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Projected Newton method for noise constrained \(\ell_p\) regularization. (English) Zbl 1455.65048
65F22 Ill-posedness and regularization problems in numerical linear algebra
65F10 Iterative numerical methods for linear systems
65K05 Numerical mathematical programming methods
49M15 Newton-type methods
Full Text: DOI
[1] Hansen P C 2010 Discrete Inverse Problems (Philadelphia, PA: SIAM) · Zbl 1197.65054
[2] Gazzola S and Novati P 2014 Automatic parameter setting for Arnoldi-Tikhonov methods J. Comput. Appl. Math.256 180-95 · Zbl 1314.65061
[3] Cornelis J, Schenkels N and Vanroose W 2020 Projected Newton method for noise constrained Tikhonov regularization Inverse Problems36 055002
[4] Lampe J, Reichel L and Voss H 2012 Large-scale Tikhonov regularization via reduction by orthogonal projection Linear Algebr. Appl.436 2845-65 · Zbl 1241.65044
[5] Calvetti D, Morigi S, Reichel L and Sgallari F 2000 Tikhonov regularization and the L-curve for large discrete ill-posed problems J. Comput. Appl. Math.123 423-46 Numerical Analysis 2000 Vol III: Linear Algebra · Zbl 0977.65030
[6] Gazzola S and Nagy J G 2014 Generalized Arnoldi-Tikhonov method for sparse reconstruction SIAM J. Sci. Comput.36 B225-47 · Zbl 1298.76248
[7] Rodriguez P and Wohlberg B 2008 An efficient algorithm for sparse representations with ℓp data fidelity term Proc. of 4th IEEE Andean Technical Conf.
[8] Chen S S, Donoho D L and Saunders M A 1998 Atomic decomposition by basis pursuit SIAM J. Sci. Comput.20 33-61 · Zbl 0919.94002
[9] Chung J and Gazzola S 2019 Flexible Krylov methods for ℓp regularization SIAM J. Sci. Comput.41 S149-71 · Zbl 1436.65043
[10] Gorodnitsky I F and Rao B D 1997 Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm IEEE Trans. Signal Process.45 600-16
[11] Chan T, Esedoglu S, Park F and Yip A 2006 Total variation image restoration: overview and recent developments Handbook of Mathematical Models in Computer Vision (Berlin: Springer) pp 17-31
[12] Wohlberg B and Rodriguez P 2007 An Iteratively reweighted norm algorithm for minimization of total variation functionals IEEE Signal Process. Lett.14 948-51
[13] Nocedal J and Wright S 2006 Numerical Optimization (Berlin: Springer)
[14] Landi G 2008 The Lagrange method for the regularization of discrete ill-posed problems Comput. Optim. Appl.39 347-68 · Zbl 1151.91732
[15] Lanza A, Morigi S, Reichel L and Sgallari F 2015 A generalized Krylov subspace method for ℓp-ℓq minimization SIAM J. Sci. Comput.37 S30-50 · Zbl 1343.65077
[16] Saheya B, Yu C-H and Chen J-S 2018 Numerical comparisons based on four smoothing functions for absolute value equation J. Appl. Math. Comput.56 131-49 · Zbl 1390.26020
[17] Herty M, Klar A, Singh A K and Spellucci P 2007 Smoothed penalty algorithms for optimization of nonlinear models Comput. Optim. Appl.37 157-76 · Zbl 1181.90222
[18] Wu C, Zhan J, Lu Y and Chen J-S 2019 Signal reconstruction by conjugate gradient algorithm based on smoothing ℓ1-norm Calcolo56 42 · Zbl 1434.90199
[19] Paige C C and Saunders M A 1975 Solution of sparse indefinite systems of linear equations SIAM J. Numer. Anal.12 617-29 · Zbl 0319.65025
[20] Paige C C and Saunders M A 1982 LSQR: an algorithm for sparse linear equations and sparse least squares ACM Trans. Math. Softw.8 43-71 · Zbl 0478.65016
[21] Golub G and Kahan W 1965 Calculating the singular values and pseudo-inverse of a matrix SIAM J. Numer. Anal. B 2 205-24 · Zbl 0194.18201
[22] Boyd S, Boyd S P and Vandenberghe L 2004 Convex Optimization (Cambridge: Cambridge University Press)
[23] Daniel J W, Gragg W B, Kaufman L and Stewart G W 1976 Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization Math. Comput.30 772-95 · Zbl 0345.65021
[24] Zhang F 2006 The Schur Complement and its Applications vol 4 (Berlin: Springer)
[25] Rodriguez P and Wohlberg B 2009 Efficient minimization method for a generalized total variation functional IEEE Trans. Image Process.18 322-32 · Zbl 1371.94316
[26] Gazzola S and Sabaté Landman M 2019 Flexible GMRES for total variation regularization Bit Numer. Math.59 721-46 · Zbl 1420.65021
[27] Gazzola S, Hansen P C and Nagy J G 2019 IR tools: a MATLAB package of iterative regularization methods and large-scale test problems Numer. Algorithms81 773-811 · Zbl 1415.65003
[28] Hansen P C 1994 Regularization tools: a MATLAB package for analysis and solution of discrete ill-posed problems Numer. Algorithms6 1-35 · Zbl 0789.65029
[29] Zhang L, Zhou W and Li D-H 2006 A descent modified Polak-Ribière-Polyak conjugate gradient method and its global convergence IMA J. Numer. Anal.26 629-40 · Zbl 1106.65056
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