caa a22 4500 475737377 CHVBK 20180406123450.0 cr unu---uuuuu 170329e20000501xx s 000 0 eng 10.1007/s001900050286 doi (NATIONALLICENCE)springer-10.1007/s001900050286 Kotsakis C. Department of Geomatics Engineering, University of Calgary, 2500 University Drive N.W., Calgary, Alberta, Canada T2N 1N4 e-mail: ckotsaki@ucalgary.ca; Tel.: +1-403-2204113; Fax: +1-403-2841980, CA aut The multiresolution character of collocation [Elektronische Daten] [C. Kotsakis] Abstract.:  An interesting theoretical connection between the statistical (non-stochastic) collocation principle and the multiresolution/wavelet framework of signal approximation is presented. The rapid developments in multiresolution analysis theory over the past few years have provided very useful (theoretical and practical) tools for approximation and spectral studies of irregularly varying signals, thus opening new possibilities for 'snon-stationary' gravity field modeling. It is demonstrated that the classic multiresolution formalism according to Mallat's pioneering work lies at the very core of some of the general approximation principles traditionally used in physical geodesy problems. In particular, it is shown that the use of a spatio-statistical (non-probabilistic) minimum mean-square-error criterion for optimal linear estimation of deterministic signals, in conjunction with regularly gridded data, always gives rise to a generalized multiresolution analysis in the Hilbert space L 2(R), under some mild constraints on the spatial covariance function and the power spectrum of the unknown field under consideration. Using the theory and the actual approximation algorithms associated with statistical collocation, a new constructive framework for building generalized multiresolution analyses in L 2(R) is presented, without the need for the usual dyadic restriction that exists in classic wavelet theory. The multiresolution and 'snon-stationary' aspects of the statistical collocation approximation procedure are also discussed, and finally some conclusions and recommendations for future work are given. Springer-Verlag Berlin Heidelberg, 2000 Key words: Multiresolution approximation - Spatio-statistical approximation - Wavelets - Collocation nationallicence https://doi.org/10.1007/s001900050286 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s001900050286 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kotsakis C. Department of Geomatics Engineering, University of Calgary, 2500 University Drive N.W., Calgary, Alberta, Canada T2N 1N4 e-mail: ckotsaki@ucalgary.ca; Tel.: +1-403-2204113; Fax: +1-403-2841980, CA aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer