueiredo, M.A.T., Nowak, R., Wright, S.J.: Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems. IEEE J. Sel. Top. Signal Process. 1(4), 586-597 (2007)
-
(2007)
IEEE J. Sel. Top. Signal Process.
, vol.1
, Issue.4
, pp. 586-597
-
-
Figueiredo, M.A.T.1
Nowak, R.2
Wright, S.J.3
-
29
-
-
56749091502
-
Exact regularization of convex programs
-
doi:10.1137/060675320
-
Friedlander, M.P., Tseng, P.: Exact regularization of convex programs. SIAM J. Optim. 18(4), 1326-1350 (2007). doi:10.1137/060675320. http://link.aip.org/link/?SJE/18/1326/1
-
(2007)
SIAM J. Optim.
, vol.18
, Issue.4
, pp. 1326-1350
-
-
Friedlander, M.P.1
Tseng, P.2
-
30
-
-
77950537175
-
Regularization paths for generalized linear models via coordinate descent
-
Friedman, J., Hastie, T., Tibshirani, R.: Regularization paths for generalized linear models via coordinate descent. J. Stat. Softw. 33(1), 1-22 (2010)
-
(2010)
J. Stat. Softw.
, vol.33
, Issue.1
, pp. 1-22
-
-
Friedman, J.1
Hastie, T.2
Tibshirani, R.3
-
31
-
-
0019602085
-
Ageneralized proximal point algorithm for certain non-convex minimization problems
-
Fukushima, M., Mine, H.:Ageneralized proximal point algorithm for certain non-convex minimization problems. Int. J. Syst. Sci. 12(8), 989-1000 (1981)
-
(1981)
Int. J. Syst. Sci.
, vol.12
, Issue.8
, pp. 989-1000
-
-
Fukushima, M.1
Mine, H.2
-
34
-
-
0005914572
-
PARNES: A rapidly convergent algorithm for accurate recovery of sparse and approximately sparse signals
-
Preprint
-
Gu, M., Lim, L.H., Wu, C.J.: PARNES: a rapidly convergent algorithm for accurate recovery of sparse and approximately sparse signals. Technical report (2009). Preprint http://arxiv.org/abs/0911.0492
-
(2009)
Technical report
-
-
Gu, M.1
Lim, L.H.2
Wu, C.J.3
-
35
-
-
0007016022
-
New proximal point algorithms for convex minimization
-
doi:10.1137/0802032
-
Güler, O.: New proximal point algorithms for convex minimization. SIAM J. Optim. 2(4), 649-664 (1992). doi:10.1137/0802032. http://link.aip.org/link/?SJE/2/649/1
-
(1992)
SIAM J. Optim.
, vol.2
, Issue.4
, pp. 649-664
-
-
Güler, O.1
-
36
-
-
69649095451
-
1-minimization: Methodology and convergence
-
1-minimization: methodology and convergence. SIAM J. Optim. 19(3), 1107-1130 (2008)
-
(2008)
SIAM J. Optim.
, vol.19
, Issue.3
, pp. 1107-1130
-
-
Hale, E.T.1
Yin, W.2
Zhang, Y.3
-
38
-
-
58149345975
-
DASSO: Connections Between the Dantzig Selector and Lasso
-
James, G., Radchenko, P., Lv, J.: DASSO: Connections Between the Dantzig Selector and Lasso. J. R. Stat. Soc. B 71, 127-142 (2009)
-
(2009)
J. R. Stat. Soc. B
, vol.71
, pp. 127-142
-
-
James, G.1
Radchenko, P.2
Lv, J.3
-
39
-
-
77951929218
-
-
Technical report, Stanford University
-
Koh, K., Kim, S.J., Boyd, S.P.: Solver for l1-regularized least squares problems. Technical report, Stanford University. http://www.stanford.edu/~boyd/l1_ls/ (2007)
-
(2007)
Solver for l1-regularized least squares problems
-
-
Koh, K.1
Kim, S.J.2
Boyd, S.P.3
-
40
-
-
78651417720
-
Primal-dual first-order methods with o(1/ε) iteration-complexity for cone programming
-
doi:10.1007/s10107-008-0261-6
-
Lan, G., Lu, Z., Monteiro, R.D.C.: Primal-dual first-order methods with o(1/ε) iteration-complexity for cone programming. Math. Program. (2009). doi:10.1007/s10107-008-0261-6. http://www. springerlink.com/index/10.1007/s10107-008-0261-6
-
(2009)
Math. Program
-
-
Lan, G.1
Lu, Z.2
Monteiro, R.D.C.3
-
42
-
-
84862272060
-
An implementable proximal point algorithmic framework for nuclear norm minimization
-
doi:10.1007/s10107-010-0437-8
-
Liu, Y.J., Sun, D., Toh, K.C.: An implementable proximal point algorithmic framework for nuclear norm minimization. Math. Program. (2011). doi:10.1007/s10107-010-0437-8
-
(2011)
Math. Program.
-
-
Liu, Y.J.1
Sun, D.2
Toh, K.C.3
-
43
-
-
84870471905
-
Constructing test instances for basis pursuit denoising
-
arXiv:1103.2897
-
Lorenz, D.: Constructing test instances for basis pursuit denoising. Technical report. arXiv:1103.2897 (2011)
-
(2011)
Technical report
-
-
Lorenz, D.1
-
44
-
-
84870422423
-
Primal-dual first-order methods for a class of cone programming
-
Preprint
-
Lu, Z.: Primal-dual first-order methods for a class of cone programming. INFORMS J. Comput. Preprint http://www.math.sfu.ca/~zhaosong/ResearchPapers/pdfirst_DS_2ndrev.pdf (2009)
-
(2009)
INFORMS J. Comput
-
-
Lu, Z.1
-
45
-
-
63049122761
-
A predual proximal point algorithm solving a non negative basis pursuit denoising model
-
Malgouyres, F., Zeng, T.: A predual proximal point algorithm solving a non negative basis pursuit denoising model. Int. J. Comput. Vis. 83(3), 294-311 (2009)
-
(2009)
Int. J. Comput. Vis.
, vol.83
, Issue.3
, pp. 294-311
-
-
Malgouyres, F.1
Zeng, T.2
-
47
-
-
0000276924
-
Proximité et dualité dans un espace hilbertien
-
Moreau, J.J.: Proximité et dualité dans un espace hilbertien. Bull. Soc. Math. France 93, 273-299 (1965)
-
(1965)
Bull. Soc. Math. France
, vol.93
, pp. 273-299
-
-
Moreau, J.J.1
-
50
-
-
17444382102
-
A method for unconstrained convex minimization problem with the rate of convergence O(1/k2)
-
Nesterov, Y.: A method for unconstrained convex minimization problem with the rate of convergence O(1/k2). Doklady AN USSR (translated as Soviet Math. Docl.) 269, 543-547 (1983)
-
(1983)
Doklady AN USSR (translated as Soviet Math. Docl.)
, vol.269
, pp. 543-547
-
-
Nesterov, Y.1
-
51
-
-
0010831555
-
On an approach to the construction of optimal methods of minimization of smooth convex functions
-
in Russian
-
Nesterov, Y.: On an approach to the construction of optimal methods of minimization of smooth convex functions. Ekonomika i Mateaticheskie Metody 24, 509-517 (1988, in Russian)
-
(1988)
Ekonomika i Mateaticheskie Metody
, vol.24
, pp. 509-517
-
-
Nesterov, Y.1
-
52
-
-
77953098740
-
Introductory Lectures on Convex Optimization: A Basic Course
-
Kluwer, Boston
-
Nesterov, Y.: Introductory Lectures on Convex Optimization: A Basic Course. Applied Optimization, vol. 87. Kluwer, Boston (2004)
-
(2004)
Applied Optimization
, vol.87
-
-
Nesterov, Y.1
-
53
-
-
17444406259
-
Smooth minimization of non-smooth functions
-
Nesterov, Y.: Smooth minimization of non-smooth functions. Math. Program. Ser. A 103, 127-152 (2005)
-
(2005)
Math. Program. Ser. A
, vol.103
, pp. 127-152
-
-
Nesterov, Y.1
-
54
-
-
67651063011
-
Gradient methods for minimizing composite objective function
-
Université Catholique de Louvain, Louvain-la-Neuve, Belgium
-
Nesterov, Y.: Gradient methods for minimizing composite objective function. Technical report, CORE 2007/76, Université Catholique de Louvain, Louvain-la-Neuve, Belgium (2007)
-
(2007)
Technical report, CORE 2007/76
-
-
Nesterov, Y.1
-
55
-
-
77349126814
-
Fast linearized Bregman iteration for compressive sensing and sparse denoising
-
Osher, S., Mao, Y., Dong, B., Yin, W.: Fast linearized Bregman iteration for compressive sensing and sparse denoising. Commun. Math. Sci. 8(1), 93-111 (2010)
-
(2010)
Commun. Math. Sci.
, vol.8
, Issue.1
, pp. 93-111
-
-
Osher, S.1
Mao, Y.2
Dong, B.3
Yin, W.4
-
56
-
-
0004267646
-
-
Princeton University Press, Princeton
-
Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
-
(1970)
Convex Analysis
-
-
Rockafellar, R.T.1
-
57
-
-
0016985417
-
Monotone operators and the proximal point algorithm
-
Rockafellar, R.T.: Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 14, 877-898 (1976)
-
(1976)
SIAM J. Control Optim.
, vol.14
, pp. 877-898
-
-
Rockafellar, R.T.1
-
59
-
-
44049111982
-
Nonlinear total variation noise removal algorithm
-
Rudin, L.I., Osher, S., Fatemi, E.:Nonlinear total variation noise removal algorithm. PhysicaD60, 259-268 (1992)
-
(1992)
PhysicaD
, vol.60
, pp. 259-268
-
-
Rudin, L.I.1
Osher, S.2
Fatemi, E.3
-
60
-
-
33750312675
-
PDCO: Primal-dual interior method for convex objectives
-
Stanford University
-
Saunders, M., Kim, B.: PDCO: Primal-dual interior method for convex objectives. Technical report, Stanford University. http://www.stanford.edu/group/SOL/software/pdco.html (2002)
-
(2002)
Technical report
-
-
Saunders, M.1
Kim, B.2
-
61
-
-
0043265073
-
Wavelets and curvelets for image deconvolution: A combined approach
-
Starck, J.L., Ngyuen, M.K., Murtagh, F.:Wavelets and curvelets for image deconvolution: a combined approach. Signal Process. 83, 2279-2283 (2003)
-
(2003)
Signal Process.
, vol.83
, pp. 2279-2283
-
-
Starck, J.L.1
Ngyuen, M.K.2
Murtagh, F.3
-
62
-
-
0001287271
-
Regression shrinkage and selection via the lasso
-
Tibshirani, R.: Regression shrinkage and selection via the lasso. J.R. Stat. Soc. B58(1), 267-288 (1996)
-
(1996)
J.R. Stat. Soc.
, vol.B58
, Issue.1
, pp. 267-288
-
-
Tibshirani, R.1
-
64
-
-
67651044298
-
Efficient schemes for total variation minimization under constraints in image processing
-
Weiss, P., Blanc-Féraud, L., Aubert, G.: Efficient schemes for total variation minimization under constraints in image processing. SIAM J. Sci. Comput. 31, 2047-2080 (2009)
-
(2009)
SIAM J. Sci. Comput.
, vol.31
, pp. 2047-2080
-
-
Weiss, P.1
Blanc-Féraud, L.2
Aubert, G.3
-
65
-
-
77955666600
-
A fast algorithm for sparse reconstruction based on shrinkage, subspace optimization and continuation
-
Wen, Z., Yin, W., Goldfarb, D., Zhang, Y.: A fast algorithm for sparse reconstruction based on shrinkage, subspace optimization and continuation. SIAM J. Sci. Comput. 32(4), 1832-1857 (2010)
-
(2010)
SIAM J. Sci. Comput.
, vol.32
, Issue.4
, pp. 1832-1857
-
-
Wen, Z.1
Yin, W.2
Goldfarb, D.3
Zhang, Y.4
-
67
-
-
67650178787
-
Sparse reconstruction by separable approximation
-
Wright, S.J., Nowak, R.D., Figueiredo, M.A.T.: Sparse reconstruction by separable approximation. IEEE Trans. Signal Process. 57(7), 2479-2493 (2009)
-
(2009)
IEEE Trans. Signal Process.
, vol.57
, Issue.7
, pp. 2479-2493
-
-
Wright, S.J.1
Nowak, R.D.2
Figueiredo, M.A.T.3
-
68
-
-
78651547900
-
Analysis and generalizations of the linearized Bregman method
-
Yin, W.: Analysis and generalizations of the linearized Bregman method. SIAM J. Imaging Sci. 3(4), 856-877 (2010). http://dx.doi.org/10.1137/090760350
-
(2010)
SIAM J. Imaging Sci.
, vol.3
, Issue.4
, pp. 856-877
-
-
Yin, W.1
|