Digital Signal Processing Reference
In-Depth Information
Figure 10.11. Pyramidal wavelet transform on the sphere. (
See color plates.
)
data are land and sea-floor elevations obtained from the ETOPO5 5-minute grid-
ded elevation data set. A thorough explanation of the data set is provided online
(http://www.ngdc.noaa.gov).
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10.5.2.2 Inverse Transform
This reconstruction is not as straightforward as in the undecimated case because
the different scales do not have the same resolution. For each resolution level, we
have to up-sample the scaling band before coadding it to the wavelet coefficients.
Algorithm 40 describes this.
The wavelet transform on the sphere and its pyramidal version both have a re-
construction operator, so they are very well designed for any restoration application
when the data contain isotropic features. In the following, we present other trans-
forms on the sphere more adapted to the analysis of anisotropic features.
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The ETOPO5 data are credited to “Data Announcement 88-MGG-02, Digital Relief of the Surface
of the Earth, NOAA, National Geophysical Data Center, Boulder, Colorado, 1988.” The HEALPix
image is available at http://astro.ic.ac.uk/
∼
pdineen/earth/index.html#earthmap.
