A generalized proximal point method for solving variational inequalities with maximal monotone operators is developed. It admits a successive approximation of the feasible set and of a symmetric component of the operator as well as an inexact solving of the regularized problems. The conditions on the approximation are coordinated with the properties of finite element methods for solving problem...

A new adaptive L₁/₂ shooting regularization method for variable selection based on the Cox's proportional hazards mode being proposed. This adaptive L₁/₂ shooting algorithm can be easily obtained by the optimization of a reweighed iterative series of L₁ penalties and a shooting strategy of L₁/₂ penalty. Simulation results based on high dimensional artificial data show that the adaptive L₁/₂ sho...

Maximum likelihood image restoration is a powerful method for three-dimensional (3D) computational optical sectioning microscopy of extended objects. With punctate specimens, however, this method produces a few very bright isolated spots and dim detail around them is lost. The commonly used regularization methods (sieves and roughness penalty) decrease the amplitude of the bright spots, but do ...

A key aspect of the recently proposed Hamiltonian Particle-Mesh (HPM) method is its time-staggered discretization combined with a regularization of the continuous governing equations. In this paper, the time discretization aspect of the HPM method is analysed for the linearized, rotating, shallow-water equations with orography and the combined effect of time-staggering and regularization is com...

In this paper we present an inversion algorithm for nonlinear ill-posed problems arising in atmospheric remote sensing. The proposed method is the iteratively regularized Gauss–Newton method. The dependence of the performance and behaviour of the algorithm on the choice of the regularization matrices and sequences of regularization parameters is studied by means of simulations. A method for imp...

We propose a regularization method for solving ill-posed problems, under the assumption that the solutions are piecewise constant functions with unknown level sets and unknown level values. A level set framework is established for the inverse problem and a Tikhonov regularization approach is proposed. Existence of generalized minimizers for the Tikhonov functional is proven. Moreover, we establ...

We report on a deconvolution method developed in a Bayesian framework for adaptive-optics corrected images of the human retina. The method takes into account the three-dimensional nature of the imaging process; it incorporates a positivity constraint and a regularization metric in order to avoid uncontrolled noise amplification. This regularization metric is designed to simultaneously smooth no...

Discretizations of inverse problems lead to systems of linear equations with a highly ill-conditioned coefficient matrix, and in order to compute stable solutions to these systems it is necessary to apply regularization methods. We show how Tikhonov’s regularization method, which in its original formulation involves a least squares problem, can be recast in a total least squares formulation sui...

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...

In this paper, we study the multi-parameter Tikhonov regularization method which adds multiple different penalties to exhibit multi-scale features of the solution. An optimal error bound of the regularization solution is obtained by a priori choice of multiple regularization parameters. Some theoretical results of the regularization solution about the dependence on regularization parameters are...