Abstract
The basic idea behind selective multiscale reconstruction of functions from error-affected data is outlined on the sphere. The selective reconstruction mechanism is based on the premise that multiscale approximation can be well-represented in terms of only a relatively small number of expansion coefficients at various resolution levels. An attempt is made within a tree algorithm (pyramid scheme) to remove the noise component from each scale coefficient using a priori statistical information (provided by an error covariance kernel of a Gaussian, stationary stochastic model).
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Freeden, W., Michel, V. & Stenger, M. Multiscale signal-to-noise thresholding. Acta Geod. Geoph. Hung 36, 55–86 (2001). https://doi.org/10.1556/AGeod.36.2001.1.6
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DOI: https://doi.org/10.1556/AGeod.36.2001.1.6