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. more...less External Links: MGP Documents Indexed: 118 Publications since 1985, including 4 Books 2 Contributions as Editor Co-Authors: 89 Co-Authors with 96 Joint Publications 1,687 Co-Co-Authors all top 5 Co-Authors 24 single-authored 11 Dong, Yiqiu 9 Fierro, Ricardo D. 7 Chan, Tony Fan-Cheong 6 Elfving, Tommy 6 O’Leary, Dianne P. 6 Zlatev, Zahari 5 Jensen, Søren Holdt 5 Nikazad, Touraj 4 Jensen, Toke Koldborg 4 Kilmer, Misha Elena 4 Ostromsky, Tzvetan 4 Yalamov, Plamen Y. 3 Andersen, Martin S. 3 Brogaard Riis, Nicolai André 3 Golub, Gene Howard 3 Hochstenbach, Michiel E. 3 Jørgensen, Jakob Sauer 3 Nagy, James Gerard 3 Sørensen, Hans Henrik B. 2 Bardsley, Johnathan M. 2 Bischof, Christian H. 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 Riis, Nicolai A. B. 2 Skelboe, Stig 2 Soltani, Sara 2 Stokbro, Kurt 2 Uribe, Felipe 2 van Lith, Bart S. 2 Waśniewski, Jerzy 1 Abe, Kuniyoshi 1 Afkham, Babak Maboudi 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, J. 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 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 8 Journal of Computational and Applied Mathematics 7 Inverse Problems 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 107 Numerical analysis (65-XX) 13 Integral equations (45-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 12 Information and communication theory, circuits (94-XX) 11 Biology and other natural sciences (92-XX) 8 Computer science (68-XX) 7 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 101 Publications have been cited 3,291 times in 1,923 Documents Cited by ▼ Year ▼ Analysis of discrete ill-posed problems by means of the L-curve. Zbl 0770.65026Hansen, Per Christian 378 1992 Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems. Zbl 0789.65029Hansen, Per Christian 303 1994 The use of the \(L\)-curve in the regularization of discrete ill-posed problems. Zbl 0789.65030Hansen, Per Christian; O’Leary, Dianne Prost 291 1993 Deblurring images. Matrices, spectra, and filtering. Zbl 1112.68127Hansen, Per Christian; Nagy, James G.; O’Leary, Dianne P. 251 2006 Rank-deficient and discrete ill-posed problems. Numerical aspects of linear inversion. Zbl 0890.65037Hansen, Per Christian 227 1997 Regularization tools version \(4.0\) for matlab \(7.3\). Zbl 1128.65029Hansen, Per Christian 209 2007 Regularization methods for large-scale problems. Zbl 0805.65058Hanke, Martin; Hansen, Per Christian 158 1993 Discrete inverse problems. Insight and algorithms. Zbl 1197.65054Hansen, Per Christian 154 2010 Tikhonov regularization and total least squares. Zbl 0945.65042Golub, Gene H.; Hansen, Per Christian; O’Leary, Dianne P. 96 1999 The truncated SVD as a method for regularization. Zbl 0633.65041Hansen, Per Christian 87 1987 AIR tools – a MATLAB package of algebraic iterative reconstruction methods. Zbl 1241.65042Hansen, Per Christian; Saxild-Hansen, Maria 67 2012 AIR tools II: algebraic iterative reconstruction methods, improved implementation. Zbl 1397.65007Hansen, Per Christian; Jørgensen, Jakob Sauer 56 2018 IR tools: a MATLAB package of iterative regularization methods and large-scale test problems. Zbl 1415.65003Gazzola, Silvia; Hansen, Per Christian; Nagy, James G. 54 2019 Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank. Zbl 0699.65029Hansen, Per Christian 51 1990 A projection-based approach to general-form Tikhonov regularization. Zbl 1140.65030Kilmer, Misha E.; Hansen, Per Christian; Español, Malena I. 45 2007 Numerical tools for analysis and solution of Fredholm integral equations of the first kind. Zbl 0782.65153Hansen, Per Christian 39 1992 Some applications of the rank revealing QR factorization. Zbl 0756.65032Chan, Tony F.; Hansen, Per Christian 38 1992 The discrete Picard condition for discrete ill-posed problems. Zbl 0723.65147Hansen, Per Christian 36 1990 The effective condition number applied to error analysis of certain boundary collocation methods. Zbl 0834.65033Christiansen, Søren; Hansen, Per Christian 31 1994 An adaptive pruning algorithm for the discrete L-curve criterion. Zbl 1101.65044Hansen, Per Christian; Jensen, Toke Koldborg; Rodriguez, Giuseppe 31 2007 Regularization, GSVD and truncated GSVD. Zbl 0682.65021Hansen, Per Christian 29 1989 \(L\)-curve curvature bounds via Lanczos bidiagonalization. Zbl 1029.65041Calvetti, D.; Hansen, P. C.; Reichel, L. 29 2002 Iterative regularization with minimum-residual methods. Zbl 1113.65037Jensen, T. K.; Hansen, P. C. 29 2007 Deconvolution and regularization with Toeplitz matrices. Zbl 1002.65145Hansen, Per Christian 29 2002 Regularization by truncated total least squares. Zbl 0891.65040Fierro, R. D.; Golub, G. H.; Hansen, P. C.; O’Leary, D. P. 28 1997 Exploiting residual information in the parameter choice for discrete ill-posed problems. Zbl 1091.65038Hansen, P. C.; Kilmer, M. E.; Kjeldsen, R. H. 27 2006 Semi-convergence properties of Kaczmarz’s method. Zbl 1296.65054Elfving, Tommy; Hansen, Per Christian; Nikazad, Touraj 24 2014 Semi-convergence and relaxation parameters for a class of SIRT algorithms. Zbl 1205.65148Elfving, Tommy; Nikazad, Touraj; Hansen, Per Christian 22 2010 The modified truncated SVD method for regularization in general form. Zbl 0760.65044Hansen, Per Christian; Sekii, Takashi; Shibahashi, Hiromoto 21 1992 Computation of the singular value expansion. Zbl 0631.65133Hansen, P. C. 19 1988 A look-ahead Levinson algorithm for general Toeplitz systems. Zbl 0756.65044Chan, Tony F.; Hansen, Per C. 19 1992 Noise propagation in regularizing iterations for image deblurring. Zbl 1171.65032Hansen, Per Christian; Jensen, Toke Koldborg 19 2008 Semiconvergence and relaxation parameters for projected SIRT algorithms. Zbl 1254.65044Elfving, Tommy; Hansen, Per Christian; Nikazad, Touraj 19 2012 Least squares data fitting with applications. Zbl 1270.65008Hansen, Per Christian; Pereyra, Víctor; Scherer, Godela 19 2013 Smoothing-norm preconditioning for regularizing minimum-residual methods. Zbl 1154.65028Hansen, Per Christian; Jensen, Toke Koldborg 17 2006 A look-ahead Levinson algorithm for indefinite Toeplitz systems. Zbl 0752.65020Chan, Tony F.; Hansen, Per Christian 15 1992 Implementation of an optimal first-order method for strongly convex total variation regularization. Zbl 1256.65063Jensen, T. L.; Jørgensen, J. H.; Hansen, P. C.; Jensen, S. H. 15 2012 Algorithms and software for total variation image reconstruction via first-order methods. Zbl 1181.94009Dahl, Joachim; Hansen, Per Christian; Jensen, Søren Holdt; Jensen, Tobias Lindstrøm 15 2010 Subspace preconditioned LSQR for discrete ill-posed problems. Zbl 1046.65030Jacobsen, M.; Hansen, P. C.; Saunders, M. A. 14 2003 A tensor-based dictionary learning approach to tomographic image reconstruction. Zbl 1355.65036Soltani, Sara; Kilmer, Misha E.; Hansen, Per Christian 13 2016 Computing truncated singular value decomposition least squares solutions by rank revealing QR-factorizations. Zbl 0699.65030Chan, Tony F.; Hansen, Per Christian 12 1990 Low-rank revealing \(UTV\) decompositions. Zbl 0887.65043Fierro, Ricardo D.; Hansen, Per Christian 11 1997 Unmatched projector/backprojector pairs: perturbation and convergence analysis. Zbl 1383.65035Elfving, Tommy; Hansen, Per Christian 10 2018 Limited-data x-ray CT for underwater pipeline inspection. Zbl 06858476Riis, N. A. B.; Frøsig, J.; Dong, Y.; Hansen, P. C. 10 2018 Structure-preserving and rank-revealing \(QR\)-factorizations. Zbl 0739.65031Bischof, Christian H.; Hansen, Per Christian 10 1991 Electrical impedance tomography: 3D reconstructions using scattering transforms. Zbl 1238.35183Delbary, Fabrice; Hansen, Per Christian; Knudsen, Kim 10 2012 UTV tools: Matlab templates for rank-revealing UTV decompositions. Zbl 0936.65054Fierro, Ricardo D.; Hansen, Per Christian; Hansen, Peter Søren Kirk 10 1999 Multicore performance of block algebraic iterative reconstruction methods. Zbl 1307.65037Sørensen, Hans Henrik B.; Hansen, Per Christian 10 2014 Oblique projections and standard-form transformations for discrete inverse problems. Zbl 1289.65097Hansen, Per Christian 9 2013 Generalized row-action methods for tomographic imaging. Zbl 1302.65285Andersen, Martin S.; Hansen, Per Christian 8 2014 Fixing nonconvergence of algebraic iterative reconstruction with an unmatched backprojector. Zbl 1420.65031Dong, Yiqiu; Hansen, Per Christian; Hochstenbach, Michiel E.; Brogaard Riis, Nicolai André 7 2019 Block tridiagonal matrix inversion and fast transmission calculations. Zbl 1135.65318Petersen, Dan Erik; Sørensen, Hans Henrik B.; Hansen, Per Christian; Skelboe, Stig; Stokbro, Kurt 7 2008 Test matrices for regularization methods. Zbl 0820.65020Hansen, Per Christian 7 1995 Convergence analysis for column-action methods in image reconstruction. Zbl 1366.65116Elfving, Tommy; Hansen, Per Christian; Nikazad, Touraj 7 2017 Perturbation bounds for discrete Tikhonov regularisation. Zbl 0695.65022Hansen, Per Christian 6 1989 A hybrid method for the parallel computation of Green’s functions. Zbl 1280.82010Petersen, Dan Erik; Li, Song; Stokbro, Kurt; Sørensen, Hans Henrik B.; Hansen, Per Christian; Skelboe, Stig; Darve, Eric 6 2009 Computing symmetric rank-revealing decompositions via triangular factorization. Zbl 1017.65039Hansen, Per Christian; Yalamov, Plamen Y. 6 2001 Regularization Tools Version 3. 0 for Matlab 5. 2. Zbl 0933.65065Hansen, Per Christian 5 1999 A locally optimized reordering algorithm and its application to a parallel sparse linear system solver. Zbl 0814.65027Gallivan, K.; Hansen, P. C.; Ostromsky, Tz.; Zlatev, Z. 5 1995 Accuracy of TSVD solutions computed from rank-revealing decompositions. Zbl 0834.65026Fierro, Ricardo D.; Hansen, Per Christian 5 1995 Simultaneous tomographic reconstruction and segmentation with class priors. Zbl 1349.92084Romanov, Mikhail; Dahl, Anders Bjorholm; Dong, Yiqiu; Hansen, Per Christian 5 2016 Rotational image deblurring with sparse matrices. Zbl 1302.65055Hansen, Per Christian; Nagy, James G.; Tigkos, Konstantinos 5 2014 R\(^3\)GMRES: including prior information in GMRES-type methods for discrete inverse problems. Zbl 1307.65049Dong, Yiqiu; Garde, Henrik; Hansen, Per Christian 5 2014 FORTRAN subroutines for general Toeplitz systems. Zbl 0894.65010Hansen, Per Christian; Chan, Tony F. 5 1992 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 5 2021 A spectral geometric model for Compton single scatter in PET based on the single scatter simulation approximation. Zbl 1400.78012Kazantsev, I. G.; Olsen, U. L.; Poulsen, H. F.; Hansen, P. C. 4 2018 An SVD analysis of linear algebraic equations derived from first kind integral equations. Zbl 0577.65116Hansen, Per Christian; Christiansen, Søren 4 1985 The 2-norm of random matrices. Zbl 0656.15013Hansen, Per Christian 4 1988 Subspace-based noise reduction for speech signals via diagonal and triangular matrix decompositions: survey and analysis. Zbl 1168.94415Hansen, Per Christian; Jensen, Søren Holdt 4 2007 Hybrid enriched bidiagonalization for discrete ill-posed problems. Zbl 1449.65093Hansen, Per Christian; Dong, Yiqiu; Abe, Kuniyoshi 4 2019 Reconstruction of single-grain orientation distribution functions for crystalline materials. Zbl 1175.82066Hansen, Per Christian; Sørensen, Henning Osholm; Sükösd, Zsuzsanna; Poulsen, Henning Friis 4 2009 MCMC algorithms for computational UQ of nonnegativity constrained linear inverse problems. Zbl 1442.65031Bardsley, Johnathan M.; Hansen, Per Christian 3 2020 A block algorithm for computing rank-revealing QR factorizations. Zbl 0761.65029Bischof, Christian H.; Hansen, Per Christian 3 1992 Fast orthogonal decomposition of rank deficient Toeplitz matrices. Zbl 0779.65027Hansen, Per Christian; Gesmar, Henrik 3 1993 Regularization and the general Gauss-Markov linear model. Zbl 0722.65020Zha, Hongyuan; Hansen, Per Christian 3 1990 User-friendly simultaneous tomographic reconstruction and segmentation with class priors. Zbl 1489.68385Kjer, Hans Martin; Dong, Yiqiu; Hansen, Per Christian 3 2017 Prewhitening for rank-deficient noise in subspace methods for noise reduction. Zbl 1370.94140Hansen, Per Christian; Jensen, Søren Holdt 3 2005 A coarse-grained parallel QR-factorization algorithm for sparse least squares problems. Zbl 0909.68071Ostromsky, Tz.; Hansen, P. C.; Zlatev, Z. 3 1998 Minimization of linear functionals defined on solutions of large-scale discrete ill-posed problems. Zbl 1084.65035Eldén, L.; Hansen, P. C.; Rojas, M. 3 2005 UTV Expansin pack: Special-purpose rank-revealing algorithms. Zbl 1079.65026Fierro, Ricardo D.; Hansen, Per Christian 3 2005 Empirical average-case relation between undersampling and sparsity in X-ray CT. Zbl 1332.90393Jørgensen, Jakob S.; Sidky, Emil Y.; Hansen, Per Christian; Pan, Xiaochuan 3 2015 Detection of near-singularity in Cholesky and \(LDL^ T\) factorizations. Zbl 0627.65040Hansen, Per Christian 2 1987 Relations between SVD and GSVD of discrete regularization problems in standard and general form. Zbl 0717.65024Hansen, Per Christian 2 1990 Truncated VSV solutions to symmetric rank-deficient problems. Zbl 1018.65054Fierro, Ricardo D.; Hansen, Per Christian 2 2002 Rank-deficient prewhitening with quotient SVD and ULV decompositions. Zbl 0901.65026Hansen, Per Christian 2 1998 Piecewise polynomial solutions without a priori break points. Zbl 0906.65056Hansen, P. C.; Mosegaard, K. 2 1996 Reduction of general broad-band noise in speech by truncated QSVD: Implementation aspects. Zbl 0826.65136Jensen, S. H.; Hansen, P. C.; Hansen, S. D.; Sørensen, J. A. 2 1995 Computed tomography with view angle estimation using uncertainty quantification. Zbl 1503.62009Brogaard Riis, Nicolai André; Dong, Yiqiu; Hansen, Per Christian 2 2021 Solution of ill-posed problems by means of truncated SVD. Zbl 0659.65041Hansen, Per Christian 1 1988 Improving the numerical stability and the performance of a parallel sparse solver. Zbl 0835.65051van Duin, A. C. N.; Hansen, P. C.; Ostromsky, Tz.; Wijshoff, H.; Zlatev, Z. 1 1995 Horseshoe priors for edge-preserving linear Bayesian inversion. Zbl 07695777Uribe, Felipe; Dong, Yiqiu; Hansen, Per Christian 1 2023 GMRES methods for tomographic reconstruction with an unmatched back projector. Zbl 1489.65060Hansen, Per Christian; Hayami, Ken; Morikuni, Keiichi 1 2022 A twin error gauge for Kaczmarz’s iterations. Zbl 1490.65072van Lith, Bart S.; Hansen, Per Christian; Hochstenbach, Michiel E. 1 2021 Multilevel fast multipole method for higher order discretizations. Zbl 1371.78309Borries, Oscar; Meincke, Peter; Jørgensen, Erik; Hansen, Per Christian 1 2014 Symmetric rank revealing factorizations. Zbl 0980.65046Hansen, P. C.; Yalamov, P. Y. 1 1999 Stabilization by perturbation of a \(4n^{2}\) Toeplitz solver. Zbl 0994.65025Hansen, Per Christian; Yalamov, Plamen Y. 1 2000 “Plug-and-play” edge-preserving regularization. Zbl 1312.65064Chen, Donghui; Kilmer, Misha E.; Hansen, Per Christian 1 2014 The Backus-Gilbert method: SVD analysis and fast implementation. Zbl 0815.65137Hansen, Per Christian 1 1994 Experience with regularizing CG iterations. Zbl 0811.65035Hansen, Per Christian 1 1994 Rank-revealing decompositions of symmetric Toeplitz matrices. Zbl 1003.65019Hansen, Per Christian; Yalamov, Plamen 1 2001 Horseshoe priors for edge-preserving linear Bayesian inversion. Zbl 07695777Uribe, Felipe; Dong, Yiqiu; Hansen, Per Christian 1 2023 GMRES methods for tomographic reconstruction with an unmatched back projector. Zbl 1489.65060Hansen, 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 5 2021 Computed tomography with view angle estimation using uncertainty quantification. Zbl 1503.62009Brogaard Riis, Nicolai André; Dong, Yiqiu; Hansen, Per Christian 2 2021 A twin error gauge for Kaczmarz’s iterations. Zbl 1490.65072van Lith, Bart S.; Hansen, Per Christian; Hochstenbach, Michiel E. 1 2021 MCMC algorithms for computational UQ of nonnegativity constrained linear inverse problems. Zbl 1442.65031Bardsley, Johnathan M.; Hansen, Per Christian 3 2020 IR tools: a MATLAB package of iterative regularization methods and large-scale test problems. Zbl 1415.65003Gazzola, Silvia; Hansen, Per Christian; Nagy, James G. 54 2019 Fixing nonconvergence of algebraic iterative reconstruction with an unmatched backprojector. Zbl 1420.65031Dong, Yiqiu; Hansen, Per Christian; Hochstenbach, Michiel E.; Brogaard Riis, Nicolai André 7 2019 Hybrid enriched bidiagonalization for discrete ill-posed problems. Zbl 1449.65093Hansen, Per Christian; Dong, Yiqiu; Abe, Kuniyoshi 4 2019 AIR tools II: algebraic iterative reconstruction methods, improved implementation. Zbl 1397.65007Hansen, Per Christian; Jørgensen, Jakob Sauer 56 2018 Unmatched projector/backprojector pairs: perturbation and convergence analysis. Zbl 1383.65035Elfving, Tommy; Hansen, Per Christian 10 2018 Limited-data x-ray CT for underwater pipeline inspection. Zbl 06858476Riis, 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 1400.78012Kazantsev, I. G.; Olsen, U. L.; Poulsen, H. F.; Hansen, P. C. 4 2018 Convergence analysis for column-action methods in image reconstruction. Zbl 1366.65116Elfving, Tommy; Hansen, Per Christian; Nikazad, Touraj 7 2017 User-friendly simultaneous tomographic reconstruction and segmentation with class priors. Zbl 1489.68385Kjer, Hans Martin; Dong, Yiqiu; Hansen, Per Christian 3 2017 Tomographic image reconstruction using training images. Zbl 1353.65017Soltani, Sara; Andersen, Martin S.; Hansen, Per Christian 1 2017 A tensor-based dictionary learning approach to tomographic image reconstruction. Zbl 1355.65036Soltani, Sara; Kilmer, Misha E.; Hansen, Per Christian 13 2016 Simultaneous tomographic reconstruction and segmentation with class priors. Zbl 1349.92084Romanov, Mikhail; Dahl, Anders Bjorholm; Dong, Yiqiu; Hansen, Per Christian 5 2016 Empirical average-case relation between undersampling and sparsity in X-ray CT. Zbl 1332.90393Jørgensen, Jakob S.; Sidky, Emil Y.; Hansen, Per Christian; Pan, Xiaochuan 3 2015 Semi-convergence properties of Kaczmarz’s method. Zbl 1296.65054Elfving, Tommy; Hansen, Per Christian; Nikazad, Touraj 24 2014 Multicore performance of block algebraic iterative reconstruction methods. Zbl 1307.65037Sørensen, Hans Henrik B.; Hansen, Per Christian 10 2014 Generalized row-action methods for tomographic imaging. Zbl 1302.65285Andersen, Martin S.; Hansen, Per Christian 8 2014 Rotational image deblurring with sparse matrices. Zbl 1302.65055Hansen, Per Christian; Nagy, James G.; Tigkos, Konstantinos 5 2014 R\(^3\)GMRES: including prior information in GMRES-type methods for discrete inverse problems. Zbl 1307.65049Dong, Yiqiu; Garde, Henrik; Hansen, Per Christian 5 2014 Multilevel fast multipole method for higher order discretizations. Zbl 1371.78309Borries, Oscar; Meincke, Peter; Jørgensen, Erik; Hansen, Per Christian 1 2014 “Plug-and-play” edge-preserving regularization. Zbl 1312.65064Chen, Donghui; Kilmer, Misha E.; Hansen, Per Christian 1 2014 Least squares data fitting with applications. Zbl 1270.65008Hansen, Per Christian; Pereyra, Víctor; Scherer, Godela 19 2013 Oblique projections and standard-form transformations for discrete inverse problems. Zbl 1289.65097Hansen, Per Christian 9 2013 AIR tools – a MATLAB package of algebraic iterative reconstruction methods. Zbl 1241.65042Hansen, Per Christian; Saxild-Hansen, Maria 67 2012 Semiconvergence and relaxation parameters for projected SIRT algorithms. Zbl 1254.65044Elfving, Tommy; Hansen, Per Christian; Nikazad, Touraj 19 2012 Implementation of an optimal first-order method for strongly convex total variation regularization. Zbl 1256.65063Jensen, T. L.; Jørgensen, J. H.; Hansen, P. C.; Jensen, S. H. 15 2012 Electrical impedance tomography: 3D reconstructions using scattering transforms. Zbl 1238.35183Delbary, Fabrice; Hansen, Per Christian; Knudsen, Kim 10 2012 Discrete inverse problems. Insight and algorithms. Zbl 1197.65054Hansen, Per Christian 154 2010 Semi-convergence and relaxation parameters for a class of SIRT algorithms. Zbl 1205.65148Elfving, Tommy; Nikazad, Touraj; Hansen, Per Christian 22 2010 Algorithms and software for total variation image reconstruction via first-order methods. Zbl 1181.94009Dahl, Joachim; Hansen, Per Christian; Jensen, Søren Holdt; Jensen, Tobias Lindstrøm 15 2010 A hybrid method for the parallel computation of Green’s functions. Zbl 1280.82010Petersen, 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 1175.82066Hansen, Per Christian; Sørensen, Henning Osholm; Sükösd, Zsuzsanna; Poulsen, Henning Friis 4 2009 Noise propagation in regularizing iterations for image deblurring. Zbl 1171.65032Hansen, Per Christian; Jensen, Toke Koldborg 19 2008 Block tridiagonal matrix inversion and fast transmission calculations. Zbl 1135.65318Petersen, 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 1128.65029Hansen, Per Christian 209 2007 A projection-based approach to general-form Tikhonov regularization. Zbl 1140.65030Kilmer, Misha E.; Hansen, Per Christian; Español, Malena I. 45 2007 An adaptive pruning algorithm for the discrete L-curve criterion. Zbl 1101.65044Hansen, Per Christian; Jensen, Toke Koldborg; Rodriguez, Giuseppe 31 2007 Iterative regularization with minimum-residual methods. Zbl 1113.65037Jensen, T. K.; Hansen, P. C. 29 2007 Subspace-based noise reduction for speech signals via diagonal and triangular matrix decompositions: survey and analysis. Zbl 1168.94415Hansen, Per Christian; Jensen, Søren Holdt 4 2007 Deblurring images. Matrices, spectra, and filtering. Zbl 1112.68127Hansen, Per Christian; Nagy, James G.; O’Leary, Dianne P. 251 2006 Exploiting residual information in the parameter choice for discrete ill-posed problems. Zbl 1091.65038Hansen, P. C.; Kilmer, M. E.; Kjeldsen, R. H. 27 2006 Smoothing-norm preconditioning for regularizing minimum-residual methods. Zbl 1154.65028Hansen, Per Christian; Jensen, Toke Koldborg 17 2006 Prewhitening for rank-deficient noise in subspace methods for noise reduction. Zbl 1370.94140Hansen, Per Christian; Jensen, Søren Holdt 3 2005 Minimization of linear functionals defined on solutions of large-scale discrete ill-posed problems. Zbl 1084.65035Eldén, L.; Hansen, P. C.; Rojas, M. 3 2005 UTV Expansin pack: Special-purpose rank-revealing algorithms. Zbl 1079.65026Fierro, Ricardo D.; Hansen, Per Christian 3 2005 Subspace preconditioned LSQR for discrete ill-posed problems. Zbl 1046.65030Jacobsen, M.; Hansen, P. C.; Saunders, M. A. 14 2003 \(L\)-curve curvature bounds via Lanczos bidiagonalization. Zbl 1029.65041Calvetti, D.; Hansen, P. C.; Reichel, L. 29 2002 Deconvolution and regularization with Toeplitz matrices. Zbl 1002.65145Hansen, Per Christian 29 2002 Truncated VSV solutions to symmetric rank-deficient problems. Zbl 1018.65054Fierro, Ricardo D.; Hansen, Per Christian 2 2002 Computing symmetric rank-revealing decompositions via triangular factorization. Zbl 1017.65039Hansen, Per Christian; Yalamov, Plamen Y. 6 2001 Rank-revealing decompositions of symmetric Toeplitz matrices. Zbl 1003.65019Hansen, Per Christian; Yalamov, Plamen 1 2001 Stabilization by perturbation of a \(4n^{2}\) Toeplitz solver. Zbl 0994.65025Hansen, Per Christian; Yalamov, Plamen Y. 1 2000 Tikhonov regularization and total least squares. Zbl 0945.65042Golub, Gene H.; Hansen, Per Christian; O’Leary, Dianne P. 96 1999 UTV tools: Matlab templates for rank-revealing UTV decompositions. Zbl 0936.65054Fierro, Ricardo D.; Hansen, Per Christian; Hansen, Peter Søren Kirk 10 1999 Regularization Tools Version 3. 0 for Matlab 5. 2. Zbl 0933.65065Hansen, Per Christian 5 1999 Symmetric rank revealing factorizations. Zbl 0980.65046Hansen, P. C.; Yalamov, P. Y. 1 1999 A coarse-grained parallel QR-factorization algorithm for sparse least squares problems. Zbl 0909.68071Ostromsky, Tz.; Hansen, P. C.; Zlatev, Z. 3 1998 Rank-deficient prewhitening with quotient SVD and ULV decompositions. Zbl 0901.65026Hansen, Per Christian 2 1998 Rank-deficient and discrete ill-posed problems. Numerical aspects of linear inversion. Zbl 0890.65037Hansen, Per Christian 227 1997 Regularization by truncated total least squares. Zbl 0891.65040Fierro, R. D.; Golub, G. H.; Hansen, P. C.; O’Leary, D. P. 28 1997 Low-rank revealing \(UTV\) decompositions. Zbl 0887.65043Fierro, Ricardo D.; Hansen, Per Christian 11 1997 Piecewise polynomial solutions without a priori break points. Zbl 0906.65056Hansen, P. C.; Mosegaard, K. 2 1996 Test matrices for regularization methods. Zbl 0820.65020Hansen, Per Christian 7 1995 A locally optimized reordering algorithm and its application to a parallel sparse linear system solver. Zbl 0814.65027Gallivan, K.; Hansen, P. C.; Ostromsky, Tz.; Zlatev, Z. 5 1995 Accuracy of TSVD solutions computed from rank-revealing decompositions. Zbl 0834.65026Fierro, Ricardo D.; Hansen, Per Christian 5 1995 Reduction of general broad-band noise in speech by truncated QSVD: Implementation aspects. Zbl 0826.65136Jensen, 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 0835.65051van 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 0789.65029Hansen, Per Christian 303 1994 The effective condition number applied to error analysis of certain boundary collocation methods. Zbl 0834.65033Christiansen, Søren; Hansen, Per Christian 31 1994 The Backus-Gilbert method: SVD analysis and fast implementation. Zbl 0815.65137Hansen, Per Christian 1 1994 Experience with regularizing CG iterations. Zbl 0811.65035Hansen, Per Christian 1 1994 The use of the \(L\)-curve in the regularization of discrete ill-posed problems. Zbl 0789.65030Hansen, Per Christian; O’Leary, Dianne Prost 291 1993 Regularization methods for large-scale problems. Zbl 0805.65058Hanke, Martin; Hansen, Per Christian 158 1993 Fast orthogonal decomposition of rank deficient Toeplitz matrices. Zbl 0779.65027Hansen, Per Christian; Gesmar, Henrik 3 1993 Analysis of discrete ill-posed problems by means of the L-curve. Zbl 0770.65026Hansen, Per Christian 378 1992 Numerical tools for analysis and solution of Fredholm integral equations of the first kind. Zbl 0782.65153Hansen, Per Christian 39 1992 Some applications of the rank revealing QR factorization. Zbl 0756.65032Chan, Tony F.; Hansen, Per Christian 38 1992 The modified truncated SVD method for regularization in general form. Zbl 0760.65044Hansen, Per Christian; Sekii, Takashi; Shibahashi, Hiromoto 21 1992 A look-ahead Levinson algorithm for general Toeplitz systems. Zbl 0756.65044Chan, Tony F.; Hansen, Per C. 19 1992 A look-ahead Levinson algorithm for indefinite Toeplitz systems. Zbl 0752.65020Chan, Tony F.; Hansen, Per Christian 15 1992 FORTRAN subroutines for general Toeplitz systems. Zbl 0894.65010Hansen, Per Christian; Chan, Tony F. 5 1992 A block algorithm for computing rank-revealing QR factorizations. Zbl 0761.65029Bischof, Christian H.; Hansen, Per Christian 3 1992 Structure-preserving and rank-revealing \(QR\)-factorizations. Zbl 0739.65031Bischof, Christian H.; Hansen, Per Christian 10 1991 Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank. Zbl 0699.65029Hansen, Per Christian 51 1990 The discrete Picard condition for discrete ill-posed problems. Zbl 0723.65147Hansen, Per Christian 36 1990 Computing truncated singular value decomposition least squares solutions by rank revealing QR-factorizations. Zbl 0699.65030Chan, Tony F.; Hansen, Per Christian 12 1990 Regularization and the general Gauss-Markov linear model. Zbl 0722.65020Zha, Hongyuan; Hansen, Per Christian 3 1990 Relations between SVD and GSVD of discrete regularization problems in standard and general form. Zbl 0717.65024Hansen, Per Christian 2 1990 Regularization, GSVD and truncated GSVD. Zbl 0682.65021Hansen, Per Christian 29 1989 Perturbation bounds for discrete Tikhonov regularisation. Zbl 0695.65022Hansen, Per Christian 6 1989 Computation of the singular value expansion. Zbl 0631.65133Hansen, P. C. 19 1988 The 2-norm of random matrices. Zbl 0656.15013Hansen, Per Christian 4 1988 Solution of ill-posed problems by means of truncated SVD. Zbl 0659.65041Hansen, Per Christian 1 1988 The truncated SVD as a method for regularization. Zbl 0633.65041Hansen, Per Christian 87 1987 Detection of near-singularity in Cholesky and \(LDL^ T\) factorizations. Zbl 0627.65040Hansen, Per Christian 2 1987 ...and 1 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,979 Authors 108 Reichel, Lothar 43 Hansen, Per Christian 35 Lesnic, Daniel 29 Nagy, James Gerard 28 Wei, Ting 25 Jbilou, Khalide 24 Sgallari, Fiorella 24 Wei, Yimin 20 Donatelli, Marco 19 Buccini, Alessandro 19 Loli Piccolomini, Elena 19 Morigi, Serena 18 Marin, Liviu 18 Rodriguez, Giuseppe 18 Sadok, Hassane 17 Chen, Wen 17 Chung, Julianne M. 17 Gazzola, Silvia 17 Huang, Ting-Zhu 17 Li, Zi-Cai 15 Huang, Hung-Tsai 15 Lv, Xiaoguang 14 Landi, Germana 13 Hochstenbach, Michiel E. 13 Johansson, B. Tomas 13 Ng, Michael Kwok-Po 12 Hon, Yiu-Chung 12 Jia, Zhongxiao 12 Lu, Shuai 12 Novati, Paolo 12 Zhao, Xile 11 Bouhamidi, Abderrahman 11 Dong, Yiqiu 11 Ingham, Derek Binns 11 Jin, Bangti 11 Noschese, Silvia 11 Ramlau, Ronny 10 Bentbib, Abdeslem Hafid 10 Calvetti, Daniela 10 Elliott, Lionel 10 Fu, Chuli 10 Karageorghis, Andreas 10 Renaut, Rosemary Anne 10 Viloche Bazán, Fermín S. 10 Yuan, Xiaoming 10 Zhang, Wenxing 9 Fu, Zhuojia 9 Lanza, Alessandro 8 Andersen, Martin S. 8 Huang, Guang-Xin 8 Huang, Jin 8 Jin, Qinian 8 Li, Junpu 8 Ling, Leevan 8 Nikazad, Touraj 8 Pourgholi, Reza 8 Serra-Capizzano, Stefano 8 Tautenhahn, Ulrich 8 Van Barel, Marc 8 Zama, Fabiana 8 Zhang, Jianjun 7 Chung, Matthias 7 Elfving, Tommy 7 Hämarik, Uno 7 Han, Deren 7 Lü, Zhongrong 7 Mitrouli, Marilena 7 Ruthotto, Lars 7 Sun, Liangliang 7 Van Huffel, Sabine 6 Bonettini, Silvia 6 Cheng, Xiaoliang 6 Dykes, Laura 6 Gu, Yan 6 Hanke-Bourgeois, Martin 6 Hayami, Ken 6 Huckle, Thomas Kilian 6 Khojasteh Salkuyeh, Davod 6 Kilmer, Misha Elena 6 Li, Ming 6 Liu, Jun 6 Luttman, Aaron 6 Ma, Yunjie 6 Needell, Deanna 6 O’Leary, Dianne P. 6 Pasha, Mirjeta 6 Pereverzev, Sergei V. 6 Porta, Federica 6 Pragliola, Monica 6 Qin, Qinghua 6 Raus, Toomas 6 Reeve, Thomas 6 Wang, Li 6 Wen, Youwei 6 Winkler, Joab R. 6 Yan, Liang 6 Yang, Fenglian 6 Zhang, Yuanxiang 5 Bardsley, Johnathan M. 5 Beik, Fatemeh Panjeh Ali ...and 2,879 more Authors all top 5 Cited in 308 Serials 119 Journal of Computational and Applied Mathematics 101 Inverse Problems in Science and Engineering 100 Inverse Problems 84 Numerical Algorithms 79 Engineering Analysis with Boundary Elements 69 Linear Algebra and its Applications 57 Applied Numerical Mathematics 51 BIT 47 SIAM Journal on Scientific Computing 45 Applied Mathematics and Computation 43 Applied Mathematical Modelling 39 Journal of Computational Physics 37 Computer Methods in Applied Mechanics and Engineering 35 Numerical Linear Algebra with Applications 30 Computers & Mathematics with Applications 30 Journal of Scientific Computing 30 Journal of Mathematical Imaging and Vision 30 SIAM Journal on Imaging Sciences 29 International Journal of Computer Mathematics 28 Inverse Problems and Imaging 24 Journal of Inverse and Ill-Posed Problems 22 ETNA. Electronic Transactions on Numerical Analysis 22 Mathematical Problems in Engineering 21 International Journal for Numerical Methods in Engineering 18 SIAM Journal on Matrix Analysis and Applications 16 Calcolo 16 Computational Optimization and Applications 13 Computational and Applied Mathematics 12 Numerische Mathematik 12 Mathematical Programming. Series A. Series B 11 Mathematics of Computation 11 Mathematics and Computers in Simulation 11 SIAM/ASA Journal on Uncertainty Quantification 10 Journal of Applied Mathematics and Computing 9 Applicable Analysis 9 Computational Mechanics 9 Neural Computation 9 Applied and Computational Harmonic Analysis 9 International Journal of Computational Methods 8 Journal of Engineering Mathematics 8 Numerical Functional Analysis and Optimization 8 COMPEL 8 Journal of Integral Equations and Applications 7 Journal of Mathematical Analysis and Applications 7 Applied Mathematics Letters 7 Computational Statistics and Data Analysis 7 Advances in Computational Mathematics 7 Computational Geosciences 6 Optimization 6 Combustion Theory and Modelling 6 Computational & Mathematical Methods in Medicine 5 Journal of Fluid Mechanics 5 Automatica 5 Journal of Optimization Theory and Applications 5 SIAM Journal on Numerical Analysis 5 Numerical Methods for Partial Differential Equations 5 Mathematical and Computer Modelling 5 Neural Networks 5 Communications in Statistics. Simulation and Computation 5 Abstract and Applied Analysis 5 Communications in Nonlinear Science and Numerical Simulation 5 Acta Numerica 5 Advances in Mathematical Physics 5 Advances in Applied Mathematics and Mechanics 5 GEM - International Journal on Geomathematics 4 Circuits, Systems, and Signal Processing 4 Physica D 4 Japan Journal of Industrial and Applied Mathematics 4 Journal of Global Optimization 4 Pattern Recognition 4 Cybernetics and Systems Analysis 4 International Journal of Computer Vision 4 Optimization Methods & Software 4 EURASIP Journal on Advances in Signal Processing 4 Science China. Mathematics 4 Results in Applied Mathematics 3 Computers and Fluids 3 International Journal of Heat and Mass Transfer 3 Journal of the Franklin Institute 3 Journal of Mathematical Biology 3 Journal of Mathematical Physics 3 Physica A 3 ACM Transactions on Mathematical Software 3 Computing 3 Information Sciences 3 Quarterly of Applied Mathematics 3 Theoretical Computer Science 3 Zeitschrift für Analysis und ihre Anwendungen 3 Applied Mathematics and Mechanics. (English Edition) 3 Acta Applicandae Mathematicae 3 Signal Processing 3 SIAM Review 3 SIAM Journal on Optimization 3 International Transactions in Operational Research 3 Mathematics and Mechanics of Solids 3 Nonlinear Dynamics 3 Journal of Inequalities and Applications 3 Mathematical Modelling and Analysis 3 Statistical Modelling 3 Journal of Computational Acoustics ...and 208 more Serials all top 5 Cited in 50 Fields 1,385 Numerical analysis (65-XX) 285 Partial differential equations (35-XX) 282 Information and communication theory, circuits (94-XX) 217 Operations research, mathematical programming (90-XX) 187 Computer science (68-XX) 153 Statistics (62-XX) 151 Linear and multilinear algebra; matrix theory (15-XX) 127 Operator theory (47-XX) 125 Biology and other natural sciences (92-XX) 117 Mechanics of deformable solids (74-XX) 87 Fluid mechanics (76-XX) 85 Integral equations (45-XX) 81 Calculus of variations and optimal control; optimization (49-XX) 80 Classical thermodynamics, heat transfer (80-XX) 66 Optics, electromagnetic theory (78-XX) 48 Geophysics (86-XX) 44 Systems theory; control (93-XX) 32 Approximations and expansions (41-XX) 32 Integral transforms, operational calculus (44-XX) 23 Probability theory and stochastic processes (60-XX) 17 Ordinary differential equations (34-XX) 16 Dynamical systems and ergodic theory (37-XX) 16 Harmonic analysis on Euclidean spaces (42-XX) 15 Real functions (26-XX) 15 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 14 Statistical mechanics, structure of matter (82-XX) 12 Quantum theory (81-XX) 10 Mechanics of particles and systems (70-XX) 9 Functional analysis (46-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 Special functions (33-XX) 5 Convex and discrete geometry (52-XX) 5 Astronomy and astrophysics (85-XX) 4 General and overarching topics; collections (00-XX) 4 Potential theory (31-XX) 3 Combinatorics (05-XX) 3 Field theory and polynomials (12-XX) 3 Commutative algebra (13-XX) 3 Difference and functional equations (39-XX) 3 Differential geometry (53-XX) 3 Relativity and gravitational theory (83-XX) 2 Sequences, series, summability (40-XX) 2 General topology (54-XX) 1 History and biography (01-XX) 1 Number theory (11-XX) 1 Algebraic geometry (14-XX) 1 Nonassociative rings and algebras (17-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Algebraic topology (55-XX) Citations by Year