We study multi-parameter regularization (multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters from the viewpoint of augmented Tikhonov regularization, and derive a new parameter choice strategy called the balanced discrepancy principle. A priori and a...

The paper studies kernel regression learning from stochastic optimization and ill-posedness point of view. Namely, the convergence properties of kernel learning estimators are investigated under a gradual elimination of the regularization parameter with rising number of observations. We derive computable non-asymptotic bounds on the deviation of the expected risk from its best possible value an...

In this paper, we study convergence of two different iterative regularization methods for nonlinear ill-posed problems in Banach spaces. One of them is a Landweber type iteration, the other one the iteratively regularized Gauss– Newton method with an a posteriori chosen regularization parameter in each step. We show that a discrepancy principle as a stopping rule renders these iteration schemes...

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...

In an earlier paper [12] we were able to show the existence of asymptotic expansions for the solutions of some regularization procedures fo r higher index differential-algebraic equations in integer powers of the regularization parameter. Recent numerical experiments have led to the conjecture that the asymptotic expansion does not contain the first order term for autonomous systems. In the pre...

We propose an information complexity-based regularization parameter selection method for solution of ill-conditioned inverse problems. The regularization parameter is selected to be the minimizer of the Kullback-Leibler (KL) distance between the unknown data-generating distribution and the fitted distribution. The KL distance is approximated by an information complexity (ICOMP) criterion develo...

The deconvolution in image processing is an inverse illposed problem which necessitates a trade-off between delity to data and smoothness of a solution adjusted by a regularization parameter. In this paper we propose two techniques for selection of a varying regularization parameter minimizing the mean squared error for every pixel of the image. The rst algorithm uses the estimate of the square...

Under the framework of the Kullback-Leibler (KL) distance, we show that a particular case of Gaussian probability function for feedforward neural networks (NNs) reduces into the first-order Tikhonov regularizer. The smooth parameter in kernel density estimation plays the role of regularization parameter. Under some approximations, an estimation formula is derived for estimating regularization p...

In this paper Tikhonov regularization for nonlinear illposed problems is investigated. The regularization term is characterized by a closed linear operator, permitting seminorm regularization in applications. Results for existence, stability, convergence and convergence rates of the solution of the regularized problem in terms of the noise level are given. An illustrating example involving para...

This paper proposes a new approach for choosing the regularization parameters in multiparameter regularization methods when applied to approximate the solution of linear discrete ill-posed problems. We consider both direct methods, such as Tikhonov regularization with two or more regularization terms, and iterative methods based on the projection of a Tikhonov-regularized problem onto Krylov su...