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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)
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)
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)
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)
‡e study the ™onvergen™e of regul—rized xewton methods —pplied to nonline—r oper—tor equ—tions in ril˜ert sp—™es if the d—t— —re pertur˜ed ˜y r—ndom noiseF st is shown th—t the expe™ted squ—re error is ˜ounded ˜y — ™onst—nt times the minim—x r—tes of the ™orresponding line—rized pro˜lem if the stopping index is ™hosen using —Epriori knowledge of the(More)
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)
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)