Edit Profile (opens in new tab) Hansen, Per Christian Co-Author Distance Author ID: hansen.per-christian Published as: Hansen, Per Christian; Hansen, P. C.; Hansen, Per C.; Christian Hansen, Per more...less External Links: MGP Documents Indexed: 122 Publications since 1985, including 4 Books and 2 Additional arXiv Preprints 2 Contributions as Editor Co-Authors: 92 Co-Authors with 100 Joint Publications 1,806 Co-Co-Authors all top 5 Co-Authors 24 single-authored 12 Dong, Yiqiu 9 Fierro, Ricardo D. 7 Chan, Tony Fan-Cheong 6 Elfving, Tommy 6 Jørgensen, Jakob Sauer 6 O’Leary, Dianne P. 6 Zlatev, Zahari 5 Jensen, Søren Holdt 5 Nikazad, Touraj 4 Afkham, Babak Maboudi 4 Brogaard Riis, Nicolai André 4 Jensen, Toke Koldborg 4 Kilmer, Misha Elena 4 Ostromsky, Tzvetan 4 Riis, Nicolai A. B. 4 Uribe, Felipe 4 Yalamov, Plamen Y. 3 Andersen, Martin S. 3 Golub, Gene Howard 3 Hochstenbach, Michiel E. 3 Nagy, James Gerard 3 Sørensen, Hans Henrik B. 2 Alghamdi, Amal Mohammed A 2 Bardsley, Johnathan M. 2 Bischof, Christian H. 2 Christensen, Silja L. 2 Christiansen, Søren 2 Eldén, Lars 2 Hanke-Bourgeois, Martin 2 Jensen, Tobias Lindstrøm 2 Mosegaard, Klaus 2 Petersen, Dan Erik 2 Poulsen, Henning Friis 2 Skelboe, Stig 2 Soltani, Sara 2 Stokbro, Kurt 2 van Lith, Bart S. 2 Waśniewski, Jerzy 1 Abe, Kuniyoshi 1 Batenburg, Kees Joost 1 Bendtsen, Claus 1 Borries, Oscar 1 Calvetti, Daniela 1 Chen, Donghui 1 Dahl, Anders Bjorholm 1 Dahl, Joachim 1 Darve, Eric 1 Delbary, Fabrice 1 Dond, Yiqiu 1 Español, Malena I. 1 Frøsig, J. 1 Gallivan, Kyle A. 1 Garde, Henrik 1 Gazzola, Silvia 1 Gesmar, Henrik 1 Hansen, Peter Søren Kirk 1 Hansen, S. D. 1 Hayami, Ken 1 Jacobson, Bo H. 1 Jørgensen, Erik 1 Jørgensen, Jakob H. 1 Kaae, P. 1 Kazantsev, Ivan G. 1 Keable, C. 1 Kjeldsen, R. H. 1 Kjer, Hans Martin 1 Knudsen, Kim M. 1 Li, Song 1 Lionheart, William Robert Breckon 1 Madsen, Kaj 1 Meincke, Peter 1 Morikuni, Keiichi 1 Nielsen, Hans Bruun 1 Olsen, Ulrik L. 1 Owczarz, Wojciech 1 Pan, Xiaochuan 1 Pinar, Mustafa Çelebi 1 Quinto, Eric Todd 1 Rasmussen, Peter Winkel 1 Reichel, Lothar 1 Rodriguez, Giuseppe 1 Romanov, Mikhail 1 Sameh, Ahmed H. 1 Saunders, Michael A. 1 Saxild-Hansen, Maria 1 Scherer, Godela 1 Sekii, Takashi 1 Shibahashi, Hiromoto 1 Sidky, Emil Y. 1 Sijbers, Jan 1 Sørensen, Henning Osholm 1 Sorensen, John Aa. 1 Sükösd, Zsuzsanna 1 Tigkos, Konstantinos 1 van Duin, Arno C. N. 1 Zha, Hongyuan all top 5 Serials 15 Numerical Algorithms 14 BIT 12 SIAM Journal on Scientific Computing 9 Inverse Problems 8 Journal of Computational and Applied Mathematics 6 SIAM Journal on Matrix Analysis and Applications 5 SIAM Journal on Scientific and Statistical Computing 5 ETNA. Electronic Transactions on Numerical Analysis 3 Numerical Linear Algebra with Applications 3 Fundamentals of Algorithms 2 Journal of Computational Physics 2 ACM Transactions on Mathematical Software 2 Computing 2 Parallel Computing 2 IEEE Transactions on Signal Processing 2 SIAM/ASA Journal on Uncertainty Quantification 1 Applicable Analysis 1 Computers & Mathematics with Applications 1 Mathematics of Computation 1 Control and Cybernetics 1 Normat 1 Numerische Mathematik 1 Surveys on Mathematics for Industry 1 Linear Algebra and its Applications 1 SIAM Review 1 Journal of Mathematical Imaging and Vision 1 IEEE Transactions on Antennas and Propagation 1 Inverse Problems in Science and Engineering 1 Lecture Notes in Earth Sciences 1 SIAM Monographs on Mathematical Modeling and Computation 1 Inverse Problems and Imaging 1 EURASIP Journal on Advances in Signal Processing 1 SIAM Journal on Imaging Sciences all top 5 Fields 108 Numerical analysis (65-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 13 Integral equations (45-XX) 13 Information and communication theory, circuits (94-XX) 12 Biology and other natural sciences (92-XX) 10 Computer science (68-XX) 9 Statistics (62-XX) 6 Integral transforms, operational calculus (44-XX) 5 Operator theory (47-XX) 4 Partial differential equations (35-XX) 4 Operations research, mathematical programming (90-XX) 3 Probability theory and stochastic processes (60-XX) 3 Optics, electromagnetic theory (78-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of deformable solids (74-XX) 1 Quantum theory (81-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 105 Publications have been cited 3,455 times in 2,019 Documents Cited by ▼ Year ▼ Analysis of discrete ill-posed problems by means of the L-curve. Zbl 0770.65026 Hansen, Per Christian 391 1992 Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems. Zbl 0789.65029 Hansen, Per Christian 314 1994 The use of the \(L\)-curve in the regularization of discrete ill-posed problems. Zbl 0789.65030 Hansen, Per Christian; O’Leary, Dianne Prost 294 1993 Deblurring images. Matrices, spectra, and filtering. Zbl 1112.68127 Hansen, Per Christian; Nagy, James G.; O’Leary, Dianne P. 275 2006 Rank-deficient and discrete ill-posed problems. Numerical aspects of linear inversion. Zbl 0890.65037 Hansen, Per Christian 234 1997 Regularization tools version \(4.0\) for matlab \(7.3\). Zbl 1128.65029 Hansen, Per Christian 219 2007 Discrete inverse problems. Insight and algorithms. Zbl 1197.65054 Hansen, Per Christian 177 2010 Regularization methods for large-scale problems. Zbl 0805.65058 Hanke, Martin; Hansen, Per Christian 162 1993 Tikhonov regularization and total least squares. Zbl 0945.65042 Golub, Gene H.; Hansen, Per Christian; O’Leary, Dianne P. 100 1999 The truncated SVD as a method for regularization. Zbl 0633.65041 Hansen, Per Christian 90 1987 AIR tools – a MATLAB package of algebraic iterative reconstruction methods. Zbl 1241.65042 Hansen, Per Christian; Saxild-Hansen, Maria 68 2012 IR tools: a MATLAB package of iterative regularization methods and large-scale test problems. Zbl 1415.65003 Gazzola, Silvia; Hansen, Per Christian; Nagy, James G. 62 2019 AIR tools II: algebraic iterative reconstruction methods, improved implementation. Zbl 1397.65007 Hansen, Per Christian; Jørgensen, Jakob Sauer 60 2018 Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank. Zbl 0699.65029 Hansen, Per Christian 53 1990 A projection-based approach to general-form Tikhonov regularization. Zbl 1140.65030 Kilmer, Misha E.; Hansen, Per Christian; Español, Malena I. 48 2007 Numerical tools for analysis and solution of Fredholm integral equations of the first kind. Zbl 0782.65153 Hansen, Per Christian 41 1992 Some applications of the rank revealing QR factorization. Zbl 0756.65032 Chan, Tony F.; Hansen, Per Christian 39 1992 The discrete Picard condition for discrete ill-posed problems. Zbl 0723.65147 Hansen, Per Christian 37 1990 Iterative regularization with minimum-residual methods. Zbl 1113.65037 Jensen, T. K.; Hansen, P. C. 32 2007 An adaptive pruning algorithm for the discrete L-curve criterion. Zbl 1101.65044 Hansen, Per Christian; Jensen, Toke Koldborg; Rodriguez, Giuseppe 32 2007 The effective condition number applied to error analysis of certain boundary collocation methods. Zbl 0834.65033 Christiansen, Søren; Hansen, Per Christian 31 1994 Regularization, GSVD and truncated GSVD. Zbl 0682.65021 Hansen, Per Christian 30 1989 Regularization by truncated total least squares. Zbl 0891.65040 Fierro, R. D.; Golub, G. H.; Hansen, P. C.; O’Leary, D. P. 30 1997 Deconvolution and regularization with Toeplitz matrices. Zbl 1002.65145 Hansen, Per Christian 30 2002 \(L\)-curve curvature bounds via Lanczos bidiagonalization. Zbl 1029.65041 Calvetti, D.; Hansen, P. C.; Reichel, L. 30 2002 Exploiting residual information in the parameter choice for discrete ill-posed problems. Zbl 1091.65038 Hansen, P. C.; Kilmer, M. E.; Kjeldsen, R. H. 27 2006 Semi-convergence properties of Kaczmarz’s method. Zbl 1296.65054 Elfving, Tommy; Hansen, Per Christian; Nikazad, Touraj 26 2014 Semi-convergence and relaxation parameters for a class of SIRT algorithms. Zbl 1205.65148 Elfving, Tommy; Nikazad, Touraj; Hansen, Per Christian 23 2010 The modified truncated SVD method for regularization in general form. Zbl 0760.65044 Hansen, Per Christian; Sekii, Takashi; Shibahashi, Hiromoto 21 1992 Computation of the singular value expansion. Zbl 0631.65133 Hansen, P. C. 20 1988 A look-ahead Levinson algorithm for general Toeplitz systems. Zbl 0756.65044 Chan, Tony F.; Hansen, Per C. 20 1992 Least squares data fitting with applications. Zbl 1270.65008 Hansen, Per Christian; Pereyra, Víctor; Scherer, Godela 20 2013 Smoothing-norm preconditioning for regularizing minimum-residual methods. Zbl 1154.65028 Hansen, Per Christian; Jensen, Toke Koldborg 19 2006 Noise propagation in regularizing iterations for image deblurring. Zbl 1171.65032 Hansen, Per Christian; Jensen, Toke Koldborg 19 2008 Semiconvergence and relaxation parameters for projected SIRT algorithms. Zbl 1254.65044 Elfving, Tommy; Hansen, Per Christian; Nikazad, Touraj 19 2012 A tensor-based dictionary learning approach to tomographic image reconstruction. Zbl 1355.65036 Soltani, Sara; Kilmer, Misha E.; Hansen, Per Christian 16 2016 Algorithms and software for total variation image reconstruction via first-order methods. Zbl 1181.94009 Dahl, Joachim; Hansen, Per Christian; Jensen, Søren Holdt; Jensen, Tobias Lindstrøm 15 2010 A look-ahead Levinson algorithm for indefinite Toeplitz systems. Zbl 0752.65020 Chan, Tony F.; Hansen, Per Christian 15 1992 Implementation of an optimal first-order method for strongly convex total variation regularization. Zbl 1256.65063 Jensen, T. L.; Jørgensen, J. H.; Hansen, P. C.; Jensen, S. H. 15 2012 Subspace preconditioned LSQR for discrete ill-posed problems. Zbl 1046.65030 Jacobsen, M.; Hansen, P. C.; Saunders, M. A. 14 2003 Computing truncated singular value decomposition least squares solutions by rank revealing QR-factorizations. Zbl 0699.65030 Chan, Tony F.; Hansen, Per Christian 12 1990 Electrical impedance tomography: 3D reconstructions using scattering transforms. Zbl 1238.35183 Delbary, Fabrice; Hansen, Per Christian; Knudsen, Kim 11 2012 Unmatched projector/backprojector pairs: perturbation and convergence analysis. Zbl 1383.65035 Elfving, Tommy; Hansen, Per Christian 11 2018 Low-rank revealing \(UTV\) decompositions. Zbl 0887.65043 Fierro, Ricardo D.; Hansen, Per Christian 11 1997 UTV tools: Matlab templates for rank-revealing UTV decompositions. Zbl 0936.65054 Fierro, Ricardo D.; Hansen, Per Christian; Hansen, Peter Søren Kirk 10 1999 Limited-data x-ray CT for underwater pipeline inspection. Zbl 06858476 Riis, N. A. B.; Frøsig, J.; Dong, Y.; Hansen, P. C. 10 2018 Structure-preserving and rank-revealing \(QR\)-factorizations. Zbl 0739.65031 Bischof, Christian H.; Hansen, Per Christian 10 1991 Multicore performance of block algebraic iterative reconstruction methods. Zbl 1307.65037 Sørensen, Hans Henrik B.; Hansen, Per Christian 10 2014 Oblique projections and standard-form transformations for discrete inverse problems. Zbl 1289.65097 Hansen, Per Christian 9 2013 Generalized row-action methods for tomographic imaging. Zbl 1302.65285 Andersen, Martin S.; Hansen, Per Christian 8 2014 Fixing nonconvergence of algebraic iterative reconstruction with an unmatched backprojector. Zbl 1420.65031 Dong, Yiqiu; Hansen, Per Christian; Hochstenbach, Michiel E.; Brogaard Riis, Nicolai André 8 2019 Block tridiagonal matrix inversion and fast transmission calculations. Zbl 1135.65318 Petersen, Dan Erik; Sørensen, Hans Henrik B.; Hansen, Per Christian; Skelboe, Stig; Stokbro, Kurt 7 2008 Test matrices for regularization methods. Zbl 0820.65020 Hansen, Per Christian 7 1995 Convergence analysis for column-action methods in image reconstruction. Zbl 1366.65116 Elfving, Tommy; Hansen, Per Christian; Nikazad, Touraj 7 2017 Computed tomography. Algorithms, insight, and just enough theory. With contributions by Martin S. Andersen, K. Joost Batenburg, Yiqiu Dond, Eric Todd Quinto and Jan Sijbers. Zbl 1482.94006 7 2021 Computing symmetric rank-revealing decompositions via triangular factorization. Zbl 1017.65039 Hansen, Per Christian; Yalamov, Plamen Y. 6 2001 A hybrid method for the parallel computation of Green’s functions. Zbl 1280.82010 Petersen, Dan Erik; Li, Song; Stokbro, Kurt; Sørensen, Hans Henrik B.; Hansen, Per Christian; Skelboe, Stig; Darve, Eric 6 2009 Perturbation bounds for discrete Tikhonov regularisation. Zbl 0695.65022 Hansen, Per Christian 6 1989 Rotational image deblurring with sparse matrices. Zbl 1302.65055 Hansen, Per Christian; Nagy, James G.; Tigkos, Konstantinos 6 2014 R\(^3\)GMRES: including prior information in GMRES-type methods for discrete inverse problems. Zbl 1307.65049 Dong, Yiqiu; Garde, Henrik; Hansen, Per Christian 6 2014 Regularization Tools Version 3. 0 for Matlab 5. 2. Zbl 0933.65065 Hansen, Per Christian 5 1999 Accuracy of TSVD solutions computed from rank-revealing decompositions. Zbl 0834.65026 Fierro, Ricardo D.; Hansen, Per Christian 5 1995 Reconstruction of single-grain orientation distribution functions for crystalline materials. Zbl 1175.82066 Hansen, Per Christian; Sørensen, Henning Osholm; Sükösd, Zsuzsanna; Poulsen, Henning Friis 5 2009 A locally optimized reordering algorithm and its application to a parallel sparse linear system solver. Zbl 0814.65027 Gallivan, K.; Hansen, P. C.; Ostromsky, Tz.; Zlatev, Z. 5 1995 FORTRAN subroutines for general Toeplitz systems. Zbl 0894.65010 Hansen, Per Christian; Chan, Tony F. 5 1992 Simultaneous tomographic reconstruction and segmentation with class priors. Zbl 1349.92084 Romanov, Mikhail; Dahl, Anders Bjorholm; Dong, Yiqiu; Hansen, Per Christian 5 2016 The 2-norm of random matrices. Zbl 0656.15013 Hansen, Per Christian 4 1988 A spectral geometric model for Compton single scatter in PET based on the single scatter simulation approximation. Zbl 1400.78012 Kazantsev, I. G.; Olsen, U. L.; Poulsen, H. F.; Hansen, P. C. 4 2018 Subspace-based noise reduction for speech signals via diagonal and triangular matrix decompositions: survey and analysis. Zbl 1168.94415 Hansen, Per Christian; Jensen, Søren Holdt 4 2007 An SVD analysis of linear algebraic equations derived from first kind integral equations. Zbl 0577.65116 Hansen, Per Christian; Christiansen, Søren 4 1985 Uncertainty quantification of inclusion boundaries in the context of X-ray tomography. Zbl 1524.65022 Afkham, Babak Maboudi; Dong, Yiqiu; Hansen, Per Christian 4 2023 Hybrid enriched bidiagonalization for discrete ill-posed problems. Zbl 1449.65093 Hansen, Per Christian; Dong, Yiqiu; Abe, Kuniyoshi 4 2019 A coarse-grained parallel QR-factorization algorithm for sparse least squares problems. Zbl 0909.68071 Ostromsky, Tz.; Hansen, P. C.; Zlatev, Z. 3 1998 Minimization of linear functionals defined on solutions of large-scale discrete ill-posed problems. Zbl 1084.65035 Eldén, L.; Hansen, P. C.; Rojas, M. 3 2005 UTV Expansin pack: Special-purpose rank-revealing algorithms. Zbl 1079.65026 Fierro, Ricardo D.; Hansen, Per Christian 3 2005 Regularization and the general Gauss-Markov linear model. Zbl 0722.65020 Zha, Hongyuan; Hansen, Per Christian 3 1990 A block algorithm for computing rank-revealing QR factorizations. Zbl 0761.65029 Bischof, Christian H.; Hansen, Per Christian 3 1992 Fast orthogonal decomposition of rank deficient Toeplitz matrices. Zbl 0779.65027 Hansen, Per Christian; Gesmar, Henrik 3 1993 Empirical average-case relation between undersampling and sparsity in X-ray CT. Zbl 1332.90393 Jørgensen, Jakob S.; Sidky, Emil Y.; Hansen, Per Christian; Pan, Xiaochuan 3 2015 Prewhitening for rank-deficient noise in subspace methods for noise reduction. Zbl 1370.94140 Hansen, Per Christian; Jensen, Søren Holdt 3 2005 User-friendly simultaneous tomographic reconstruction and segmentation with class priors. Zbl 1489.68385 Kjer, Hans Martin; Dong, Yiqiu; Hansen, Per Christian 3 2017 Computed tomography with view angle estimation using uncertainty quantification. Zbl 1503.62009 Brogaard Riis, Nicolai André; Dong, Yiqiu; Hansen, Per Christian 3 2021 MCMC algorithms for computational UQ of nonnegativity constrained linear inverse problems. Zbl 1442.65031 Bardsley, Johnathan M.; Hansen, Per Christian 3 2020 Detection of near-singularity in Cholesky and \(LDL^ T\) factorizations. Zbl 0627.65040 Hansen, Per Christian 2 1987 Rank-deficient prewhitening with quotient SVD and ULV decompositions. Zbl 0901.65026 Hansen, Per Christian 2 1998 Reduction of general broad-band noise in speech by truncated QSVD: Implementation aspects. Zbl 0826.65136 Jensen, S. H.; Hansen, P. C.; Hansen, S. D.; Sørensen, J. A. 2 1995 Piecewise polynomial solutions without a priori break points. Zbl 0906.65056 Hansen, P. C.; Mosegaard, K. 2 1996 Truncated VSV solutions to symmetric rank-deficient problems. Zbl 1018.65054 Fierro, Ricardo D.; Hansen, Per Christian 2 2002 Relations between SVD and GSVD of discrete regularization problems in standard and general form. Zbl 0717.65024 Hansen, Per Christian 2 1990 A twin error gauge for Kaczmarz’s iterations. Zbl 1490.65072 van Lith, Bart S.; Hansen, Per Christian; Hochstenbach, Michiel E. 2 2021 A hybrid Gibbs sampler for edge-preserving tomographic reconstruction with uncertain view angles. Zbl 1502.92005 Uribe, Felipe; Bardsley, Johnathan M.; Dong, Yiqiu; Hansen, Per Christian; Riis, Nicolai A. B. 2 2022 Horseshoe priors for edge-preserving linear Bayesian inversion. Zbl 07695777 Uribe, Felipe; Dong, Yiqiu; Hansen, Per Christian 2 2023 CUQIpy. II: Computational uncertainty quantification for PDE-based inverse problems in Python. Zbl 07813324 Alghamdi, Amal M. A.; Riis, Nicolai A. B.; Afkham, Babak M.; Uribe, Felipe; Christensen, Silja L.; Christian Hansen, Per; Jørgensen, Jakob S. 2 2024 Solution of ill-posed problems by means of truncated SVD. Zbl 0659.65041 Hansen, Per Christian 1 1988 Stabilization by perturbation of a \(4n^{2}\) Toeplitz solver. Zbl 0994.65025 Hansen, Per Christian; Yalamov, Plamen Y. 1 2000 Improving the numerical stability and the performance of a parallel sparse solver. Zbl 0835.65051 van Duin, A. C. N.; Hansen, P. C.; Ostromsky, Tz.; Wijshoff, H.; Zlatev, Z. 1 1995 Symmetric rank revealing factorizations. Zbl 0980.65046 Hansen, P. C.; Yalamov, P. Y. 1 1999 Rank-revealing decompositions of symmetric Toeplitz matrices. Zbl 1003.65019 Hansen, Per Christian; Yalamov, Plamen 1 2001 The Backus-Gilbert method: SVD analysis and fast implementation. Zbl 0815.65137 Hansen, Per Christian 1 1994 Experience with regularizing CG iterations. Zbl 0811.65035 Hansen, Per Christian 1 1994 CUQIpy. II: Computational uncertainty quantification for PDE-based inverse problems in Python. Zbl 07813324 Alghamdi, Amal M. A.; Riis, Nicolai A. B.; Afkham, Babak M.; Uribe, Felipe; Christensen, Silja L.; Christian Hansen, Per; Jørgensen, Jakob S. 2 2024 Uncertainty quantification of inclusion boundaries in the context of X-ray tomography. Zbl 1524.65022 Afkham, Babak Maboudi; Dong, Yiqiu; Hansen, Per Christian 4 2023 Horseshoe priors for edge-preserving linear Bayesian inversion. Zbl 07695777 Uribe, Felipe; Dong, Yiqiu; Hansen, Per Christian 2 2023 A hybrid Gibbs sampler for edge-preserving tomographic reconstruction with uncertain view angles. Zbl 1502.92005 Uribe, Felipe; Bardsley, Johnathan M.; Dong, Yiqiu; Hansen, Per Christian; Riis, Nicolai A. B. 2 2022 GMRES methods for tomographic reconstruction with an unmatched back projector. Zbl 1489.65060 Hansen, Per Christian; Hayami, Ken; Morikuni, Keiichi 1 2022 Computed tomography. Algorithms, insight, and just enough theory. With contributions by Martin S. Andersen, K. Joost Batenburg, Yiqiu Dond, Eric Todd Quinto and Jan Sijbers. Zbl 1482.94006 7 2021 Computed tomography with view angle estimation using uncertainty quantification. Zbl 1503.62009 Brogaard Riis, Nicolai André; Dong, Yiqiu; Hansen, Per Christian 3 2021 A twin error gauge for Kaczmarz’s iterations. Zbl 1490.65072 van Lith, Bart S.; Hansen, Per Christian; Hochstenbach, Michiel E. 2 2021 Computed tomography reconstruction with uncertain view angles by iteratively updated model discrepancy. Zbl 1524.94029 Riis, Nicolai André Brogaard; Dong, Yiqiu; Hansen, Per Christian 1 2021 MCMC algorithms for computational UQ of nonnegativity constrained linear inverse problems. Zbl 1442.65031 Bardsley, Johnathan M.; Hansen, Per Christian 3 2020 IR tools: a MATLAB package of iterative regularization methods and large-scale test problems. Zbl 1415.65003 Gazzola, Silvia; Hansen, Per Christian; Nagy, James G. 62 2019 Fixing nonconvergence of algebraic iterative reconstruction with an unmatched backprojector. Zbl 1420.65031 Dong, Yiqiu; Hansen, Per Christian; Hochstenbach, Michiel E.; Brogaard Riis, Nicolai André 8 2019 Hybrid enriched bidiagonalization for discrete ill-posed problems. Zbl 1449.65093 Hansen, Per Christian; Dong, Yiqiu; Abe, Kuniyoshi 4 2019 AIR tools II: algebraic iterative reconstruction methods, improved implementation. Zbl 1397.65007 Hansen, Per Christian; Jørgensen, Jakob Sauer 60 2018 Unmatched projector/backprojector pairs: perturbation and convergence analysis. Zbl 1383.65035 Elfving, Tommy; Hansen, Per Christian 11 2018 Limited-data x-ray CT for underwater pipeline inspection. Zbl 06858476 Riis, N. A. B.; Frøsig, J.; Dong, Y.; Hansen, P. C. 10 2018 A spectral geometric model for Compton single scatter in PET based on the single scatter simulation approximation. Zbl 1400.78012 Kazantsev, I. G.; Olsen, U. L.; Poulsen, H. F.; Hansen, P. C. 4 2018 Convergence analysis for column-action methods in image reconstruction. Zbl 1366.65116 Elfving, Tommy; Hansen, Per Christian; Nikazad, Touraj 7 2017 User-friendly simultaneous tomographic reconstruction and segmentation with class priors. Zbl 1489.68385 Kjer, Hans Martin; Dong, Yiqiu; Hansen, Per Christian 3 2017 Tomographic image reconstruction using training images. Zbl 1353.65017 Soltani, Sara; Andersen, Martin S.; Hansen, Per Christian 1 2017 A tensor-based dictionary learning approach to tomographic image reconstruction. Zbl 1355.65036 Soltani, Sara; Kilmer, Misha E.; Hansen, Per Christian 16 2016 Simultaneous tomographic reconstruction and segmentation with class priors. Zbl 1349.92084 Romanov, Mikhail; Dahl, Anders Bjorholm; Dong, Yiqiu; Hansen, Per Christian 5 2016 Empirical average-case relation between undersampling and sparsity in X-ray CT. Zbl 1332.90393 Jørgensen, Jakob S.; Sidky, Emil Y.; Hansen, Per Christian; Pan, Xiaochuan 3 2015 Semi-convergence properties of Kaczmarz’s method. Zbl 1296.65054 Elfving, Tommy; Hansen, Per Christian; Nikazad, Touraj 26 2014 Multicore performance of block algebraic iterative reconstruction methods. Zbl 1307.65037 Sørensen, Hans Henrik B.; Hansen, Per Christian 10 2014 Generalized row-action methods for tomographic imaging. Zbl 1302.65285 Andersen, Martin S.; Hansen, Per Christian 8 2014 Rotational image deblurring with sparse matrices. Zbl 1302.65055 Hansen, Per Christian; Nagy, James G.; Tigkos, Konstantinos 6 2014 R\(^3\)GMRES: including prior information in GMRES-type methods for discrete inverse problems. Zbl 1307.65049 Dong, Yiqiu; Garde, Henrik; Hansen, Per Christian 6 2014 Multilevel fast multipole method for higher order discretizations. Zbl 1371.78309 Borries, Oscar; Meincke, Peter; Jørgensen, Erik; Hansen, Per Christian 1 2014 “Plug-and-play” edge-preserving regularization. Zbl 1312.65064 Chen, Donghui; Kilmer, Misha E.; Hansen, Per Christian 1 2014 Least squares data fitting with applications. Zbl 1270.65008 Hansen, Per Christian; Pereyra, Víctor; Scherer, Godela 20 2013 Oblique projections and standard-form transformations for discrete inverse problems. Zbl 1289.65097 Hansen, Per Christian 9 2013 AIR tools – a MATLAB package of algebraic iterative reconstruction methods. Zbl 1241.65042 Hansen, Per Christian; Saxild-Hansen, Maria 68 2012 Semiconvergence and relaxation parameters for projected SIRT algorithms. Zbl 1254.65044 Elfving, Tommy; Hansen, Per Christian; Nikazad, Touraj 19 2012 Implementation of an optimal first-order method for strongly convex total variation regularization. Zbl 1256.65063 Jensen, T. L.; Jørgensen, J. H.; Hansen, P. C.; Jensen, S. H. 15 2012 Electrical impedance tomography: 3D reconstructions using scattering transforms. Zbl 1238.35183 Delbary, Fabrice; Hansen, Per Christian; Knudsen, Kim 11 2012 Discrete inverse problems. Insight and algorithms. Zbl 1197.65054 Hansen, Per Christian 177 2010 Semi-convergence and relaxation parameters for a class of SIRT algorithms. Zbl 1205.65148 Elfving, Tommy; Nikazad, Touraj; Hansen, Per Christian 23 2010 Algorithms and software for total variation image reconstruction via first-order methods. Zbl 1181.94009 Dahl, Joachim; Hansen, Per Christian; Jensen, Søren Holdt; Jensen, Tobias Lindstrøm 15 2010 A hybrid method for the parallel computation of Green’s functions. Zbl 1280.82010 Petersen, Dan Erik; Li, Song; Stokbro, Kurt; Sørensen, Hans Henrik B.; Hansen, Per Christian; Skelboe, Stig; Darve, Eric 6 2009 Reconstruction of single-grain orientation distribution functions for crystalline materials. Zbl 1175.82066 Hansen, Per Christian; Sørensen, Henning Osholm; Sükösd, Zsuzsanna; Poulsen, Henning Friis 5 2009 Noise propagation in regularizing iterations for image deblurring. Zbl 1171.65032 Hansen, Per Christian; Jensen, Toke Koldborg 19 2008 Block tridiagonal matrix inversion and fast transmission calculations. Zbl 1135.65318 Petersen, Dan Erik; Sørensen, Hans Henrik B.; Hansen, Per Christian; Skelboe, Stig; Stokbro, Kurt 7 2008 Regularization tools version \(4.0\) for matlab \(7.3\). Zbl 1128.65029 Hansen, Per Christian 219 2007 A projection-based approach to general-form Tikhonov regularization. Zbl 1140.65030 Kilmer, Misha E.; Hansen, Per Christian; Español, Malena I. 48 2007 Iterative regularization with minimum-residual methods. Zbl 1113.65037 Jensen, T. K.; Hansen, P. C. 32 2007 An adaptive pruning algorithm for the discrete L-curve criterion. Zbl 1101.65044 Hansen, Per Christian; Jensen, Toke Koldborg; Rodriguez, Giuseppe 32 2007 Subspace-based noise reduction for speech signals via diagonal and triangular matrix decompositions: survey and analysis. Zbl 1168.94415 Hansen, Per Christian; Jensen, Søren Holdt 4 2007 Deblurring images. Matrices, spectra, and filtering. Zbl 1112.68127 Hansen, Per Christian; Nagy, James G.; O’Leary, Dianne P. 275 2006 Exploiting residual information in the parameter choice for discrete ill-posed problems. Zbl 1091.65038 Hansen, P. C.; Kilmer, M. E.; Kjeldsen, R. H. 27 2006 Smoothing-norm preconditioning for regularizing minimum-residual methods. Zbl 1154.65028 Hansen, Per Christian; Jensen, Toke Koldborg 19 2006 Minimization of linear functionals defined on solutions of large-scale discrete ill-posed problems. Zbl 1084.65035 Eldén, L.; Hansen, P. C.; Rojas, M. 3 2005 UTV Expansin pack: Special-purpose rank-revealing algorithms. Zbl 1079.65026 Fierro, Ricardo D.; Hansen, Per Christian 3 2005 Prewhitening for rank-deficient noise in subspace methods for noise reduction. Zbl 1370.94140 Hansen, Per Christian; Jensen, Søren Holdt 3 2005 Subspace preconditioned LSQR for discrete ill-posed problems. Zbl 1046.65030 Jacobsen, M.; Hansen, P. C.; Saunders, M. A. 14 2003 Deconvolution and regularization with Toeplitz matrices. Zbl 1002.65145 Hansen, Per Christian 30 2002 \(L\)-curve curvature bounds via Lanczos bidiagonalization. Zbl 1029.65041 Calvetti, D.; Hansen, P. C.; Reichel, L. 30 2002 Truncated VSV solutions to symmetric rank-deficient problems. Zbl 1018.65054 Fierro, Ricardo D.; Hansen, Per Christian 2 2002 Computing symmetric rank-revealing decompositions via triangular factorization. Zbl 1017.65039 Hansen, Per Christian; Yalamov, Plamen Y. 6 2001 Rank-revealing decompositions of symmetric Toeplitz matrices. Zbl 1003.65019 Hansen, Per Christian; Yalamov, Plamen 1 2001 Stabilization by perturbation of a \(4n^{2}\) Toeplitz solver. Zbl 0994.65025 Hansen, Per Christian; Yalamov, Plamen Y. 1 2000 Tikhonov regularization and total least squares. Zbl 0945.65042 Golub, Gene H.; Hansen, Per Christian; O’Leary, Dianne P. 100 1999 UTV tools: Matlab templates for rank-revealing UTV decompositions. Zbl 0936.65054 Fierro, Ricardo D.; Hansen, Per Christian; Hansen, Peter Søren Kirk 10 1999 Regularization Tools Version 3. 0 for Matlab 5. 2. Zbl 0933.65065 Hansen, Per Christian 5 1999 Symmetric rank revealing factorizations. Zbl 0980.65046 Hansen, P. C.; Yalamov, P. Y. 1 1999 A coarse-grained parallel QR-factorization algorithm for sparse least squares problems. Zbl 0909.68071 Ostromsky, Tz.; Hansen, P. C.; Zlatev, Z. 3 1998 Rank-deficient prewhitening with quotient SVD and ULV decompositions. Zbl 0901.65026 Hansen, Per Christian 2 1998 Rank-deficient and discrete ill-posed problems. Numerical aspects of linear inversion. Zbl 0890.65037 Hansen, Per Christian 234 1997 Regularization by truncated total least squares. Zbl 0891.65040 Fierro, R. D.; Golub, G. H.; Hansen, P. C.; O’Leary, D. P. 30 1997 Low-rank revealing \(UTV\) decompositions. Zbl 0887.65043 Fierro, Ricardo D.; Hansen, Per Christian 11 1997 Piecewise polynomial solutions without a priori break points. Zbl 0906.65056 Hansen, P. C.; Mosegaard, K. 2 1996 Test matrices for regularization methods. Zbl 0820.65020 Hansen, Per Christian 7 1995 Accuracy of TSVD solutions computed from rank-revealing decompositions. Zbl 0834.65026 Fierro, Ricardo D.; Hansen, Per Christian 5 1995 A locally optimized reordering algorithm and its application to a parallel sparse linear system solver. Zbl 0814.65027 Gallivan, K.; Hansen, P. C.; Ostromsky, Tz.; Zlatev, Z. 5 1995 Reduction of general broad-band noise in speech by truncated QSVD: Implementation aspects. Zbl 0826.65136 Jensen, S. H.; Hansen, P. C.; Hansen, S. D.; Sørensen, J. A. 2 1995 Improving the numerical stability and the performance of a parallel sparse solver. Zbl 0835.65051 van Duin, A. C. N.; Hansen, P. C.; Ostromsky, Tz.; Wijshoff, H.; Zlatev, Z. 1 1995 Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems. Zbl 0789.65029 Hansen, Per Christian 314 1994 The effective condition number applied to error analysis of certain boundary collocation methods. Zbl 0834.65033 Christiansen, Søren; Hansen, Per Christian 31 1994 The Backus-Gilbert method: SVD analysis and fast implementation. Zbl 0815.65137 Hansen, Per Christian 1 1994 Experience with regularizing CG iterations. Zbl 0811.65035 Hansen, Per Christian 1 1994 The use of the \(L\)-curve in the regularization of discrete ill-posed problems. Zbl 0789.65030 Hansen, Per Christian; O’Leary, Dianne Prost 294 1993 Regularization methods for large-scale problems. Zbl 0805.65058 Hanke, Martin; Hansen, Per Christian 162 1993 Fast orthogonal decomposition of rank deficient Toeplitz matrices. Zbl 0779.65027 Hansen, Per Christian; Gesmar, Henrik 3 1993 Analysis of discrete ill-posed problems by means of the L-curve. Zbl 0770.65026 Hansen, Per Christian 391 1992 Numerical tools for analysis and solution of Fredholm integral equations of the first kind. Zbl 0782.65153 Hansen, Per Christian 41 1992 Some applications of the rank revealing QR factorization. Zbl 0756.65032 Chan, Tony F.; Hansen, Per Christian 39 1992 The modified truncated SVD method for regularization in general form. Zbl 0760.65044 Hansen, Per Christian; Sekii, Takashi; Shibahashi, Hiromoto 21 1992 A look-ahead Levinson algorithm for general Toeplitz systems. Zbl 0756.65044 Chan, Tony F.; Hansen, Per C. 20 1992 A look-ahead Levinson algorithm for indefinite Toeplitz systems. Zbl 0752.65020 Chan, Tony F.; Hansen, Per Christian 15 1992 FORTRAN subroutines for general Toeplitz systems. Zbl 0894.65010 Hansen, Per Christian; Chan, Tony F. 5 1992 A block algorithm for computing rank-revealing QR factorizations. Zbl 0761.65029 Bischof, Christian H.; Hansen, Per Christian 3 1992 Structure-preserving and rank-revealing \(QR\)-factorizations. Zbl 0739.65031 Bischof, Christian H.; Hansen, Per Christian 10 1991 Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank. Zbl 0699.65029 Hansen, Per Christian 53 1990 The discrete Picard condition for discrete ill-posed problems. Zbl 0723.65147 Hansen, Per Christian 37 1990 Computing truncated singular value decomposition least squares solutions by rank revealing QR-factorizations. Zbl 0699.65030 Chan, Tony F.; Hansen, Per Christian 12 1990 Regularization and the general Gauss-Markov linear model. Zbl 0722.65020 Zha, Hongyuan; Hansen, Per Christian 3 1990 Relations between SVD and GSVD of discrete regularization problems in standard and general form. Zbl 0717.65024 Hansen, Per Christian 2 1990 Regularization, GSVD and truncated GSVD. Zbl 0682.65021 Hansen, Per Christian 30 1989 Perturbation bounds for discrete Tikhonov regularisation. Zbl 0695.65022 Hansen, Per Christian 6 1989 Computation of the singular value expansion. Zbl 0631.65133 Hansen, P. C. 20 1988 ...and 5 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,112 Authors 110 Reichel, Lothar 45 Hansen, Per Christian 35 Lesnic, Daniel 29 Nagy, James Gerard 28 Wei, Ting 26 Wei, Yimin 25 Jbilou, Khalide 24 Sgallari, Fiorella 21 Buccini, Alessandro 21 Donatelli, Marco 20 Marin, Liviu 19 Gazzola, Silvia 19 Loli Piccolomini, Elena 19 Morigi, Serena 18 Chen, Wen 18 Rodriguez, Giuseppe 18 Sadok, Hassane 17 Chung, Julianne M. 17 Huang, Ting-Zhu 17 Li, Zi-Cai 15 Huang, Hung-Tsai 15 Lv, Xiaoguang 14 Landi, Germana 14 Ng, Michael Kwok-Po 13 Hochstenbach, Michiel E. 13 Jia, Zhongxiao 13 Johansson, B. 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