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Earth and Space Science, 2020 Tikhonov regularization is critical for accurately specifying both the background (B) and observational (R) error covariances in four‐dimensional variational data assimilation (4DVar). The ratio of the background and observation error variances (referred
Xiangjun Tian, Rui Han, Hongqin Zhang
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Tikhonov Regularization and Total Least Squares [PDF]
SIAM Journal on Matrix Analysis and Applications, 1999 The regularized total least squares (TLS) method of the TLS problem is introduced and its regularizing properties are studied. It is also proved that, in certain cases, the new method is superior to standard regularization methods.
Gene H. Golub +2 more
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Ozone profile smoothness as a priori information in the inversion of limb measurements [PDF]
Annales Geophysicae, 2004 In this work we discuss inclusion of a priori information about the smoothness of atmospheric profiles in inversion algorithms. The smoothness requirement can be formulated in the form of Tikhonov-type regularization, where the smoothness of ...
V. F. Sofieva +4 more
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Bayesian regularization: From Tikhonov to horseshoe [PDF]
WIREs Computational Statistics, 2019 Bayesian regularization is a central tool in modern‐day statistical and machine learning methods. Many applications involve high‐dimensional sparse signal recovery problems. The goal of our paper is to provide a review of the literature on penalty‐based regularization approaches, from Tikhonov (Ridge, Lasso) to horseshoe regularization.This article is ...
Polson, Nicholas G., Sokolov, Vadim
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Spatially Adaptive Tensor Total Variation-Tikhonov Model for Depth Image Super Resolution
IEEE Access, 2017 Depth images play an important role in 3-D applications. However, due to the limitation of depth acquisition equipment, the acquired depth images are usually in limited resolution. In this paper, a spatially adaptive tensor total variation-Tikhonov model
Gang Zhong, Sen Xiang, Peng Zhou, Li Yu
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An Exponential Filtering Based Inversion Method for Microwave Imaging [PDF]
Radioengineering, 2021 In this paper, a new methodology based on the exponential filtering of singular values is adopted to solve the linear ill-posed problem of microwave imaging.
A. Magdum +2 more
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International Journal of Mathematics and Mathematical Sciences, 2020 In this work, a new robust regularized shrinkage regression method is proposed to recover and align high-dimensional images via affine transformation and Tikhonov regularization. To be more resilient with occlusions and illuminations, outliers, and heavy
Habte Tadesse Likassa +2 more
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Reconstruction of Mercury's internal magnetic field beyond the octupole [PDF]
Annales Geophysicae, 2022 The reconstruction of Mercury's internal magnetic field enables us to take a look into the inner heart of Mercury. In view of the BepiColombo mission, Mercury's magnetosphere is simulated using a hybrid plasma code, and the multipoles of the internal ...
S. Toepfer +10 more
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Arnoldi–Tikhonov regularization methods
Journal of Computational and Applied Mathematics, 2009 The problem is to solve a large, ill-conditioned linear system \(Ax=b\) of size \(n\), where \(b=\hat{b}+e\) with \(\hat{b}\) the ``true'' vector and \(e\) some error. Tikhonov regularization minimizes \(\|Ax-b\|^2+\mu^{-1}\|x\|\) with \(\mu\) a regularization parameter.
Lewis, Bryan, Reichel, Lothar
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Discrepancy Sets for Combined Least Squares Projection and Tikhonov Regularization
Mathematical Modelling and Analysis, 2017 To solve a linear ill-posed problem, a combination of the finite dimensional least squares projection method and the Tikhonov regularization is considered. The dimension of the projection is treated as the second parameter of regularization.
Teresa Reginska
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