chaidisheng / Convex_Optimization

convex optimization

Convex optimization about image processing

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My emial is [e-mail].

Alternating Direction Method of Multipliers(ADMM)

Linear ADMM

Proximal Gradient Method

Douglas−Rachford Splitting Method

Pock-Chambolle Method(Primal Dual Method)

Half Quadratic Splitting Method

Approximate Message Passing Method

Reference

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[2]PARIKH N, BOYD S. Proximal algorithms[J]. Foundations and Trends in Optimization, 2014, 1 (3):127-239.
[3]BOYD S P, VANDENBERGHE L. Convex optimization[M]. [S.l.]: Cambridge University Press,2014.
[4]GOLDSTEIN T, STUDER C, BARANIUK R G. A field guide to forward-backward splitting with a FASTA implementation[J]. CoRR, 2014, abs/1411.3406.
[5]HEIDE F, DIAMOND S, NIENER M, et al. Proximal: effcient image optimization using proximal algorithms[J]. Acm Transactions on Graphics, 2016, 35(4):84.
[6]MÖLLENHOFF T, STREKALOVSKIY E, MÖLLER M, et al. The primal-dual hybrid gradient method for semiconvex splittings[J]. SIAM J. Imaging Sci., 2015, 8(2):827-857.
[7]CHAMBOLLE A, POCK T. A first-order primal-dual algorithm for convex problems with applications to imaging[J]. J. Math. Imaging Vis., 2011, 40(1):120-145.
[8]CHAMBOLLE A, EHRHARDT M J, RICHTÁRIK P, et al. Stochastic primal-dual hybrid gradient algorithm with arbitrary sampling and imaging applications[J]. SIAM J. Optim., 2018, 28(4):2783-2808.
[9]THEMELIS A, PATRINOS P. Douglas-rachford splitting and ADMM for nonconvex optimization: Tight convergence results[J]. SIAM J. Optim., 2020, 30(1):149-181.
[10]XU Z, FIGUEIREDO M A T, YUAN X, et al. Adaptive relaxed ADMM: convergence theory and practical implementation[C]//CVPR. [S.l.]: IEEE Computer Society, 2017: 7234-7243.
[11]BIAN F, ZHANG X. A generalized douglas-rachford splitting algorithm for nonconvex optimization. [J]. arXiv: Optimization and Control, 2019.
[12]BURGER M, SAWATZKY A, STEIDL G. First order algorithms in variational image processing[J]. CoRR, 2014, abs/1412.4237.
[13]BURGER M, SAWATZKY A, STEIDL G. First order algorithms in variational image processing[J]. ArXiv, 2014, abs/1412.4237.
[14]BUZZARD G T, CHAN S H, SREEHARI S, et al. Plug-and-play unplugged: Optimization-free reconstruction using consensus equilibrium[J]. SIAM J. Imaging Sci., 2018, 11(3):2001-2020.