In our paper, we consider Tikhonov regularization in the reproducing Kernel Hilbert Spaces. In this space we derive upper and lower bound of the interval which contains the optimal value of Tikhonov regularization parameter with respect to the sensitivity of the solution without computing the singular values of the corresponding matrix. For the case of normalized kernel, we give an explicit for...

We propose an original spatio-temporal deconvolution approach for perfusion-weighted MRI applied to cerebral ischemia. The regularization of the underlying inverse problem is achieved with spatio-temporal priors and the resulting optimization problem is solved by half-quadratic minimization. Our approach offers strong convergence guarantees, including when the spatial priors are non-convex. Mor...

We examine the use of truncated singular value decomposition and Tikhonov regularization in standard form to address ill-posed least squares problems Ax = b that frequently arise molecular mechanics force field parameter optimization. illustrate these approaches by applying them dihedral optimization genotoxic polycyclic aromatic hydrocarbon-DNA adducts are interest study chemical carcinogenesi...

Gust and turbulence events are of primary importance for the analysis flight incidents, design gust load alleviation systems calculation loads in airframe. cannot be measured directly but they can obtained through direct or optimisation-based methods. In method discretisation Fredholm Integral equation is associated with an ill conditioned matrix. this work effects regularisation methods includ...

In this paper, we newly propose an adaptive relaxation algorithm for inverse filter design of the multichannel sound reproduction system. The inverse filter of the conventional method often amplifies the background noise and line noise when the room transfer function changes. In order to resolve the problem, the adaptive relaxation algorithm based on the truncated singular value decomposition (...

the grace mission has provided scientific community time-variable gravity field solutions with high precision and on a global scale. the grace mission was launched on march 2003. this mission consists of two satellites that pursue each other in their orbit. distance between two satellites in orbit is measured continuously to an accuracy of better than 1 micron using kbr system placed in satelli...

Regularization algorithms are often used to produce reasonable solutions to ill-posed problems. The L-curve is a plot-for all valid regularization parameters-of the size of the regularized solution versus the size of the corresponding residual. Two main results are established. First a unifying characterization of various regularization methods is given and it is shown that the measurement of "...

In this paper we compare a new regularizing scheme based on the exponential lter function with two classical regularizing methods: Tikhonov regularization and a variant of truncated singular value regularization. The lter functions for the former methods are smooth, but for the latter discontinuous. These regularization methods are applied to the restoration of images degraded by blur and noise...

Truncated singular value decomposition is a reduced version of the in which only few largest values are retained. This paper presents novel perturbation analysis for truncated real matrices. First, we describe expansions truncation order r . We extend results subspace to derive first-order expansion operator about matrix with rank greater than or equal Observing that can be greatly simplified w...

Abstract. The χ-principle generalizes the Morozov discrepancy principle to the augmented residual of the Tikhonov regularized least squares problem. For weighting of the data fidelity by a known Gaussian noise distribution on the measured data and, when the stabilizing, or regularization, term is considered to be weighted by unknown inverse covariance information on the model parameters, the mi...