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Title: Interpolation and extrapolation of point patterns based on variation analysis on measures
Author: Khatun, Mahmuda
ISNI:       0000 0004 2670 8816
Awarding Body: The University of Strathclyde
Current Institution: University of Strathclyde
Date of Award: 2008
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Suppose that we observe a point pattern in an observation window W₀ C Rd. In this study we pose ourselves the following two main questions: How can one extend the pattern in a 'reasonable way' to a larger window W ) W₀? Can one predict possible gaps in the observed point pattern where points were 'expected' but somehow failed to realise. We address these questions by assuming that the point pattern is an observed part of a realisation of a non-homogeneous Poisson process in W and estimate its intensity so that to mimic a given distributional characteristic of the pattern, for instance, its sample nearest neighbour distribution. The project aims to develop prediction and extrapolation techniques for random points processes and related techniques of optimisation of functionals depending on a measure. Applications are numerous and important, including restoration of images, detection of impurities in material science, prediction of anomalies in geology, etc.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available