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An adaptive Tikhonov regularization method for fluorescence molecular tomography
Medical & Biological Engineering & Computing, 2013The high degree of absorption and scattering of photons propagating through biological tissues makes fluorescence molecular tomography (FMT) reconstruction a severe ill-posed problem and the reconstructed result is susceptible to noise in the measurements.
Xu Cao +6 more
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On Krylov projection methods and Tikhonov regularization [PDF]
, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gazzola S, Novati P, Russo M.R.
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Tikhonov Regularization Methods for Variational Inequality Problems
Journal of Optimization Theory and Applications, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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jiip, 1998
The Tikhonov regularization method for the operator equation \(Tu=f\) with an injective linear closed operator in Banach spaces is considered. The method consists in minimization of the functional \[ \| Tu-f_\delta\| ^p+\alpha\| Lu\| ^q \] on \(D(T)\cap D(L)\), for some linear closed operator \(L\) and \(\alpha>0\), \(p>1\), \(q>1\).
Menikhes, L. D., Tanana, V. P.
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The Tikhonov regularization method for the operator equation \(Tu=f\) with an injective linear closed operator in Banach spaces is considered. The method consists in minimization of the functional \[ \| Tu-f_\delta\| ^p+\alpha\| Lu\| ^q \] on \(D(T)\cap D(L)\), for some linear closed operator \(L\) and \(\alpha>0\), \(p>1\), \(q>1\).
Menikhes, L. D., Tanana, V. P.
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A Tikhonov Regularization Method for Image Reconstruction
1993Many problems of image reconstruction from projection data have the following mathematical form $$ Am = d $$ (1) where m is the unknown model, d is the observed data and A is a known operator. If A is independent of the model m, the tomographic problem is linear; otherwise it is nonlinear.
Chengbin Peng +2 more
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Extension of Tikhonov regularization method using linear fractional programming
Journal of Computational and Applied Mathematics, 2020Given a real $m\times n$ matrix $A$ with $m\geq n$ and a noisy vector $b$, this paper focuses on the following least-squares problem: $\min_{x\in \mathbb{R}^n}\|Ax-b\|^2$. Here $\|\cdot\|$ is the Euclidean norm. This problem is commonly studied in the framework of the Tikhonov regularization which consists of solving the regularized least-squares ...
Somaieh Mohammady, M. R. Eslahchi
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Proceedings 2000 International Conference on Image Processing (Cat. No.00CH37101), 2002
This paper presents a systematic and computable method for choosing the regularization parameter appearing in Tikhonov-type regularization based on non-quadratic regularizers. First, we extend the notion of the L-curve, originally defined for quadratically regularized problems, to the case of non-quadratic functions. We then associate the optimal value
Soontorn Oraintara +3 more
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This paper presents a systematic and computable method for choosing the regularization parameter appearing in Tikhonov-type regularization based on non-quadratic regularizers. First, we extend the notion of the L-curve, originally defined for quadratically regularized problems, to the case of non-quadratic functions. We then associate the optimal value
Soontorn Oraintara +3 more
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Tikhonov Regularization Methods for the Inverse Scalp Electroencephalography
Volume 2: Biomedical and Biotechnology Engineering, 2009Electroencephalography (EEG) source localization of brain activity is of high diagnostic value. Noninvasive numerical procedures can be developed to help reconstruct the cortical brain activities from the low-spatial-resolution scalp EEG measurement.
Menglu Wu, Xiaolin Chen
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A Tikhonov-type regularization method for Caputo fractional derivative
Numerical AlgorithmszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nguyen Van Duc +5 more
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On the condition number of matrices arising in the tikhonov regularization method
Acta Applicandae Mathematicae, 1994An integral equation of the first kind (1) \((Kf)(s) = \int^ b_ a k(s,t) f(t)dt = g(s)\), \(K : L^ 2 [a,b] \to L^ 2 [a,b]\), \(k \in L^ 2 ([a,b] \times [a,b])\) is known to be an ill-posed problem. As an expression of this ill-posedness, for many numerical methods (e.g., Galerkin, collocation) the approximate solution of (1) fails in general to the ...
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