An adjustment scheme for the regularization parameter of a Moreau-Yosida-based regularization, or relaxation, approach to the numerical solution of pointwise state constrained elliptic optimal control problems is introduced. The method utilizes error estimates of an associated finite element discretization of the regularized problems for the optimal selection of the regularization parameter in ...

The automated spatially dependent regularization parameter selection framework of [9] for multi-scale image restoration is applied to total generalized variation (TGV) of order two. Well-posedness of the underlying continuous models is discussed and an algorithm for the numerical solution is developed. Experiments confirm that due to the spatially adapted regularization parameter the method all...

Parameter choice is crucial to regularization-based image deblurring. In this paper, a Monte Carlo method is used to approximate the optimal regularization parameter in the sense of Stein’s unbiased risk estimate (SURE) which has been applied to image deblurring. The proposed algorithm is suitable for the exact deblurring functions as well as those of not being expressed analytically. We justif...

To obtain smooth solutions to ill-posed problems, the standard Tikhonov regularization method is most often used. For the practical choice of the regularization parameter α we can then employ the well-known L-curve criterion, based on the L-curve which is a plot of the norm of the regularized solution versus the norm of the corresponding residual for all valid regularization parameters. This pa...

An l(p) (0 < p ≤ 1) sparsity regularization is applied to time-domain diffuse optical tomography with a gradient-based nonlinear optimization scheme to improve the spatial resolution and the robustness to noise. The expression of the l(p) sparsity regularization is reformulated as a differentiable function of a parameter to avoid the difficulty in calculating its gradient in the optimization pr...

Careful tuning of a regularization parameter is indispensable in many machine learning tasks because it has a significant impact on generalization performances. Nevertheless, current practice of regularization parameter tuning is more of an art than a science, e.g., it is hard to tell how many grid-points would be needed in cross-validation (CV) for obtaining a solution with sufficiently small ...

Image acquisition systems invariably introduce blur, which necessitates the use of deblurring algorithms for image restoration. Restoration techniques involving regularization require appropriate selection of the regularization parameter that controls the quality of the restored result. We focus on the problem of automatic adjustment of this parameter for nonlinear image restoration using analy...

This paper reports studies on the influence of the regularization parameter and the first estimate on the performance of iterative image restoration algorithms. We discuss regularization parameter estimation methods that have been developed for the linear Tikhonov-Miller filter to restore images distorted by additive Gaussian noise. We have performed experiments on synthetic data to show that t...

We review the information approach to regularization parameter selection and its information complexity extension for the solution of discrete ill posed problems. An information criterion for regularization parameter selection was first proposed by Shibata in the context of ridge regression as an extension of Takeuchi’s information criterion. In the information approach, the regularization para...

Owing to the edge preserving ability and low computational cost of the total variation (TV), variational models with the TV regularization have been widely investigated in the field of multiplicative noise removal. The key points of the successful application of these models lie in: the optimal selection of the regularization parameter which balances the data-fidelity term with the TV regulariz...