Sparse Grids

This paper investigates the application of statistical pattern recognition methods in the framework of the dynamic link matching approach. This method describes objects by means of local frequency information on nodes of a sparse grid. Matching of an input image with a reference is achieved by displacement and deformation of the grid. This method is applied here to the authentication

ABSTRACT Scaling information is an important tool for the description of natural processes. Many applications of SAR (differential) interferometry lead to a set of sparse phase measurements, e.g. the monitoring of permanent scatterers. In this case, the atmospheric phase screen component of a given SAR image can be estimated over the PS sparse grid. Usually such data have to be unwrapped and then interpolated on a regular grid. We investigate the utility of the scaling information, valid for atmospheric phase screen data, in the process of unwrapping a set of sparse measurements. We show how the power-law behaviour of the data variogram can be used as an a priori constraint for optimization through techniques such as simulated annealing. The results are interpreted in view of operational applications to real data.

Fuzzy arithmetic provides a powerful tool to introduce uncertainty into mathematical models. With Zadeh's extension principle, one can obtain a fuzzy-valued extension of any real-valued objective function. An efficient and accurate approach to computing expensive multivariate functions of fuzzy numbers is given by fuzzy arithmetic based on sparse grids. In many cases, not all uncertain input parameters carry equal weight, or the objective model exhibits separable structure. These characteristics can be exploited by dimension-adaptive algorithms. As a result, the treatment of even higher-dimensional problems becomes possible. This is demonstrated in this paper by a case study involving two large-scale finite element models in vibration engineering that are subjected to fuzzy-valued input data.