We investigate the simultaneous regularization and discretization of an optimal control problem with pointwise control constraints. Typically such problems exhibit bang-bang solutions: the optimal control almost everywhere takes values at the control bounds. We derive discretization error estimates that are robust with respect to the regularization parameter. These estimates can be used to make...

Segmentation of time-varying systems and signals into models whose parameters are piecewise constant in time is an important and well studied problem. It is here formulated as a least-squares problem with sumof-norms regularization over the state parameter jumps, a generalization of `1-regularization. A nice property of the suggested formulation is that it only has one tuning parameter, the reg...

, super-resolution image restoration approach is an ill-posed problem and its inversion is by regularization. It is important to set proper regularization parameter. Furthermore in ctical situations the blurring process is generally unknown or is known only to within a set ters, it is necessary to incorporate the blur identification into the restoration procedure. geometric warp matrixes are kn...

Segmentation of time-varying systems and signals into models whose parameters are piecewise constant in time is an important and well studied problem. It is here formulated as a least-squares problem with sum-ofnorms regularization over the state parameter jumps, a generalization of `1-regularization. A nice property of the suggested formulation is that it only has one tuning parameter, the reg...

Choosing the regularization parameter for an ill-posed problem is an art based on good heuristics and prior knowledge of the noise in the observations. In this work, we propose choosing the parameter, without a priori information, by approximately minimizing the distance between the true solution to the discrete problem and the family of regularized solutions. We demonstrate the usefulness of t...

We present a method to automatically select the regularization parameter in the two-term compound cost function used in image registration. Our method is called CFS (Constant Flow Sampling). It samples the regularization parameter using the constraint that the warpinduced image flow be of constant magnitude on average. Compared to other methods, CFS provably provides a global solution at a spec...

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...

Although confocal microscopes have considerably smaller contribution of out-of-focus light than widefield microscopes, the confocal images can still be enhanced mathematically if the optical and data acquisition effects are accounted for. For that, several deconvolution algorithms have been proposed. As a practical solution, maximum-likelihood algorithms with regularization have been used. Howe...

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 ...

Regularization schemes are frequently used for performing ranking tasks. This topic has been intensively studied in recent years. However, to be effective a regularization scheme should be equipped with a suitable strategy for choosing a regularization parameter. In the present study we discuss an approach, which is based on the idea of a linear combination of regularized rankers corresponding ...