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- Frank Bauer, Sergei V. Pereverzyev, Lorenzo Rosasco
- J. Complexity
- 2007

In this paper we discuss a relation between Learning Theory and Regularization of linear ill-posed inverse problems. It is well known that Tikhonov regularization can be profitably used in the context of supervised learning, where it usually goes under the name of regularized least-squares algorithm. Moreover the gradient descent algorithm was studied… (More)

- Frank Bauer, Mark A. Lukas
- Mathematics and Computers in Simulation
- 2011

In the literature on regularization, many different parameter choice methods have been proposed in both deterministic and stochastic settings. However, based on the available information, it is not always easy to know how well a particular method will perform in a given situation and how it compares to other methods. This paper reviews most of the existing… (More)

We prove the following estimate for the spectrum of the normalized Laplace operator ∆ on a finite graph G, 1 − (1 − k[t]) 1 t ≤ λ 1 ≤ · · · ≤ λ N −1 ≤ 1 + (1 − k[t]) 1 t , ∀ integers t ≥ 1. Here k[t] is a lower bound for the Ollivier-Ricci curvature on the neighborhood graph G[t] (here we use the convention G[1] = G), which was introduced by Bauer-Jost. In… (More)

- Frank Bauer, Markus Reiß
- 2008

The quasi-optimality criterion chooses the regularization parameter in inverse problems without taking into account the noise level. This rule works remarkably well in practice, although Bakushinskii has shown that there are always counterexamples with very poor performance. We propose an average case analysis of quasi-optimality for spectral cutoff… (More)

- Holger Schöner, Bernhard Moser, Adrian A. Dorrington, Andrew D. Payne, Michael J. Cree, Bettina Heise +1 other
- 2008 International Conference on Computational…
- 2008

A relatively new technique for measuring the 3D structure of visual scenes is provided by time of flight (TOF) cameras. Reflections of modulated light waves are recorded by a parallel pixel array structure. The time series at each pixel of the resulting image stream is used to estimate travelling time and thus range information. This measuring technique… (More)

- Frank Bauer, Thorsten Hohage, Axel Munk
- SIAM J. Numerical Analysis
- 2009

e study the onvergene of regulrized xewton methods pplied to nonliner opertor equtions in rilert spes if the dt re pertured y rndom noiseF st is shown tht the expeted squre error is ounded y onstnt times the minimx rtes of the orresponding linerized prolem if the stopping index is hosen using Epriori knowledge of the… (More)

- Bernhard Moser, Frank Bauer, Peter Elbau, Bettina Heise, Holger Schöner
- Three-Dimensional Image Capture and Applications
- 2008

- Christian Siegl, Matteo Colaianni, Lucas Thies, Justus Thies, Michael Zollhöfer, Shahram Izadi +2 others
- ACM Trans. Graph.
- 2015

Using projection mapping enables us to bring virtual worlds into shared physical spaces. In this paper, we present a novel, adaptable and real-time projection mapping system, which supports multiple projectors and high quality rendering of dynamic content on surfaces of complex geometrical shape. Our system allows for smooth blending across multiple… (More)

- Frank Bauer, Joseph T. Lizier
- ArXiv
- 2012

- Luis Pizarro, Stephan Didas, Frank Bauer, Joachim Weickert
- SCIA
- 2007

Recently, an energy-based unified framework for image de-noising was proposed by Mrázek et al. [10], from which existing nonlinear filters such as M-smoothers, bilateral filtering, diffusion filtering and reg-ularisation approaches, are obtained as special cases. Such a model offers several degrees of freedom (DOF) for tuning a desired filter. In this paper… (More)