On large scales, a chaotic deterministic signal is indistinguishable from a random process. Determinism becomes visible only below a critical length scale. We analyse the dependence of this scale on the entropy of the signal and the minimal embedding dimension for state space reconstruction. Also the problem of the optimal choice of the delay time for ow data can be discussed in this framework.

This paper gives an abstract sufficient condition on Riesz basis with parentheses property for the generators of C0-groups in Hilbert spaces whose eigenvalues are comprised of some finite unification of separable sets after taking the algebraic multiplicities into account. The condition is then applied to the closed-loop system of a serially connected string system under joint damping feedbacks...

The reconstruction of dynamic magnetic resonance imaging (dMRI) from partially sampled k-space data has to deal with a trade-off between the spatial resolution and temporal resolution. In this paper, a low-rank and sparse decomposition model is introduced to resolve this issue, which is formulated as an inverse problem regularized by robust principal component analysis (RPCA). The inverse probl...

Image reconstruction from a fiducial collection of scale space interest points and attributes (e.g. in terms of image derivatives) can be used to make the amount of information contained in them explicit. Previous work by various authors includes both linear and non-linear image reconstruction schemes. In this paper, the authors present new results on image reconstruction using a top point repr...

Scale space interest points capture important photometric and deep structure information of an image. The information content of such points can be made explicit using image reconstruction. In this paper we will consider the problem of combining multiple types of interest points used for image reconstruction. It is shown that ordering the complete set of points by differential (quadratic) TV-no...

The problem is to reconstruct a function f : R → C from finitely many linear functional values. To model the operator that transforms f into the data vector, we need to select an ambient space containing f . Typically, we choose a Hilbert space. The selection of the inner product provides an opportunity to incorporate prior knowledge about f into the reconstructon. The inner product induces a n...

is stable. For infinite-dimensional systems the situation is more complicated. Although the eigenvalues still possess the same property as in the finite dimensional situation, they don’t longer rule the stability. Since many years it is an open question whether the stability of (1.1) and (1.2) are equivalent. For Banach spaces it is not hard to find a counter example, and so we concentrate on t...

A probabilistic framework for vision based volumetric reconstruction and marker free tracking of hand and face volumes is presented, which exclusively relies on off-the-shelf hardware components and can be applied in standard office environments. Here a 3D reconstruction of the interaction environment (user-space) is derived from multiple camera viewpoints which serve as input sources for mixtu...

Due to its wide applications in information retrieval, document summarization is attracting increasing attention in natural language processing. A large body of recent literature has implemented document summarization by extracting sentences that cover the main topics of a document with a minimum redundancy. In this paper, we take a different perspective from data reconstruction and propose a n...