This thesis investigates the generalization problem in artificial neural networks, attacking it from two major approaches: regularization and model selection. On the regularization side, under the framework of Kullback–Leibler divergence for feedforward neural networks, we develop a new formula for the regularization parameter in Gaussian density kernel estimation based on available training da...

Recent attention to the problem of controlling multiple loudspeakers to create sound zones has been directed towards practical issues arising from system robustness concerns. In this study, the effects of regularization are analyzed for three representative sound zoning methods. Regularization governs the control effort required to drive the loudspeaker array, via a constraint in each optimizat...

this paper presents results of applying a new approach on 2d inversion of magnetotelluric (mt) data in order to enhance resolution and stability of the inversion results. due to non-linearity and limited coverage of data acquisition in an mt field campaign, minimizing the error by linearization of the problem in least squares inversion usually leads to an ill-posed problem. in general, an inver...

Given a compact operator G, we consider the ill-posed problem, given y , solve Gφ = y (approximately). Typically, in the presence of noise y / ∈ Range(G). We consider the iterated Tikhonov method for this problem. The method selects a regularization parameter based on stability and corrects several times to increase accuracy. We show that it gives a higher accuracy approximation to the noise-fr...

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...

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...