We study the qualitative properties of optimal regularisation parameters in variational models for image restoration. The parameters are solutions of bilevel optimisation problems with the image restoration problem as constraint. A general type of regulariser is considered, which encompasses total variation (TV), total generalized variation (TGV) and infimal-convolution total variation (ICTV). ...

In variational optical flow estimation, second order regularisation plays an important role, since it offers advantages in the context of non-fronto-parallel motion. However, in contrast to first order smoothness constraints, most second order regularisers are limited to isotropic concepts. Moreover, the few existing anisotropic concepts are lacking a comparison so far. Hence, our contribution ...

This manuscript considers the convergence rate of boosting under a large class of losses, including the exponential and logistic losses, where the best previous rate of convergence was O(exp(1/ )). First, it is established that the setting of weak learnability aids the entire class, granting a rate O(ln(1/ )). Next, the (disjoint) conditions under which the infimal empirical risk is attainable ...

<p style='text-indent:20px;'>Abel inversion tomography plays an important role in dynamic experiments, while most known studies are started with a single Gaussian assumption. This paper proposes mixed Poisson-Laplace-Gaussian distribution to characterize the noise charge-coupled-device (CCD) sensed radiographic data, and develops multi-convex optimization model address reconstruction prob...

this article presents a unified approach to the abstract notions of partial convolution and involution in $l^p$-function spaces over semi-direct product of locally compact groups. let $h$ and $k$ be locally compact groups and $tau:hto aut(k)$ be a continuous homomorphism.  let $g_tau=hltimes_tau k$ be the semi-direct product of $h$ and $k$ with respect to $tau$. we define left and right $tau$-c...

In Part 1, we developed a new technique based on Lipschitz pushforwards for proving the jump set containment property H(Ju \ Jf ) = 0 of solutions u to total variation denoising. We demonstrated that the technique also applies to Huber-regularised TV. Now, in this Part 2, we extend the technique to higher-order regularisers. We are not quite able to prove the property for total generalised vari...

We present an efficient scenario decomposition algorithm for solving large-scale convex stochastic programming problems that involve a particular class of downside risk measures. The considered risk functionals encompass coherent and convex measures of risk that can be represented as an infimal convolution of a convex certainty equivalent, and include well-known measures, such as conditional va...

We show that any finitely generated non-elementary Kleinian group has a co-final family of finite index normal subgroups with respect to which it has Property τ . As a consequence, any closed hyperbolic 3-manifold has a co-final family of finite index normal subgroups for which the infimal Heegaard gradient is positive.

This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K)$ be a continuous homomorphism.  Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-c...

the weighted semigroup algebra mb (s, w) is studied via its identification with mb (s) together with a weighted algebra product *w so that (mb (s, w), *) is isometrically isomorphic to (mb (s), *w). this identification enables us to study the relation between regularity and amenability of mb (s, w) and mb (s), and improve some old results from discrete to general case.