Related papers: Denoising of Sphere- and SO(3)-Valued Data by Rela…

It is common to have to process signals, whose values are points on the 3-D sphere. We consider a Tikhonov-type regularization model to smoothen or interpolate sphere-valued signals defined on arbitrary graphs. We propose a convex…

Circle- and sphere-valued data play a significant role in inverse problems like magnetic resonance phase imaging and radar interferometry, in the analysis of directional information, and in color restoration tasks. In this paper, we aim to…

The handling of manifold-valued data, for instance, plays a central role in color restoration tasks relying on circle- or sphere-valued color models, in the study of rotational or directional information related to the special orthogonal…

It is common to have to process signals or images whose values are cyclic and can be represented as points on the complex circle, like wrapped phases, angles, orientations, or color hues. We consider a Tikhonov-type regularization model to…

We introduce a novel relaxation strategy for denoising hyperbolic-valued data. The main challenge is here the non-convexity of the hyperbolic sheet. Instead of considering the denoising problem directly on the hyperbolic space, we exploit…

We propose regularization schemes for deformable registration and efficient algorithms for their numerical approximation. We treat image registration as a variational optimal control problem. The deformation map is parametrized by its…

Modern signal and image acquisition systems are able to capture data that is no longer real-valued, but may take values on a manifold. However, whenever measurements are taken, no matter whether manifold-valued or not, there occur tiny…

A critical task in graph signal processing is to estimate the true signal from noisy observations over a subset of nodes, also known as the reconstruction problem. In this paper, we propose a node-adaptive regularization for graph signal…

Variational methods for revealing visual concepts learned by convolutional neural networks have gained significant attention during the last years. Being based on noisy gradients obtained via back-propagation such methods require the…

Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…

Graph-based variational methods have recently shown to be highly competitive for various classification problems of high-dimensional data, but are inherently difficult to handle from an optimization perspective. This paper proposes a convex…

Image de-blurring is important in many cases of imaging a real scene or object by a camera. This project focuses on de-blurring an image distorted by an out-of-focus blur through a simulation study. A pseudo-inverse filter is first explored…

In this manuscript we would like to address the classical optimization problem of minimizing a proper, convex and lower semicontinuous function via the second order in time dynamics, combining viscous and Hessian-driven damping with a…

A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…

We consider the estimation of the regularization parameter for the simultaneous deblurring of multiple noisy images via Tikhonov regularization. We approach the problem in three ways. We first reduce the problem to a single-image deblurring…

We study the behaviour of Tikhonov regularisation on topological spaces with multiple regularisation terms. The main result of the paper shows that multi-parameter regularisation is well-posed in the sense that the results depend…

This work is concerned with linear inverse problems where a distributed parameter is known a priori to only take on values from a given discrete set. This property can be promoted in Tikhonov regularization with the aid of a suitable convex…

Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…

Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, which are a necessity due to the ill-posedness of inverse problems. Tikhonov-type regularization methods are very popular in…

In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such…