Introduction Minimizing the total Variation (TV) norm term in conjunction with a fidelity term has been effectively applied to Magnetic Resonance (MR) image reconstruction with partially acquired data [1, 3]. However, an inappropriate ratio, determined by the regularization parameter, between these two terms may result in either residual artifact or reduced spatial resolution. The optimization ...

In this paper a nonlinear regularized iterative image restoration algorithm is proposed, according to which no prior knowledge about the noise variance is assumed. The algorithm results from a set-theoretic regularization approach, where bounds of the stabilizing functional and the noise variance, which determine the reg-ularization parameter, are updated at each iteration step. Sufficient cond...

In this paper, we consider the problem for determining an unknown source in the heat equation. The Tikhonov regularization method in Hilbert scales is presented to deal with ill-posedness of the problem and error estimates are obtained with a posteriori choice rule to find the regularization parameter. The smoothness parameter and the a priori bound of exact solution are not needed for the choi...

In this paper, we consider an elliptic partial differential equation where a small parameter is multiplied with one or both of the second derivatives. Four types of basic spectral regularization methods such as Showalter’s, Tikhonov’s, Lardy’s and Lavrentiev’s are applied to approximate the solution by introducing another large (or small) parameter. Convergence of the regularized solutions to t...

We demonstrate how one can choose the smoothing parameter in image denoising by a statistical multiresolution criterion, both globally and locally. Using inhomogeneous diffusion and total variation regularization as examples for localized regularization schemes, we present an efficient method for locally adaptive image denoising. As expected, the smoothing parameter serves as an edge detector i...

Recently, L1 regularization have been attracted extensive attention and successfully applied in mean-variance portfolio selection for promoting out-of-sample properties and decreasing transaction costs. However, L1 regularization approach is ineffective in promoting sparsity and selecting regularization parameter on index tracking with the budget and no-short selling constraints, since the 1-no...

We derive sharp performance bounds for least squares regression with L1 regularization from parameter estimation accuracy and feature selection quality perspectives. The main result proved for L1 regularization extends a similar result in [Ann. Statist. 35 (2007) 2313–2351] for the Dantzig selector. It gives an affirmative answer to an open question in [Ann. Statist. 35 (2007) 2358–2364]. Moreo...

This paper deals with an inverse problem of simultaneously determining the dispersion coefficients and the space-dependent source magnitude in 2D advection dispersion equation with finite observations at the final time. The forward problem is solved by using the alternating direction implicit (ADI) finite difference scheme, and then the optimal perturbation algorithm with the regularization par...

The regularization parameter of support vector machines is intended to improve their generalization performance. Since the feasible region of binary class support vector machines with finite dimensional feature space is a polytope, we note that classifiers at vertices of this unbounded polytope correspond to certain ranges of the regularization parameter. This reduces the search for a suitable ...