For image filtering applications, it has been observed recently that both diffusion filtering and associated regularization models provide similar filtering properties. The comparison has been performed for regularization functionals with convex penalization functional. In this paper we discuss the relation between non-convex regularization functionals and associated time dependent diffusion fi...

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...

Let G be a finite simple graph of order n, maximum degree ∆, and minimum degree δ. A compact regularization of G is a ∆-regular graph H of which G is an induced subgraph: H is symmetric if every automorphism of G can be extended to an automorphism of H. The index |H : G| of a regularization H of G is the ratio |V (H)|/|V (G)|. Let mcr(G) denote the index of a minimum compact regularization of G...

We consider the problem of finding regularized solutions to ill-posed Volterra integral equations. The method we consider is a sequential form of Tikhonov regularization that is particularly suited to problems of Volterra type. We prove that when this sequential regularization method is coupled with several standard discretizations of the integral equation (collocation, rectangular and midpoint...

In this study, we first propose the use of edge-preserving regularization in optimizing an ill-conditioned problem in the reconstruction procedure for diffuse optical tomography to prevent unwanted edge smoothing, which usually degrades the attributes of images for distinguishing tumors from background tissues when using Tikhonov regularization. In the edge-preserving regularization method pres...

The problem of learning a sparse conic combination of kernel functions or kernel matrices for classification or regression can be achieved via the regularization by a block 1-norm [1]. In this paper, we present an algorithm that computes the entire regularization path for these problems. The path is obtained by using numerical continuation techniques, and involves a running time complexity that...

Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring question in regularization approaches is the selection of regularization parameters, and its effect on the solution and on the optimal value of the optimization problem. The sensitivity of the value function to the regularization parameter can be linked directly to the Lagrange multipliers...

We present subjective evaluations of example-based regualrization, total variation regularization, and a proposed joint example-based and total variation regularization for image estimation problems. We focus on the noisy deblurring problem, which generalizes image superresolution and denoising. Controlled subjective experiments show that the proposed joint regularization can yield significant ...

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...

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...