The basic idea behind selective m ultiscale reconstruction of functions from error{a ected 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 coe cients at various resolution levels. An attempt is made within a tree algorithm (pyramid scheme) to remove the noise component from each scale coe cient using a priori statistical information (provided by an error covariance kernel of a Gaussian, stationary stochastic model).
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