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Compressive optical deflectometric tomography: A constrained total-variation minimization approach
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A variational algorithm for the detection of line segments
An inner-outer regularizing method for ill-posed problems
1. | IIT - CNR Via G. Moruzzi 1, 56124 Pisa, Italy |
2. | Dipart. di Matematica e Informatica, University of Parma, Viale G. Usberti 53/A, 43100 Parma, Italy |
3. | Dipart. di Informatica, University of Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy, Italy |
References:
[1] |
M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging, Institute of Physics Publishing, Bristol, 1998.
doi: 10.1887/0750304359. |
[2] |
B. Eicke, A. K. Louis and R. Plato, The instability of some gradient methods for ill-posed problems, Numer. Math., 58 (1990), 129-134.
doi: 10.1007/BF01385614. |
[3] |
P. Favati, G. Lotti, O. Menchi and F. Romani, Generalized Cross-Validation Applied to Conjugate Gradient for Discrete Ill-Posed Problems, Technical Report IIT TR-09/2013. Available from: http://www.iit.cnr.it/sites/default/files/TR-09-2013.pdf |
[4] |
D. A. Girard, A fast ‘Monte-Carlo Cross-Validation' procedure for large least squares problems with noisy data, Numer. Math., 56 (1989), 1-23.
doi: 10.1007/BF01395775. |
[5] |
G. H. Golub, M. Heath and G. Wahba, Generalized cross-validation as a method for choosing a good ridge parameter, Technometrics, 21 (1979), 215-223.
doi: 10.1080/00401706.1979.10489751. |
[6] |
M. Hanke, Conjugate Gradient Type Methods for Ill-Posed Problems, Pitman Research Notes in Mathematics, Longman, Harlow, 1995. |
[7] |
P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems, SIAM Monographs on Mathematical Modeling and Computation, Philadelphia, 1998.
doi: 10.1137/1.9780898719697. |
[8] |
P. C. Hansen, Regularization tools, Numer. Algo., 46 (2007), 189-194.
doi: 10.1007/s11075-007-9136-9. |
[9] |
B. Jin, Y. Zhao and J. Zou, Iterative parameter choice by discrepancy principle, IMA J. Numer. Anal., 32 (2012), 1714-1732.
doi: 10.1093/imanum/drr051. |
[10] |
K. Kunisch and J. Zou, Iterative choices of regularization parameters in linear inverse problems, Inverse Problems, 14 (1998), 1247-1264.
doi: 10.1088/0266-5611/14/5/010. |
[11] |
R. Plato, Optimal algorithms for linear ill-posed problems yield regularization methods, Num. Funct. Anal. and Optimiz., 11 (1990), 111-118.
doi: 10.1080/01630569008816364. |
[12] |
R. J. Santos and A. R. De Pierro, The effect of the nonlinearity on GCV applied to Conjugate Gradients in computerized tomography, Comput. Appl. Math., 25 (2006), 111-128.
doi: 10.1590/S0101-82052006000100006. |
[13] |
C. Vogel, Computational Methods for Inverse Problems, SIAM Frontier in Applied Mathematics, Philadelphia, 2002.
doi: 10.1137/1.9780898717570. |
[14] |
G. Wahba, Practical approximate solutions to linear operator equations when the data are noisy, SIAM J. Numer. Anal., 14 (1977), 651-667.
doi: 10.1137/0714044. |
[15] |
Y. Wang, A restarted conjugate gradient method for ill-posed problems, Acta Mathematicae Applicatae Sinica, English Series, 19 (2003), 31-40.
doi: 10.1007/s10255-003-0078-2. |
[16] |
J. Xie and J. Zou, An improved model function method for choosing regularization parameters in linear inverse problems, Inverse Problems, 18 (2002), 631-643.
doi: 10.1088/0266-5611/18/3/307. |
[17] |
F. Zama and E. Loli Piccolomini, A descent method for regularization of ill-posed problems, Optimization Methods and Software, 20 (2005), 615-628.
doi: 10.1080/10556780500140409. |
show all references
References:
[1] |
M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging, Institute of Physics Publishing, Bristol, 1998.
doi: 10.1887/0750304359. |
[2] |
B. Eicke, A. K. Louis and R. Plato, The instability of some gradient methods for ill-posed problems, Numer. Math., 58 (1990), 129-134.
doi: 10.1007/BF01385614. |
[3] |
P. Favati, G. Lotti, O. Menchi and F. Romani, Generalized Cross-Validation Applied to Conjugate Gradient for Discrete Ill-Posed Problems, Technical Report IIT TR-09/2013. Available from: http://www.iit.cnr.it/sites/default/files/TR-09-2013.pdf |
[4] |
D. A. Girard, A fast ‘Monte-Carlo Cross-Validation' procedure for large least squares problems with noisy data, Numer. Math., 56 (1989), 1-23.
doi: 10.1007/BF01395775. |
[5] |
G. H. Golub, M. Heath and G. Wahba, Generalized cross-validation as a method for choosing a good ridge parameter, Technometrics, 21 (1979), 215-223.
doi: 10.1080/00401706.1979.10489751. |
[6] |
M. Hanke, Conjugate Gradient Type Methods for Ill-Posed Problems, Pitman Research Notes in Mathematics, Longman, Harlow, 1995. |
[7] |
P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems, SIAM Monographs on Mathematical Modeling and Computation, Philadelphia, 1998.
doi: 10.1137/1.9780898719697. |
[8] |
P. C. Hansen, Regularization tools, Numer. Algo., 46 (2007), 189-194.
doi: 10.1007/s11075-007-9136-9. |
[9] |
B. Jin, Y. Zhao and J. Zou, Iterative parameter choice by discrepancy principle, IMA J. Numer. Anal., 32 (2012), 1714-1732.
doi: 10.1093/imanum/drr051. |
[10] |
K. Kunisch and J. Zou, Iterative choices of regularization parameters in linear inverse problems, Inverse Problems, 14 (1998), 1247-1264.
doi: 10.1088/0266-5611/14/5/010. |
[11] |
R. Plato, Optimal algorithms for linear ill-posed problems yield regularization methods, Num. Funct. Anal. and Optimiz., 11 (1990), 111-118.
doi: 10.1080/01630569008816364. |
[12] |
R. J. Santos and A. R. De Pierro, The effect of the nonlinearity on GCV applied to Conjugate Gradients in computerized tomography, Comput. Appl. Math., 25 (2006), 111-128.
doi: 10.1590/S0101-82052006000100006. |
[13] |
C. Vogel, Computational Methods for Inverse Problems, SIAM Frontier in Applied Mathematics, Philadelphia, 2002.
doi: 10.1137/1.9780898717570. |
[14] |
G. Wahba, Practical approximate solutions to linear operator equations when the data are noisy, SIAM J. Numer. Anal., 14 (1977), 651-667.
doi: 10.1137/0714044. |
[15] |
Y. Wang, A restarted conjugate gradient method for ill-posed problems, Acta Mathematicae Applicatae Sinica, English Series, 19 (2003), 31-40.
doi: 10.1007/s10255-003-0078-2. |
[16] |
J. Xie and J. Zou, An improved model function method for choosing regularization parameters in linear inverse problems, Inverse Problems, 18 (2002), 631-643.
doi: 10.1088/0266-5611/18/3/307. |
[17] |
F. Zama and E. Loli Piccolomini, A descent method for regularization of ill-posed problems, Optimization Methods and Software, 20 (2005), 615-628.
doi: 10.1080/10556780500140409. |
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