1 |
HadamardJ. Sur les Problemes aux Derivees Partielles et Leur Signification Physique. Princeton University Bulletin, 1902, 13: 49–52
|
2 |
KabanikhinS I. Inverse and Ill-Posed Problems: Theory and Applications. Berlin: Water De Gruyter, 2011
https://doi.org/10.1515/9783110224016
|
3 |
ZhangB Y, XuD H, LiuT W. Stabilized algorithms for ill-posed problems in signal processing. In: Proceedings of the IEEE International Conferences on Info-tech and Info-net. 2001, 1: 375–380
https://doi.org/10.1109/ICII.2001.982776
|
4 |
ScherzerO. Handbook of Mathematical Methods in Imaging. Springer Science & Business Media, 2011
https://doi.org/10.1007/978-0-387-92920-0
|
5 |
GroetschC W. Inverse problems in the mathematical sciences. Mathematics of Computation, 1993, 63(5): 799–811
https://doi.org/10.1007/978-3-322-99202-4
|
6 |
RudinL I, OsherS, FatemiE. Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena, 1992, 60(1): 259–268
https://doi.org/10.1016/0167-2789(92)90242-F
|
7 |
TikhonovA N. Solution of incorrectly formulated problems and the regularization method. Soviet Math, 1963, 4: 1035–1038
|
8 |
TikhonovA N, Arsenin V I. Solutions of Ill-posed Problems. Washington, DC: V. H. Winston & Sons, 1977
|
9 |
LandweberL. An iteration formula for Fredholm integral equations of the first kind. American Journal of Mathematics, 1951, 73(3): 615–624
https://doi.org/10.2307/2372313
|
10 |
HestenesM R, Stiefel E. Methods of conjugate gradients for solving linear systems. Journal of Research of the National Bureau of Standards, 1952, 49(6): 409–436
https://doi.org/10.6028/jres.049.044
|
11 |
VogelC R. Computational Methods for Inverse Problems. Society for Industrial and Applied Mathematics, 2002, 23
https://doi.org/10.1137/1.9780898717570
|
12 |
HansenP C. The truncated SVD as a method for regularization. Bit Numerical Mathematics, 1987, 27(4): 534–553
https://doi.org/10.1007/BF01937276
|
13 |
HonerkampJ, WeeseJ. Tikhonovs regularization method for ill-posed problems. Continuum Mechanics and Thermodynamics, 1990,2(1): 17–30
https://doi.org/10.1007/BF01170953
|
14 |
ZhangX Q, BurgerM, BressonX, Osher S. Bregmanized nonlocal regularization for deconvolution and sparse reconstruction. SIAM Journal on Imaging Sciences, 2010, 3(3): 253–276
https://doi.org/10.1137/090746379
|
15 |
DebK. Multi-Objective Optimization Using Evolutionary Algorithms. New York: John Wiley & Sons, 2001, 16
|
16 |
FonsecaC M, Fleming P J. An overview of evolutionary algorithms in multiobjective optimization. Evolutionary Computation, 1995, 3(1): 1–16
https://doi.org/10.1162/evco.1995.3.1.1
|
17 |
CoelloC A C, Van Veldhuizen D A, LamontG B . Evolutionary Algorithms for Solving Multi-objective Problems. New York: Kluwer Academic, 2002
https://doi.org/10.1007/978-1-4757-5184-0
|
18 |
TanK C, KhorE F, LeeT H. Multiobjective Evolutionary Algorithms and Applications. Springer Science & Business Media, 2005
|
19 |
KnowlesJ, CorneD, DebK. Multiobjective Problem Solving from Nature: from Concepts to Applications. Springer Science & Business Media, 2008
https://doi.org/10.1007/978-3-540-72964-8
|
20 |
RaquelC, YaoX. Dynamic multi-objective optimization: a survey of the state-of-the-art. In: YangS X , YaoX, eds. Evolutionary Computation for Dynamic Optimization Problems. Springer Berlin Heidelberg, 2013, 85–106
https://doi.org/10.1007/978-3-642-38416-5_4
|
21 |
LückenC V, Barán B, BrizuelaC . A survey on multi-objective evolutionary algorithms for many-objective problems. Computational Optimization and Applications, 2014, 58(3): 707–756
https://doi.org/10.1007/s10589-014-9644-1
|
22 |
HwangC L, MasudA S M.Multiple Objective Decision Making- Methods and Applications. Springer Science & Business Media, 1979, 164
https://doi.org/10.1007/978-3-642-45511-7
|
23 |
GirosiF, JonesM B, PoggioT. Regularization theory and neural networks architectures. Neural Computation, 1995, 7(2): 219–269
https://doi.org/10.1162/neco.1995.7.2.219
|
24 |
BelgeM, KilmerM E, MillerE L. Efficient determination of multiple regularization parameters in a generalized L-curve framework. Inverse Problems, 2002, 18(4): 1161
https://doi.org/10.1088/0266-5611/18/4/314
|
25 |
HansenP C. Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion. American Mathematical Monthly, 1997, 4(5): 491
|
26 |
ErikssonP, Jiménez C, BuehlerS A . Qpack, a general tool for instrument simulation and retrieval work.Journal of Quantitative Spectroscopy and Radiative Transfer, 2005, 91(1): 47–64
https://doi.org/10.1016/j.jqsrt.2004.05.050
|
27 |
GiustiE. Minimal Surfaces and Functions of Bounded Variation. Springer Science & Business Media, 1984, 80
https://doi.org/10.1007/978-1-4684-9486-0
|
28 |
CattéF, CollT.Image selective smoothing and edge detection by nonlinear diffusion. SIAM Journal on Numerical Analysis, 1992, 29(1): 182–193
https://doi.org/10.1137/0729012
|
29 |
BjörckA. Numerical Methods for Least Squares Problems. Society for Industrial and Applied Mathematics, 1996
https://doi.org/10.1137/1.9781611971484
|
30 |
GroetschC W. The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind. Pitman Advanced Publishing Program, 1984
|
31 |
HansonR J. A numerical method for solving Fredholm integral equationstific and Statistical Computing, 1992, 13(5): 1142–1150
|
32 |
StewartG W. Rank degeneracy. SIAM Journal on Scientific and Statistical Computing, 1984, 5(2): 403–413
https://doi.org/10.1137/0905030
|
33 |
HansenP C, SekiiT, ShibahashiH . The modified truncated SVD method for regularization in general form. SIAM Journal on Sciendependent Component Analysis and Blind Source Separation. 2006, 206–213
|
34 |
Van LoanC F. Generalizing the singular value decomposition. SIAM Journal on Numerical Analysis, 1976, 13(1): 76–83
https://doi.org/10.1137/0713009
|
35 |
HansenP C.Regularization, GSVD and truncated GSVD. BIT Numerical Mathematics, 1989, 29(3): 491–504
https://doi.org/10.1007/BF02219234
|
36 |
PaigeC C. Computing the generalized singular value decomposition. SIAM Journal on Scientific and Statistical Computing, 1986, 7(4): 1126–1146
https://doi.org/10.1137/0907077
|
37 |
MorigiS, Reichel L, SgallariF . A truncated projected SVD method for linear discrete ill-posed problems. Numerical Algorithms, 2006, 43(3): 197–213
https://doi.org/10.1007/s11075-006-9053-3
|
38 |
FernandoK V, Hammarling S. A product induced singular value decomposition (ΠSVD) for two matrices and balanced realization. In: Proceedings of SIAM Conference on Linear Algebra in Signals, Systems and Control. 1988, 128–140
|
39 |
ZhaH Y. The restricted singular value decomposition of matrix triplets. SIAM Journal on Matrix Analysis and Applications, 1991, 12(1): 172–194
https://doi.org/10.1137/0612014
|
40 |
De MoorB, GolubG H. The restricted singular value decomposition: properties and applications. SIAM Journal on Matrix Analysis and Applications, 1991, 12(3): 401–425
https://doi.org/10.1137/0612029
|
41 |
De MoorB, ZhaH Y. A tree of generalizations of the ordinary singular value decomposition. Linear Algebra and Its Applications, 1991, 147: 469–500
https://doi.org/10.1016/0024-3795(91)90243-P
|
42 |
De MoorB. Generalizations of the OSVD: structure, properties and applications. In: VaccaroR J, ed.SVD & Signal Processing, II: Algorithms, Analysis & Applications. 1991, 83–98
|
43 |
NoscheseS, Reichel L. A modified TSVD method for discrete illposed problems. Numerical Linear Algebra with Applications, (in press)
|
44 |
DykesL, Noschese S, ReichelL . Rescaling the GSVD with application to ill-posed problems. Numerical Algorithms, 2015, 68(3): 531–545
https://doi.org/10.1007/s11075-014-9859-3
|
45 |
EdoL, FrancoW, MartinssonP G , RokhlinV, TygertM. Randomized algorithms for the low-rank approximation of matrices. Proceedings of the National Academy of Sciences, 2007, 104(51): 20167–20172
https://doi.org/10.1073/pnas.0709640104
|
46 |
WoolfeF, Liberty E, RokhlinV , TygertM. A fast randomized algorithm for the approximation of matrices. Applied & Computational Harmonic Analysis, 2008, 25(3): 335–366
https://doi.org/10.1016/j.acha.2007.12.002
|
47 |
SifuentesJ, Gimbutas Z, GreengardL . Randomized methods for rankdeficient linear systems. Electronic Transactions on Numerical Analysis, 2015, 44: 177–188
|
48 |
LiuY G, LeiY J, LiC G, Xu W Z, PuY F . A random algorithm for low-rank decomposition of large-scale matrices with missing entries. IEEE Transactions on Image Processing, 2015, 24(11): 4502–4511
https://doi.org/10.1109/TIP.2015.2458176
|
49 |
SekiiT. Two-dimensional inversion for solar internal rotation. Publications of the Astronomical Society of Japan, 1991, 43: 381–411
|
50 |
ScalesJ A. Uncertainties in seismic inverse calculations. In: Jacobsen B H, MosegaardK , SibaniP, eds. Inverse Methods. Berlin: Springer- Verlag, 1996, 79–97
https://doi.org/10.1007/BFb0011766
|
51 |
LawlessJ F, WangP. A simulation study of ridge and other regression estimators. Communications in Statistics-Theory and Methods, 1976, 5(4): 307–323
https://doi.org/10.1080/03610927608827353
|
52 |
DempsterA P, Schatzoff M, WermuthN . A simulation study of alternatives to ordinary least squares. Journal of the American Statistical Association, 1977, 72(357): 77–91
https://doi.org/10.1080/01621459.1977.10479910
|
53 |
HansenP C, O’Leary D P. The use of the L-curve in the regularization of discrete ill-posed problems. SIAM Journal on Scientific Computing, 1993, 14(6): 1487–1503
https://doi.org/10.1137/0914086
|
54 |
HansenP C. Analysis of discrete ill-posed problems by means of the L-curve. SIAM Review, 1992, 34(4): 561–580
https://doi.org/10.1137/1034115
|
55 |
XuP L. Truncated SVD methods for discrete linear ill-posed problems. Geophysical Journal International, 1998, 135(2): 505–514
https://doi.org/10.1046/j.1365-246X.1998.00652.x
|
56 |
WuZ M, BianS F, XiangC B, Tong Y D. A new method for TSVD regularization truncated parameter selection. Mathematical Problems in Engineering, 2013
https://doi.org/10.1155/2013/161834
|
57 |
ChiccoD, Masseroli M. A discrete optimization approach for SVD best truncation choice based on ROC curves. In: Proceedings of the 13th IEEE International Conference on Bioinformatics and Bioengineering. 2013: 1–4
https://doi.org/10.1109/BIBE.2013.6701705
|
58 |
GolubG H, HeathM, WahbaG. Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics, 1979, 21(2): 215–223
https://doi.org/10.1080/00401706.1979.10489751
|
59 |
JbilouK, Reichel L, SadokH . Vector extrapolation enhanced TSVD for linear discrete ill-posed problems. Numerical Algorithms, 2009, 51(2): 195–208
https://doi.org/10.1007/s11075-008-9229-0
|
60 |
BouhamidiA, JbilouK, ReichelL, Sadok H, WangZ . Vector extrapolation applied to truncated singular value decomposition and truncated iteration. Journal of Engineering Mathematics, 2015, 93(1): 99–112
https://doi.org/10.1007/s10665-013-9677-y
|
61 |
VogelC R. Computational Methods for Inverse Problems. Society for Industrial and Applied Mathematics, 2002
https://doi.org/10.1137/1.9780898717570
|
62 |
DoicuA, Trautmann T, SchreierF . Numerical Regularization for Atmospheric Inverse Problems. Springer Science & Business Media, 2010
https://doi.org/10.1007/978-3-642-05439-6
|
63 |
BakushinskyA B, Goncharsky A V. Iterative Methods for the Solution of Incorrect Problems. Moscow: Nauka, 1989
|
64 |
RiederA. Keine Probleme mit Inversen Problemen: Eine Einführung in ihre stabile Lösung. Berlin: Springer-Verlag, 2013
|
65 |
NemirovskiyA S, PolyakB T.Iterative methods for solving linear illposed problems under precise information. Engineering Cybernetics, 1984, 22(4): 50–56
|
66 |
BrakhageH. On ill-posed problems and the method of conjugate gradients. Inverse and Ill-posed Problems, 1987, 4: 165–175
https://doi.org/10.1016/B978-0-12-239040-1.50014-4
|
67 |
HankeM. Accelerated Landweber iterations for the solution of illposed equations. Numerische Mathematik, 1991, 60(1): 341–373
https://doi.org/10.1007/BF01385727
|
68 |
BarzilaiJ, Borwein J M. Two-point step size gradient methods. IMA Journal of Numerical Analysis, 1988, 8(1): 141–148
https://doi.org/10.1093/imanum/8.1.141
|
69 |
AxelssonO. Iterative Solution Methods. Cambridge:Cambridge University Press, 1996
|
70 |
Van der SluisA, Van der Vorst H A. The rate of convergence of conjugate gradients. Numerische Mathematik, 1986, 48(5): 543–560
https://doi.org/10.1007/BF01389450
|
71 |
ScalesJ A, Gersztenkorn A. Robust methods in inverse theory. Inverse Problems, 1988, 4(4): 1071–1091
https://doi.org/10.1088/0266-5611/4/4/010
|
72 |
BjörckÅ, Eldén L. Methods in numerical algebra for ill-posed problems. Technical Report LiTH-MAT-R-33-1979. 1979
|
73 |
TrefethenL N, BauD. Numerical Linear Algebra. Society for Industrial and Applied Mathematics, 1997
https://doi.org/10.1137/1.9780898719574
|
74 |
CalvettiD, LewisB, ReichelL. On the regularizing properties of the GMRES method. Numerische Mathematik, 2002, 91(4): 605–625
https://doi.org/10.1007/s002110100339
|
75 |
CalvettiD, LewisB, ReichelL. Alternating Krylov subspace image restoration methods. Journal of Computational and Applied Mathematics, 2012, 236(8): 2049–2062
https://doi.org/10.1016/j.cam.2011.09.030
|
76 |
BrianziP, FavatiP, MenchiO, Romani F. A framework for studying the regularizing properties of Krylov subspace methods.Inverse Problems, 2006, 22(3): 1007–1021
https://doi.org/10.1088/0266-5611/22/3/017
|
77 |
SonneveldP, Van Gijzen M B. IDR(s): a family of simple and fast algorithms for solving large nonsymmetric systems of linear equations. SIAM Journal on Scientific Computing, 2008, 31(2): 1035–1062
https://doi.org/10.1137/070685804
|
78 |
FongD C L, Saunders M. LSMR: an iterative algorithm for sparse least-squares problems. SIAM Journal on Scientific Computing, 2011, 33(5): 2950–2971
https://doi.org/10.1137/10079687X
|
79 |
ZhaoC, HuangT Z, ZhaoX L, Deng L J. Two new efficient iterative regularization methods for image restoration problems. Abstract & Applied Analysis, 2013
https://doi.org/10.1155/2013/129652
|
80 |
PerezA, Gonzalez R C. An iterative thresholding algorithm for image segmentation. IEEE Transactions on Pattern Analysis & Machine Intelligence, 1987, 9(6): 742–751
https://doi.org/10.1109/TPAMI.1987.4767981
|
81 |
BeckA, Teboulle M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences, 2009, 2(1): 183–202
https://doi.org/10.1137/080716542
|
82 |
Bioucas-DiasJ M, Figueiredo M A T. Two-step algorithms for linear inverse problems with non-quadratic regularization. In: Proceedings of the IEEE International Conference on Image Processing. 2007, 105–108
https://doi.org/10.1109/icip.2007.4378902
|
83 |
Bioucas-DiasJ M, Figueiredo M A T. A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration. IEEE Transactions on Image Processing. 2007, 16(12): 2992–3004
https://doi.org/10.1109/TIP.2007.909319
|
84 |
BayramI, Selesnick I W. A subband adaptive iterative shrinkage/ thresholding algorithm. IEEE Transactions on Signal Processing, 2010, 58(3): 1131–1143
https://doi.org/10.1109/TSP.2009.2036064
|
85 |
YamagishiM, YamadaI. Over-relaxation of the fast iterative shrinkage-thresholding algorithm with variable stepsize. Inverse Problems, 2011, 27(10): 105008–105022
https://doi.org/10.1088/0266-5611/27/10/105008
|
86 |
BhottoM Z A, AhmadM O, SwamyM N S. An improved fast iterative shrinkage thresholding algorithm for image deblurring. SIAM Journal on Imaging Sciences, 2015, 8(3): 1640–1657
https://doi.org/10.1137/140970537
|
87 |
ZhangY D, DongZ C, PhillipsP, Wang S H, JiG L , YangJ Q. Exponential wavelet iterative shrinkage thresholding algorithm for compressed sensing magnetic resonance imaging. Information Sciences, 2015, 322: 115–132
https://doi.org/10.1016/j.ins.2015.06.017
|
88 |
ZhangY D, WangS H, JiG L, Dong Z C. Exponential wavelet iterative shrinkage thresholding algorithm with random shift for compressed sensing magnetic resonance imaging. IEEJ Transactions on Electrical and Electronic Engineering, 2015, 10(1): 116–117
https://doi.org/10.1002/tee.22059
|
89 |
WuG M, LuoS Q. Adaptive fixed-point iterative shrinkage/ thresholding algorithm for MR imaging reconstruction using compressed sensing. Magnetic Resonance Imaging, 2014, 32(4): 372–378
https://doi.org/10.1016/j.mri.2013.12.009
|
90 |
FangE X, WangJ J, HuD F, Zhang J Y, ZouW , ZhouY. Adaptive monotone fast iterative shrinkage thresholding algorithm for fluorescence molecular tomography. IET Science Measurement Technology, 2015, 9(5): 587–595
https://doi.org/10.1049/iet-smt.2014.0030
|
91 |
ZuoW M, MengD Y, ZhangL, Feng X C, ZhangD . A generalized iterated shrinkage algorithm for non-convex sparse coding. In: Proceedings of the IEEE International Conference on Computer Vision. 2013, 217–224
https://doi.org/10.1109/iccv.2013.34
|
92 |
KrishnanD, FergusR. Fast image deconvolution using hyperlaplacian priors. In: BengioY , SchuurmansD, Lafferty J D, et al., eds. Advances in Neural Information Processing Systems 22. 2009, 1033–1041
|
93 |
ChartrandR, YinW. Iteratively reweighted algorithms for compressive sensing. In: Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing. 2008, 3869–3872
https://doi.org/10.1109/icassp.2008.4518498
|
94 |
SheY Y. An iterative algorithm for fitting nonconvex penalized generalized linear models with grouped predictors. Computational Statistics & Data Analysis, 2012, 56(10): 2976–2990
https://doi.org/10.1016/j.csda.2011.11.013
|
95 |
GongP H, ZhangC S, LuZ S, Huang J Z, YeJ P . A general iterative shrinkage and thresholding algorithm for non-convex regularized optimization problems. In: Proceedings of International Conference on Machine Learning. 2013, 37–45
|
96 |
BrediesK, LorenzD A. Linear convergence of iterative softthresholding.Journal of Fourier Analysis and Applications, 2008, 14(5–6): 813–837
https://doi.org/10.1007/s00041-008-9041-1
|
97 |
KowalskiM. Thresholding rules and iterative shrinkage/thresholding algorithm: a convergence study. In: Proceedings of the IEEE International Conference on Image Processing. 2014, 4151–4155
https://doi.org/10.1109/icip.2014.7025843
|
98 |
ChambolleA, DossalC. On the convergence of the iterates of the “fast iterative shrinkage/thresholding algorithm”. Journal of Optimization Theory & Applications, 2015, 166(3): 968–982
https://doi.org/10.1007/s10957-015-0746-4
|
99 |
JohnstoneP R, MoulinP. Local and global convergence of an inertial version of forward-backward splitting. Advances in Neural Information Processing Systems, 2014, 1970–1978
|
100 |
MorozovV A. On the solution of functional equations by the method of regularization. Soviet Mathematics Doklady, 1966, 7(11): 414–417
|
101 |
VainikkoG M. The discrepancy principle for a class of regularization methods. USSR Computational Mathematics and Mathematical Physics, 1982, 22(3): 1–19
https://doi.org/10.1016/0041-5553(82)90120-3
|
102 |
VainikkoG M. The critical level of discrepancy in regularization methods. USSR Computational Mathematics and Mathematical Physics, 1983, 23(6): 1–9
https://doi.org/10.1016/S0041-5553(83)80068-8
|
103 |
PlatoR. On the discrepancy principle for iterative and parametric methods to solve linear ill-posed equations. Numerische Mathematik, 1996, 75(1): 99–120
https://doi.org/10.1007/s002110050232
|
104 |
BorgesL S, Bazán F S V, CunhaM C C . Automatic stopping rule for iterative methods in discrete ill-posed problems. Computational & Applied Mathematics, 2015, 34(3): 1175–1197
https://doi.org/10.1007/s40314-014-0174-3
|
105 |
DziwokiG, Izydorczyk J. Stopping criteria analysis of the OMP algorithm for sparse channels estimation. In: Proceedings of the International Conference on Computer Networks. 2015, 250–259
https://doi.org/10.1007/978-3-319-19419-6_24
|
106 |
FavatiP, LottiG, MenchiO, Romani F.Stopping rules for iterative methods in nonnegatively constrained deconvolution. Applied Numerical Mathematics, 2014, 75: 154–166
https://doi.org/10.1016/j.apnum.2013.07.006
|
107 |
EnglH W, HankeM, NeubauerA. Regularization of Inverse Problems. Springer Science & Business Media, 1996
https://doi.org/10.1007/978-94-009-1740-8
|
108 |
AmsterP. Iterative Methods. Universitext, 2014, 53–82
https://doi.org/10.1007/978-1-4614-8893-4_3
|
109 |
WaseemM. On some iterative methods for solving system of nonlinear equations. Dissertation for the Doctoral Degree.Islamabad: COMSATS Institute of Information Technology, 2012
|
110 |
BurgerM, OsherS. A guide to the TV zoo. In: BurgerM, Mennucci A C G, OsherS , et al., eds. Level Set and PDE Based Reconstruction Methods in Imaging. Springer International Publishing, 2013, 1–70
https://doi.org/10.1007/978-3-319-01712-9_1
|
111 |
TikhonovA N. Regularization of incorrectly posed problems. Soviet Mathematics Doklady, 1963, 4(1): 1624–1627
|
112 |
NikolovaM. Analysis of the recovery of edges in images and signals by minimizing nonconvex regularized least-squares. Multiscale Modeling & Simulation, 2005, 4(3): 960–991
https://doi.org/10.1137/040619582
|
113 |
BurgerM, OsherS. Convergence rates of convex variational regularization. Inverse Problems, 2004, 20(5): 1411–1421
https://doi.org/10.1088/0266-5611/20/5/005
|
114 |
HofmannB, Kaltenbacher B, PöschlC , ScherzerO. A convergence rates result for Tikhonov regularization in Banach spaces with nonsmooth operators. Inverse Problems, 2007, 23(3): 987–1010
https://doi.org/10.1088/0266-5611/23/3/009
|
115 |
ResmeritaE. Regularization of ill-posed problems in Banach spaces:convergence rates. Inverse Problems, 2005, 21(4): 1303–1314
https://doi.org/10.1088/0266-5611/21/4/007
|
116 |
ResmeritaE, Scherzer O. Error estimates for non-quadratic regularization and the relation to enhancement. Inverse Problems, 2006, 22(3): 801–814
https://doi.org/10.1088/0266-5611/22/3/004
|
117 |
EnglH W. Discrepancy principles for Tikhonov regularization of illposed problems leading to optimal convergence rates. Journal of Optimization Theory and Applications, 1987, 52(2): 209–215
https://doi.org/10.1007/BF00941281
|
118 |
GfrererH. An a posteriori parameter choice for ordinary and iterated Tikhonov regularization of ill-posed problems leading to optimal convergence rates. Mathematics of Computation, 1987, 49(180): 507–522
https://doi.org/10.1090/S0025-5718-1987-0906185-4
|
119 |
NattererF. Error bounds for Tikhonov regularization in Hilbert scales. Applicable Analysis, 1984, 18(1–2): 29–37
https://doi.org/10.1080/00036818408839508
|
120 |
NeubauerA. An a posteriori parameter choice for Tikhonov regularization in the presence of modeling error. Applied Numerical Mathematics, 1988, 4(6): 507–519
https://doi.org/10.1016/0168-9274(88)90013-X
|
121 |
EnglH W, Kunisch K, NeubauerA . Convergence rates for Tikhonov regularisation of non-linear ill-posed problems. Inverse Problems, 1989, 5(4): 523–540
https://doi.org/10.1088/0266-5611/5/4/007
|
122 |
ScherzerO, EnglH W, KunischK. Optimal a posteriori parameter choice for Tikhonov regularization for solving nonlinear ill-posed problems. SIAM Journal on Numerical Analysis, 1993, 30(6): 1796–1838
https://doi.org/10.1137/0730091
|
123 |
VarahJ M. On the numerical solution of ill-conditioned linear systems with applications to ill-posed problems. SIAM Journal on Numerical Analysis, 1973, 10(2): 257–267
https://doi.org/10.1137/0710025
|
124 |
VinodH D, UllahA. Recent Advances in Regression Methods. Danbury: Marcel Dekker Incorporated, 1981
|
125 |
O’SullivanF. A statistical perspective on ill-posed inverse problems. Statistical Science, 1986, 1(4): 502–518
https://doi.org/10.1214/ss/1177013525
|
126 |
GrafarendE W, Schaffrin B. Ausgleichungsrechnung in linearen modellen. BI Wissenschaftsverlag Mannheim, 1993
|
127 |
RodgersC D. Inverse Methods for Atmospheric Sounding: Theory and Practice. Singapore: World Scientific, 2000
https://doi.org/10.1142/3171
|
128 |
CeccheriniS. Analytical determination of the regularization parameter in the retrieval of atmospheric vertical profiles. Optics Letters, 2005, 30(19): 2554–2556
https://doi.org/10.1364/OL.30.002554
|
129 |
MallowsC L. Some comments on Cp. Technometrics, 1973, 15(4): 661–675
|
130 |
RiceJ. Choice of smoothing parameter in deconvolution problems. Contemporary Mathematics, 1986, 59: 137–151
https://doi.org/10.1090/conm/059/10
|
131 |
HankeM, RausT. A general heuristic for choosing the regularization parameter in ill-posed problems. SIAM Journal on Scientific Computing, 1996, 17(4): 956–972
https://doi.org/10.1137/0917062
|
132 |
WuL M. A parameter choice method for Tikhonov regularization. Electronic Transactions on Numerical Analysis, 2003, 16: 107–128
|
133 |
GaoW, YuK P. A new method for determining the Tikhonov regularization parameter of load identification. In: Proceedings of the International Symposium on Precision Engineering Measurement and Instrumentation. 2015
|
134 |
ItoK, JinB, TakeuchiT. Multi-parameter Tikhonov regularizationan augmented approach. Chinese Annals of Mathematics, Series B, 2014, 35(03): 383–398
https://doi.org/10.1007/s11401-014-0835-y
|
135 |
JinB, LorenzD A. Heuristic parameter-choice rules for convex variational regularization based on error estimates. SIAM Journal on Numerical Analysis, 2010, 48(3): 1208–1229
https://doi.org/10.1137/100784369
|
136 |
PazosF, BhayaA. Adaptive choice of the Tikhonov regularization parameter to solve ill-posed linear algebraic equations via Liapunov optimizing control. Journal of Computational and Applied Mathematics, 2015, 279: 123–132
https://doi.org/10.1016/j.cam.2014.10.022
|
137 |
HämarikU, PalmR, RausT. A family of rules for parameter choice in Tikhonov regularization of ill-posed problems with inexact noise level. Journal of Computational and Applied Mathematics, 2012, 236(8): 2146–2157
https://doi.org/10.1016/j.cam.2011.09.037
|
138 |
ReichelL, Rodriguez G. Old and new parameter choice rules for discrete ill-posed problems. Numerical Algorithms, 2013, 63(1): 65–87
https://doi.org/10.1007/s11075-012-9612-8
|
139 |
KryanevA V. An iterative method for solving incorrectly posed problems. USSR Computational Mathematics and Mathematical Physics, 1974, 14(1): 24–35
https://doi.org/10.1016/0041-5553(74)90133-5
|
140 |
KingJ T, Chillingworth D. Approximation of generalized inverses by iterated regularization. Numerical Functional Analysis & Optimization, 1979, 1(5): 499–513
https://doi.org/10.1080/01630567908816031
|
141 |
FakeevA G. A class of iterative processes for solving degenerate systems of linear algebraic equations. USSR Computational Mathematics and Mathematical Physics, 1981, 21(3): 15–22
https://doi.org/10.1016/0041-5553(81)90060-4
|
142 |
BrillM, SchockE. Iterative solution of ill-posed problems: a survey. In: Proceedings of the 4th International Mathematical Geophysics Seminar. 1987
|
143 |
HankeM, Groetsch C W. Nonstationary iterated Tikhonov regularization. Journal of Optimization Theory and Applications, 1998, 98(1): 37–53
https://doi.org/10.1023/A:1022680629327
|
144 |
LampeJ, Reichel L, VossH . Large-scale Tikhonov regularization via reduction by orthogonal projection. Linear Algebra and Its Applications, 2012, 436(8): 2845–2865
https://doi.org/10.1016/j.laa.2011.07.019
|
145 |
ReichelL, YuX B. Tikhonov regularization via flexible Arnoldi reduction. BIT Numerical Mathematics, 2015, 55(4): 1145–1168
https://doi.org/10.1007/s10543-014-0542-9
|
146 |
HuangG, Reichel L, YinF . Projected nonstationary iterated Tikhonov regularization. BIT Numerical Mathematics, 2016, 56(2): 467–487
https://doi.org/10.1007/s10543-015-0568-7
|
147 |
AmbrosioL, FuscoN, PallaraD. Functions of Bounded Variation and Free Discontinuity Problems. Oxford: Oxford University Press, 2000
|
148 |
AcarR, VogelC R. Analysis of bounded variation penalty methods for ill-posed problems. Inverse Problems, 1997, 10(6): 1217–1229
https://doi.org/10.1088/0266-5611/10/6/003
|
149 |
HuntB R. The application of constrained least squares estimation to image restoration by digital computer. IEEE Transactions on Computers, 1973, 100(9): 805–812
https://doi.org/10.1109/TC.1973.5009169
|
150 |
DemomentG. Image reconstruction and restoration: overview of common estimation structures and problems. IEEE Transactions on Acoustics, Speech and Signal Processing, 1989, 37(12): 2024–2036
https://doi.org/10.1109/29.45551
|
151 |
KatsaggelosA K. Iterative image restoration algorithms. Optical Engineering, 1989, 28(7): 735–748
https://doi.org/10.1117/12.7977030
|
152 |
KatsaggelosA K, Biemond J, SchaferR W , MersereauR M. A regularized iterative image restoration algorithm. IEEE Transactions on Signal Processing, 1991, 39(4): 914–929
https://doi.org/10.1109/78.80914
|
153 |
BabacanS D, MolinaR, KatsaggelosA K . Parameter estimation in TV image restoration using variational distribution approximation. IEEE Transactions on Image Processing, 2008, 17(3): 326–339
https://doi.org/10.1109/TIP.2007.916051
|
154 |
WenY W, ChanR H. Parameter selection for total-variation-based image restoration using discrepancy principle. IEEE Transactions on Image Processing, 2012, 21(4): 1770–1781
https://doi.org/10.1109/TIP.2011.2181401
|
155 |
ChenA, HuoB M, WenC W. Adaptive regularization for color image restoration using discrepancy principle. In: Proceedings of the IEEE International Conference on Signal processing, Comminications and Computing. 2013, 1–6
https://doi.org/10.1109/icspcc.2013.6663988
|
156 |
LinY, Wohlberg B, GuoH . UPRE method for total variation parameter selection. Signal Processing, 2010, 90(8): 2546–2551
https://doi.org/10.1016/j.sigpro.2010.02.025
|
157 |
SteinC M. Estimation of the mean of a multivariate normal distribution. Annals of Statistics, 1981, 9(6): 1135–1151
https://doi.org/10.1214/aos/1176345632
|
158 |
RamaniS, BluT, UnserM. Monte-Carlo SURE: a black-box optimization of regularization parameters for general denoising algorithms. IEEE Transactions on Image Processing, 2008, 17(9): 1540–1554
https://doi.org/10.1109/TIP.2008.2001404
|
159 |
PalssonF, Sveinsson J R, UlfarssonM O , BenediktssonJ A. SAR image denoising using total variation based regularization with surebased optimization of regularization parameter. In: Proceedings of the IEEE International Conference on Geoscience and Remote Sensing Symposium. 2012, 2160–2163
|
160 |
LiaoH Y, LiF, NgM K. Selection of regularization parameter in total variation image restoration. Journal of the Optical Society of America A, 2009, 26(11): 2311–2320
https://doi.org/10.1364/JOSAA.26.002311
|
161 |
BertalmíoM, Caselles V, RougéB , SoléA. TV based image restoration with local constraints. Journal of Scientific Computing, 2003, 19(1–3): 95–122
https://doi.org/10.1023/A:1025391506181
|
162 |
AlmansaA, Ballester C, CasellesV , HaroG. A TV based restoration model with local constraints. Journal of Scientific Computing, 2008, 34(3): 209–236
https://doi.org/10.1007/s10915-007-9160-x
|
163 |
VogelC R, OmanM E. Iterative methods for total variation denoising. SIAM Journal on Scientific Computing, 1997, 17(1): 227–238
https://doi.org/10.1137/0917016
|
164 |
ChanT F, GolubG H, MuletP. A nonlinear primal-dual method for total variation-based image restoration. Lecture Notes in Control & Information Sciences, 1995, 20(6): 1964–1977
|
165 |
ChambolleA. An algorithm for total variation minimization and applications. Journal ofMathematical Imaging & Vision, 2004, 20(1–2): 89–97
|
166 |
HuangY M, NgM K, WenY W. A fast total variation minimization method for image restoration. SIAM Journal on Multiscale Modeling & Simulation, 2008, 7(2): 774–795
https://doi.org/10.1137/070703533
|
167 |
BressonX, ChanT F. Fast dual minimization of the vectorial total variation norm and applications to color image processing. Inverse Problems & Imaging, 2008, 2(4): 455–484
https://doi.org/10.3934/ipi.2008.2.455
|
168 |
NgM K, QiL Q, YangY F, Huang Y M. On semismooth Newton’s methods for total variation minimization. Journal of Mathematical Imaging & Vision, 2007, 27(3): 265–276
https://doi.org/10.1007/s10851-007-0650-0
|
169 |
ZhuM Q, ChanT F. An efficient primal-dual hybrid gradient algorithm for total variation image restoration. UCLA CAM Report. 2008, 8–34
|
170 |
ZhuM Q, WrightS J, ChanT F. Duality-based algorithms for totalvariation- regularized image restoration. Computational Optimization and Applications, 2010, 47(3): 377–400
https://doi.org/10.1007/s10589-008-9225-2
|
171 |
KrishnanD, LinP, YipA M. A primal-dual active-set method for non-negativity constrained total variation deblurring problems. IEEE Transactions on Image Processing, 2007, 16(11): 2766–2777
https://doi.org/10.1109/TIP.2007.908079
|
172 |
KrishnanD, PhamQ V, YipA M. A primal-dual active-set algorithm for bilaterally constrained total variation deblurring and piecewise constant Mumford-Shah segmentation problems. Advances in Computational Mathematics, 2009, 31(1–3): 237–266
https://doi.org/10.1007/s10444-008-9101-8
|
173 |
OsherS, BurgerM, GoldfarbD, Xu J J, YinW T . An iterative regularization method for total variation-based image restoration. Multiscale Modeling & Simulation, 2005, 4(2): 460–489
https://doi.org/10.1137/040605412
|
174 |
GoldsteinT, OsherS. The split Bregman method forl1-regularized problems. SIAM Journal on Imaging Sciences, 2009, 2(2): 323–343
https://doi.org/10.1137/080725891
|
175 |
GlowinskiR, Le Tallec P. Augmented Lagrangian and Operator- Splitting Methods in Nonlinear Mechanics. Society for Industrial and Applied Mathematics, 1989
https://doi.org/10.1137/1.9781611970838
|
176 |
WuC C, TaiX C. Augmented Lagrangian method, dual methods, and split Bregman iteration for ROF, vectorial TV, and high order models. SIAM Journal on Imaging Sciences, 2010, 3(3): 300–339
https://doi.org/10.1137/090767558
|
177 |
DarbonJ, Sigelle M. Image restoration with discrete constrained total variation part I: fast and exact optimization. Journal of Mathematical Imaging & Vision, 2006, 26(3): 261–276
https://doi.org/10.1007/s10851-006-8803-0
|
178 |
DuanY P, TaiX C. Domain decomposition methods with graph cuts algorithms for total variation minimization. Advances in Computational Mathematics, 2012, 36(2): 175–199
https://doi.org/10.1007/s10444-011-9213-4
|
179 |
FuH Y, NgM K, NikolovaM, Barlow J L. Efficient minimization methods of mixed l2-l1 and l1-l1 norms for image restoration. SIAM Journal on Scientific Computing, 2005, 27(6): 1881–1902
https://doi.org/10.1137/040615079
|
180 |
GoldfarbD, YinW T. Second-order cone programming methods for total variation-based image restoration. SIAM Journal on Scientific Computing, 2005, 27(2): 622–645
https://doi.org/10.1137/040608982
|
181 |
OliveiraJ P, Bioucas-Dias J M, FigueiredoM A T . Adaptive total variation image deblurring: a majorization-minimization approach. Signal Processing, 2009, 89(9): 1683–1693
https://doi.org/10.1016/j.sigpro.2009.03.018
|
182 |
Bioucas-DiasJ M, Figueiredo M A T, OliveiraJ P . Total variationbased image deconvolution: a majorization-minimization approach, In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing. 2006, 861–864
|
183 |
ChanT F, Esedoglu S. Aspects of total variation regularized l1 function approximation. SIAM Journal on Applied Mathematics, 2004, 65(5): 1817–1837
https://doi.org/10.1137/040604297
|
184 |
HeL, BurgerM, OsherS. Iterative total variation regularization with non-quadratic fidelity. Journal of Mathematical Imaging & Vision, 2006, 26(1–2): 167–184
https://doi.org/10.1007/s10851-006-8302-3
|
185 |
JonssonE, HuangS C, ChanT F. Total variation regularization in positron emission tomography. CAM Report. 1998
|
186 |
PaninV Y, ZengG L, GullbergG T . Total variation regulated EM algorithm. IEEE Transactions on Nuclear Science, 1999, 46(6): 2202–2210
https://doi.org/10.1109/23.819305
|
187 |
LeT, Chartrand R, AsakiT J . A variational approach to reconstructing images corrupted by Poisson noise. Journal of Mathematical Imaging & Vision, 2007, 27(3): 257–263
https://doi.org/10.1007/s10851-007-0652-y
|
188 |
RudinL, LionsP L, OsherS. Multiplicative denoising and deblurring: theory and algorithms. In: OsherS, Paragios N, eds. Geometric Level Set Methods in Imaging, Vision, and Graphics. New York: Springer, 2003, 103–119
https://doi.org/10.1007/0-387-21810-6_6
|
189 |
HuangY M, NgM K, WenY W. A new total variation method for multiplicative noise removal. SIAM Journal on Imaging Sciences, 2009, 2(1): 20–40
https://doi.org/10.1137/080712593
|
190 |
BoneskyT, Kazimierski K S, MaassP , SchöpferF, Schuster T. Minimization of Tikhonov functionals in Banach spaces. Abstract & Applied Analysis, 2008, 2008(1): 1563–1569
https://doi.org/10.1155/2008/192679
|
191 |
MeyerY. Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, University Lecture Series. Rhode Island: American Mathematical Society, 2002
|
192 |
BlomgrenP, ChenT F. Color TV: total variation methods for restoration of vector valued images. IEEE Transactions on Image Processing, 1970, 7(3): 304–309
https://doi.org/10.1109/83.661180
|
193 |
SetzerS, SteidlG, PopilkaB, Burgeth B. Variational methods for denoising matrix fields. In: LaidlawD , WeickertJ, eds. Visualization and Processing of Tensor Fields. Berlin: Springer Berlin Heidelberg, 2009, 341–360
https://doi.org/10.1007/978-3-540-88378-4_17
|
194 |
EsedogluS, OsherS. Decomposition of images by the anisotropic Rudin-Osher-Fatemi model. Communications on Pure and Applied Mathematics, 2004, 57(12): 1609–1626
https://doi.org/10.1002/cpa.20045
|
195 |
ShiY Y, ChangQ S. Efficient algorithm for isotropic and anisotropic total variation deblurring and denoising. Journal of Applied Mathematics, 2013
https://doi.org/10.1155/2013/797239
|
196 |
MarquinaA, OsherS. Explicit algorithms for a new time dependent model based on level set motion for nonlinear deblurring and noise removal. SIAM Journal on Scientific Computing, 2000, 22(2): 387–405
https://doi.org/10.1137/S1064827599351751
|
197 |
ChanT F, Marquina A, MuletP . High-order total variation-based image restoration. SIAM Journal on Scientific Computing, 2000, 22(2): 503–516
https://doi.org/10.1137/S1064827598344169
|
198 |
GilboaG, OsherS. Nonlocal operators with applications to image processing. SIAM Journal on Multiscale Modeling & Simulation, 2008, 7(3): 1005–1028
https://doi.org/10.1137/070698592
|
199 |
KindermannS, OsherS, JonesP W. Deblurring and denoising of images by nonlocal functionals. SIAM Journal on Multiscale Modeling & Simulation, 2005, 4(4): 1091–1115
https://doi.org/10.1137/050622249
|
200 |
HuY, JacobM. Higher degree total variation (HDTV) regularization for image recovery. IEEE Transactions on Image Processing, 2012, 21(5): 2559–2571
https://doi.org/10.1109/TIP.2012.2183143
|
201 |
YangJ S, YuH Y, JiangM, Wang G. High-order total variation minimization for interior SPECT. Inverse Problems, 2012, 28(1): 15001–15024
https://doi.org/10.1088/0266-5611/28/1/015001
|
202 |
LiuX W, HuangL H. A new nonlocal total variation regularization algorithm for image denoising. Mathematics and Computers in Simulation, 2014, 97: 224–233
https://doi.org/10.1016/j.matcom.2013.10.001
|
203 |
RenZ M, HeC J, ZhangQ F. Fractional order total variation regularization for image super-resolution. Signal Processing, 2013, 93(9): 2408–2421
https://doi.org/10.1016/j.sigpro.2013.02.015
|
204 |
OhS, WooH, YunS, Kang M. Non-convex hybrid total variation for image denoising. Journal of Visual Communication & Image Representation, 2013, 24(3): 332–344
https://doi.org/10.1016/j.jvcir.2013.01.010
|
205 |
DonohoD L. Compressed sensing. IEEE Transactions on Information Theory, 2006, 52(4): 1289–1306
https://doi.org/10.1109/TIT.2006.871582
|
206 |
CandèE J, Wakin M B. An introduction to compressive sampling. IEEE Signal Processing Magazine, 2008, 25(2): 21–30
https://doi.org/10.1109/MSP.2007.914731
|
207 |
TsaigY, DonohoD L. Extensions of compressed sensing. Signal Processing, 2006, 86(3): 549–571
https://doi.org/10.1016/j.sigpro.2005.05.029
|
208 |
CandèsE J, Romberg J, TaoT . Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory, 2006, 52(2): 489–509
https://doi.org/10.1109/TIT.2005.862083
|
209 |
CandèsE J, Tao T. Near-optimal signal recovery from random projections: Universal encoding strategies?. IEEE Transactions on Information Theory, 2006, 52(12): 5406–5425
https://doi.org/10.1109/TIT.2006.885507
|
210 |
DonohoD L, EladM. Optimally sparse representation in general (nonorthogonal) dictionaries via l1 minimization. Proceedings of National Academy of Sciences, 2003, 100(5): 2197–2202
https://doi.org/10.1073/pnas.0437847100
|
211 |
WrightJ, MaY. Dense error correction via l1-minimization. IEEE Transactions on Information Theory, 2010, 56(7): 3540–3560
https://doi.org/10.1109/TIT.2010.2048473
|
212 |
YangJ F, ZhangY. Alternating direction algorithms for l1-problems in compressive sensing. SIAM Journal on Scientific Computing, 2011, 33(1): 250–278.
https://doi.org/10.1137/090777761
|
213 |
NatarajanB K. Sparse approximate solutions to linear systems. SIAM Journal on Computing, 1995, 24(2): 227–234
https://doi.org/10.1137/S0097539792240406
|
214 |
MallatS G, ZhangZ. Matching pursuits with time-frequency dictionaries. IEEE Transactions on Signal Processing, 1993, 41(12): 3397–3415
https://doi.org/10.1109/78.258082
|
215 |
TroppJ, Gilbert A C. Signal recovery from random measurements via orthogonal matching pursuit. IEEE Transactions on Information Theory, 2007, 53(12): 4655–4666
https://doi.org/10.1109/TIT.2007.909108
|
216 |
BlumensathT, DaviesM E. Iterative thresholding for sparse approximations. Journal of Fourier Analysis and Applications, 2008, 14(5–6): 629–654
https://doi.org/10.1007/s00041-008-9035-z
|
217 |
GorodnitskyI F, RaoB D. Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm. IEEE Transactions on Signal Processing, 1997, 45(3): 600–616
https://doi.org/10.1109/78.558475
|
218 |
BaoC L, JiH, QuanY H, Shen Z W. l0 norm based dictionary learning by proximal methods with global convergence. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 2014, 3858–3865
https://doi.org/10.1109/cvpr.2014.493
|
219 |
FoucartS, LaiM J. Sparsest solutions of underdetermined linear systems via lq-minimization for 0<q≤1. Applied and Computational Harmonic Analysis, 2009, 26(3): 395–407
https://doi.org/10.1016/j.acha.2008.09.001
|
220 |
CaiT T, WangL, XuG. Shifting inequality and recovery of sparse signals. IEEE Transactions on Signal Processing, 2010, 58(3): 1300–1308
https://doi.org/10.1109/TSP.2009.2034936
|
221 |
CaiT T, WangL, XuG. New bounds for restricted isometry constants. IEEE Transactions on Information Theory, 2010, 56(9): 4388–4394
https://doi.org/10.1109/TIT.2010.2054730
|
222 |
ChenS S, DonohoD L, SaundersM A . Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing, 1998, 20(1): 33–61
https://doi.org/10.1137/S1064827596304010
|
223 |
EfronB, HastieT, JohnstoneI, Tibshirani R. Least angle regression. The Annals of Statistics, 2004, 32(2): 407–499
https://doi.org/10.1214/009053604000000067
|
224 |
FigueiredoM A T, Nowak R D. An EM algorithm for wavelet-based image restoration. IEEE Transactions on Image Processing, 2002, 12(8): 906–916
https://doi.org/10.1109/TIP.2003.814255
|
225 |
StarckJ L, MaiK N, MurtaghF. Wavelets and curvelets for image deconvolution: a combined approach. Signal Processing, 2003, 83(10): 2279–2283
https://doi.org/10.1016/S0165-1684(03)00150-6
|
226 |
HerrholzE, Teschke G. Compressive sensing principles and iterative sparse recovery for inverse and ill-posed problems. Inverse Problems, 2010, 26(12): 125012–125035
https://doi.org/10.1088/0266-5611/26/12/125012
|
227 |
JinB, LorenzD, SchifflerS. Elastic-net regularization: error estimates and active set methods. Inverse Problems, 2009, 25(11): 1595–1610
https://doi.org/10.1088/0266-5611/25/11/115022
|
228 |
FigueiredoM A T, Nowak R D, WrightS J . Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE Journal of Selected Topics in Signal Processing, 2007, 1(4): 586–597
https://doi.org/10.1109/JSTSP.2007.910281
|
229 |
KimS J, KohK, LustigM, Boyd S, GorinevskyD . An interior-point method for large-scale l1-regularized least squares. IEEE Journal of Selected Topics in Signal Processing, 2007, 1(4): 606–617
https://doi.org/10.1109/JSTSP.2007.910971
|
230 |
DonohoD L, TsaigY. Fast solution of l1-norm minimization problems when the solution may be sparse. IEEE Transactions on Information Theory, 2008, 54(11): 4789–4812
https://doi.org/10.1109/TIT.2008.929958
|
231 |
CombettesP L, WajsE R. Signal recovery by proximal forwardbackward splitting. SIAM Journal on Multiscale Modeling & Simulation, 2005, 4(4): 1168–1200
https://doi.org/10.1137/050626090
|
232 |
BeckerS, BobinJ, CandésE J . NESTA: a fast and accurate firstorder method for sparse recovery. SIAM Journal on Imaging Sciences, 2011, 4(1): 1–39
https://doi.org/10.1137/090756855
|
233 |
OsborneM R, Presnell B, TurlachB A . A new approach to variable selection in least squares problems. IMA Journal of Numerical Analysis, 1999, 20(3): 389–403
https://doi.org/10.1093/imanum/20.3.389
|
234 |
LiL, YaoX, StolkinR, Gong M G, HeS . An evolutionary multiobjective approach to sparse reconstruction. IEEE Transactions on Evolutionary Computation,2014, 18(6): 827–845
https://doi.org/10.1109/TEVC.2013.2287153
|
235 |
ChartrandR. Exact reconstruction of sparse signals via nonconvex minimization. IEEE Signal Processing Letters, 2007, 14(10): 707–710
https://doi.org/10.1109/LSP.2007.898300
|
236 |
CandesE J, TaoT. Decoding by linear programming. IEEE Transactions on Information Theory, 2005, 51(12): 4203–4215
https://doi.org/10.1109/TIT.2005.858979
|
237 |
SaabR, Chartrand R, YilmazÖ . Stable sparse approximations via nonconvex optimization. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing. 2008, 3885–3888
https://doi.org/10.1109/icassp.2008.4518502
|
238 |
TibshiraniR. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B, 1996, 58(1): 267–288
|
239 |
ZhangC H. Nearly unbiased variable selection under minimax concave penalty. The Annals of Statistics, 2010, 38(2): 894–942
https://doi.org/10.1214/09-AOS729
|
240 |
FanJ Q, LiR. Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 2001, 96(456): 1348–1360
https://doi.org/10.1198/016214501753382273
|
241 |
NikolovaM, NgM K, ZhangS, Ching W K. Efficient reconstruction of piecewise constant images using nonsmooth nonconvex minimization. SIAM Journal on Imaging Sciences, 2008, 1(1): 2–25
https://doi.org/10.1137/070692285
|
242 |
FrankL E, Friedman J H. A statistical view of some chemometrics regression tools. Technometrics, 1993, 35(2): 109–135
https://doi.org/10.1080/00401706.1993.10485033
|
243 |
FuW J. Penalized regressions: the bridge versus the lasso. Journal of Computational and Graphical Statistics, 1998, 7(3): 397–416
|
244 |
LyuQ, LinZ C, SheY Y, Zhang C. A comparison of typical lp minimization algorithms. Neurocomputing, 2013, 119: 413–424
https://doi.org/10.1016/j.neucom.2013.03.017
|
245 |
CandesE J, WakinM B, BoydS P. Enhancing sparsity by reweighted l1 minimization. Journal of Fourier Analysis and Applications, 2008, 14(5–6): 877–905
https://doi.org/10.1007/s00041-008-9045-x
|
246 |
RaoB D, Kreutz-Delgado K. An affine scaling methodology for best basis selection. IEEE Transactions on Signal Processing, 1999, 47(1): 187–200
https://doi.org/10.1109/78.738251
|
247 |
SheY Y. Thresholding-based iterative selection procedures for model selection and shrinkage. Electronic Journal of Statistics, 2009, 3: 384–415
https://doi.org/10.1214/08-EJS348
|
248 |
XuZ B, ZhangH, WangY, Chang X Y, LiangY .L1/2 regularization. Science China Information Sciences, 2010, 53(6): 1159–1169
https://doi.org/10.1007/s11432-010-0090-0
|
249 |
XuZ B, GuoH L, WangY, Zhang H. Representative of L1/2 regularization among lq (0<q≤1) regularizations: an experimental study based on phase diagram. Acta Automatica Sinica, 2012, 38(7): 1225–1228
https://doi.org/10.1016/s1874-1029(11)60293-0
|
250 |
CandesE J, PlanY. Matrix completion with noise. Proceedings of the IEEE, 2009, 98(6): 925–936
https://doi.org/10.1109/JPROC.2009.2035722
|
251 |
CaiJ F, CandesE J, ShenZ. A singular value thresholding algorithm for matrix completion. SIAM Journal on Optimization, 2010, 20(4): 1956–1982
https://doi.org/10.1137/080738970
|
252 |
BoydS, ParikhN, ChuE, Peleato B, EcksteinJ . Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations & Trends in Machine Learning, 2011, 3(1): 1–122
https://doi.org/10.1561/2200000016
|
253 |
QianJ J, YangJ, ZhangF L, Lin Z C. Robust low-rank regularized regression for face recognition with occlusion. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops. 2014, 21–26
https://doi.org/10.1109/cvprw.2014.9
|
254 |
LiuY J, SunD, TohK C. An implementable proximal point algorithmic framework for nuclear norm minimization. Mathematical Programming, 2012, 133(1–2): 399–436
https://doi.org/10.1007/s10107-010-0437-8
|
255 |
YangJ F, YuanX M. Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization. Mathematics of Computation, 2013, 82(281): 301–329
https://doi.org/10.1090/S0025-5718-2012-02598-1
|
256 |
LiT, WangW W, XuL, FengX C. Image denoising using lowrank dictionary and sparse representation. In: Proceedings of the 10th IEEE International Conference on Computational Intelligence and Security. 2014, 228–232
|
257 |
WatersA E, Sankaranarayanan A C, BaraniukR G . SpaRCS: recovering low-rank and sparse matrices from compressive measurements. In: Proceedings of the Neural Information Processing Systems Conference. 2011, 1089–1097
|
258 |
LiQ, LuZ B, LuQ B, Li H Q, LiW P . Noise reduction for hyperspectral images based on structural sparse and low-rank matrix decomposition. In: Proceedings of the IEEE International on Geoscience and Remote Sensing Symposium. 2013, 1075–1078
https://doi.org/10.1109/igarss.2013.6721350
|
259 |
ZhouT Y, TaoD C. Godec: randomized low-rank & sparse matrix decomposition in noisy case. In: Proceedings of the 28th International Conference on Machine Learning. 2011, 33–40
|
260 |
ZhangH Y, HeW, ZhangL P, Shen H F, YuanQ Q . Hyperspectral image restoration using low-rank matrix recovery.IEEE Transactions on Geoscience & Remote Sensing, 2014, 52(8): 4729–4743
https://doi.org/10.1109/TGRS.2013.2284280
|
261 |
ZhangZ, XuY, YangJ, Li X L, ZhangD . A survey of sparse representation: algorithms and applications. IEEE Access, 2015, 3: 490–530
https://doi.org/10.1109/ACCESS.2015.2430359
|
262 |
BurgerM, FranekM, SchÖnliebC B . Regularized regression and density estimation based on optimal transport. Applied Mathematics Research eXpress, 2012, 2012(2): 209–253
|
263 |
OsherS, Solè A, VeseL . Image decomposition and restoration using total variation minimization and the H1 norm. Multiscale Modeling & Simulation, 2003, 1(3): 349–370
https://doi.org/10.1137/S1540345902416247
|
264 |
BarbaraK. Iterative regularization methods for nonlinear ill-posed problems. Algebraic Curves & Finite Fields Cryptography & Other Applications, 2008, 6
|
265 |
MiettinenK. Nonlinear Multiobjective Optimization. Springer Science & Business Media, 2012
|
266 |
MarlerR T, AroraJ S. Survey of multi-objective optimization methods for engineering. Structural and Multidisciplinary Optimization, 2004, 26(6): 369–395
https://doi.org/10.1007/s00158-003-0368-6
|
267 |
GongM G, JiaoL C, YangD D, Ma W P. Research on evolutionary multi-objective optimization algorithms. Journal of Software, 2009, 20(20): 271–289
https://doi.org/10.3724/SP.J.1001.2009.00271
|
268 |
FonsecaC M, Fleming P J. Genetic algorithm for multiobjective optimization: formulation, discussion and generation. In: Proceedings of the International Conference on Genetic Algorithms. 1993, 416–423
|
269 |
SrinivasN, DebK. Multiobjective optimization using non-dominated sorting in genetic algorithms. Evolutionary Computation, 1994, 2(3): 221–248
https://doi.org/10.1162/evco.1994.2.3.221
|
270 |
HornJ, Nafpliotis N, GoldbergD E . A niched Pareto genetic algorithm for multiobjective optimization. In: Proceedings of the 1st IEEE Conference on Evolutionary Computation. 1994, 1: 82–87
https://doi.org/10.1109/icec.1994.350037
|
271 |
ZitzlerE, ThieleL. Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Transactions on Evolutionary Computation, 1999, 3(4): 257–271
https://doi.org/10.1109/4235.797969
|
272 |
ZitzlerE, Laumanns M, ThieleL . SPEA2: improving the strength Pareto evolutionary algorithm. Eurogen, 2001, 3242(103): 95–100
|
273 |
KimM, Hiroyasu T, MikiM , WatanabeS. SPEA2+: improving the performance of the strength Pareto evolutionary algorithm 2. In: Proceedings of the International Conference on Parallel Problem Solving from Nature. 2004, 742–751
https://doi.org/10.1007/978-3-540-30217-9_75
|
274 |
KnowlesJ D, CorneD W. Approximating the non-dominated front using the Pareto archived evolution strategy. Evolutionary Computation, 2000, 8(2): 149–172
https://doi.org/10.1162/106365600568167
|
275 |
CorneD W, Knowles J D, OatesM J . The Pareto-envelope based selection algorithm for multi-objective optimization. In: Proceedings of the Internatioal Conference on Parallel Problem Solving from Nature. 2000, 869–878
|
276 |
CorneD W, JerramN R, KnowlesJ D, Oates M J. PESA-II: regionbased selection in evolutionary multi-objective optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference. 2001, 283–290
|
277 |
DebK, Agrawal S, PratapA , MeyarivanT. A fast elitist nondominated sorting genetic algorithm for multi-objective optimization: NSGA-II. Lecture Notes in Computer Science, 2000, 1917: 849–858
|
278 |
ZhangQ F, LiH. MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation, 2007, 11(6): 712–731
https://doi.org/10.1109/TEVC.2007.892759
|
279 |
IshibuchiH, SakaneY, TsukamotoN, Nojima Y. Simultaneous use of different scalarizing functions in MOEA/D. In: Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation. 2010, 519–526
https://doi.org/10.1145/1830483.1830577
|
280 |
WangL P, ZhangQ F, ZhouA M, Gong M G, JiaoL C . Constrained subproblems in decomposition based multiobjective evolutionary algorithm. IEEE Transactions on Evolutionary Computation, 2016, 20(3): 475–480
https://doi.org/10.1109/TEVC.2015.2457616
|
281 |
LiK, FialhoA, KwongS, Zhang Q F. Adaptive operator selection with bandits for a multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation, 2014, 18(1): 114–130
https://doi.org/10.1109/TEVC.2013.2239648
|
282 |
KeL J, ZhangQ F, BattitiR. Hybridization of decomposition and local search for multiobjective optimization.IEEE Transactions on Cybernetics, 2014, 44(10): 1808–1820
https://doi.org/10.1109/TCYB.2013.2295886
|
283 |
CaiX Y, WeiO. A hybrid of decomposition and domination based evolutionary algorithm for multi-objective software next release problem. In: Proceedings of the 10th IEEE International Conference on Control and Automation. 2013, 412–417
https://doi.org/10.1109/icca.2013.6565143
|
284 |
DebK, JainH. An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Transactions on Evolutionary Computation , 2014, 18(4): 577–601
https://doi.org/10.1109/TEVC.2013.2281535
|
285 |
YuanY, XuH, WangB. An improved NSGA-III procedure for evolutionary many-objective optimization. In: Proceedings of ACM Annual Conference on Genetic & Evolutionary Computation. 2014, 661–668
https://doi.org/10.1145/2576768.2598342
|
286 |
SeadaH, DebK. U-NSGA-III: a unified evolutionary optimization procedure for single, multiple, and many objectives: proof-ofprinciple results. In: Proceedings of the International Conference on Evolutionary Multi-Criterion Optimization. 2015, 34–49
https://doi.org/10.1007/978-3-319-15892-1_3
|
287 |
ZhuZ X, XiaoJ, LiJ Q, Zhang Q F. Global path planning of wheeled robots using multi-objective memetic algorithms. Integrated Computer-Aided Engineering, 2015, 22(4): 387–404
https://doi.org/10.3233/ICA-150498
|
288 |
ZhuZ X, JiaS, HeS, SunY W, JiZ, ShenL L. Three-dimensional Gabor feature extraction for hyperspectral imagery classification using a memetic framework. Information Sciences, 2015, 298: 274–287
https://doi.org/10.1016/j.ins.2014.11.045
|
289 |
ZhuZ X, XiaoJ, HeS, JiZ, SunY W. A multi-objective memetic algorithm based on locality-sensitive hashing for one-to-many-to-one dynamic pickup-and-delivery problem. Information Sciences, 2015, 329: 73–89
https://doi.org/10.1016/j.ins.2015.09.006
|
290 |
LiH, GongM G, WangQ, Liu J, SuL Z . A multiobjective fuzzy clustering method for change detection in synthetic aperture radar images. Applied Soft Computing, 2016, 46: 767–777
https://doi.org/10.1016/j.asoc.2015.10.044
|
291 |
JinY, Sendhoff B. Pareto based approach to machine learning: an overview and case studies. IEEE Transactions on Systems, Man, and Cybernetics, Part C, 2008, 38(3): 397–415
|
292 |
PlumbleyM D. Recovery of sparse representations by polytope faces pursuit. In: Proceedings of the 6th International Conference on In of the first kind using singular values. SIAM Journal on Numerical Analysis, 1971, 8(3): 616–622
|
293 |
WrightS J, NowakR D, FigueiredoM A T . Sparse reconstruction by separable approximation. IEEE Transactions on Signal Processing, 2009, 57(7): 2479–2493
https://doi.org/10.1109/TSP.2009.2016892
|
294 |
YangY, YaoX, ZhouZ H. On the approximation ability of evolutionary optimization with application to minimum set cover. Artificial Intelligence, 2012, 180(2): 20–33
|
295 |
QianC, YuY, ZhouZ H. An analysis on recombination in multiobjective evolutionary optimization. Artificial Intelligence, 2013, 204(1): 99–119
https://doi.org/10.1016/j.artint.2013.09.002
|
296 |
GongM G, ZhangM Y, YuanY. Unsupervised band selection based on evolutionary multiobjective optimization for hyperspectral images. IEEE Transactions on Geoscience and Remote Sensing, 2016, 54(1): 544–557
https://doi.org/10.1109/TGRS.2015.2461653
|
297 |
QianC, YuY, ZhouZ H.Pareto ensemble pruning. In: Proceedings of AAAI Conference on Artificial Intelligence. 2015, 2935–2941
|
298 |
QianC, YuY, ZhouZ H. On constrained Boolean Pareto optimization. In: Proceedings of the 24th International Joint Conference on Artificial Intelligence. 2015, 389–395
|
299 |
QianC, YuY, ZhouZ H. Subset selection by Pareto optimization. In: Proceedings of the Neural Information Processing Systems Conference. 2015, 1765–1773
|
300 |
GongM G, LiuJ, LiH, CaiQ, SuL Z. A multiobjective sparse feature learning model for deep neural networks. IEEE Transactions on Neural Networks and Learning Systems, 2015, 26(12): 3263–3277
https://doi.org/10.1109/TNNLS.2015.2469673
|