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An Adaptive Pruning Algorithm for the Discrete L-Curve Criterion [PDF]
We describe a robust and adaptive implementation of the L-curve criterion, i.e., for locating the corner of a discrete L-curve consisting of a log-log plot of corresponding residual and solution norms of regularized solutions from a method with a discrete regularization parameter (such as truncated SVD or regularizing CG iterations).
Hansen, Per Christian +2 more
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Advances in superresolution using L-curve
ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196), 2002Subsequent to the work of Kim, Bose, and Valenzuela in 1990 on the simultaneous filtering and interpolation of a registered sequence of undersampled noisy and shift-invariant blur degraded images, Bose and Boo tackled in 1998 the problem of reconstructing a high-resolution image from multiple undersampled, shifted, degraded frames with subpixel ...
N.K. Bose, S. Lertrattanapanich, J. Koo
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L-Curve and Curvature Bounds for Tikhonov Regularization
Numerical Algorithms, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Calvetti, D., Reichel, L., Shuibi, A.
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Estimation of the L-Curve via Lanczos Bidiagonalization
BIT Numerical Mathematics, 1999A new approach is proposed to determine a value of the regularization parameter in solving ill-conditioned systems of linear equations with a right-hand side contamined by errors of unknown norm. The approach is based on computing an \(L\)-ribbon that contains the \(L\)-curve in its interior.
Calvetti, D., Golub, G. H., Reichel, L.
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GMRES, L-Curves, and Discrete Ill-Posed Problems
BIT Numerical Mathematics, 2002The application of the generalized minimal residual (GMRES) method is discussed for solving large systems of linear equations that arise from the discretization of linear ill-posed problems. The situation is considered when the right-hand side vector is contaminated by measurement errors.
Calvetti, D., Lewis, B., Reichel, L.
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Super-Resolution Image Restoration with L-Curve
2008 Congress on Image and Signal Processing, 2008In this paper, we present an improved algorithm for super-resolution image restoration which used L-Curve regularization to Maximum A-Posteriori method. Super-Resolution as the second-generation problem of image restoration is also an ill-posed question because of an insufficient number of LR images and ill-conditioned blur operators.
Hong-Zhi Wang, Shuang Zhao, Hong-Wu Lv
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Using the L--curve for determining optimal regularization parameters
Numerische Mathematik, 1994It has been known for some time that a conventional use of the \(L\)-curve criterion for choice of the regularization parameter in the Tikhonov method for ill-posed linear operator equations does not lead to convergence (with respect to the error level in the data).
Engl, Heinz W., Grever, Wilhelm
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L‐curve analysis of radiotherapy optimization problems
Medical Physics, 2005We attempt to select an optimal value of regularization parameter in the optimization problems for intensity‐modulated radiotherapy which are solved using a variational regularization technique. We apply to inverse treatment planning the L‐curve method which was developed to determine the regularization parameter in the discrete ill‐posed problems. The
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Optimization of equivalent uniform dose using the L-curve criterion
Physics in Medicine and Biology, 2007Optimization of equivalent uniform dose (EUD) in inverse planning for intensity-modulated radiation therapy (IMRT) prevents variation in radiobiological effect between different radiotherapy treatment plans, which is due to variation in the pattern of dose nonuniformity.
Alexei V, Chvetsov +2 more
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L curve for spherical triangle region quadtrees
Science in China Series E, 2004The sequence of facets and nodes has a direct influence on the efficiency ofaccess to spherical triangle region quadtree. Based on the labeling schema by Lee, spatial curves both for facets and nodes are proposed and the main algorithms for coordinate translation, node L sequence generation and visiting nodes are presented. In particular, constant time
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