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20 September 2007 Multiscale representation for data on the sphere and applications to geopotential data
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Abstract
We develop a wavelet transform on the sphere, based on the spherical HEALPix coordinate system (Hierarchical Equal Area iso-Latitude Pixelization). HEALPix is heavily used for astronomical data processing applications; it is intrinsically multiscale and locally euclidean, hence appealing for building multiscale system. Furthermore, the equal-area pixelization enables us to employ average-interpolating refinement, giving wavelets of local support. HEALPix wavelets have numerous applications in geopotential modeling. A statistical analysis demonstrates wavelet compressibility of the geopotential field and shows that geopotential wavelet coefficients have many of the statistical properties that were previously observed with wavelet coefficients of natural images. The HEALPix wavelet expansion allows to evaluate a gravimetric quantity over a local region far more rapidly than the classic approach based on spherical harmonics. Our software tools are specifically tailored to demonstrate these advantages.
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Morteza Shahram, David Donoho, and Jean-Luc Starck "Multiscale representation for data on the sphere and applications to geopotential data", Proc. SPIE 6701, Wavelets XII, 67010A (20 September 2007); https://doi.org/10.1117/12.735175
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