Multiscale Representations for Manifold-Valued Data

@article{Rahman2005MultiscaleRF,
  title={Multiscale Representations for Manifold-Valued Data},
  author={Inam Ur Rahman and Iddo Drori and Victoria Stodden and David L. Donoho and Peter Schr{\"o}der},
  journal={Multiscale Model. Simul.},
  year={2005},
  volume={4},
  pages={1201-1232}
}
We describe multiscale representations for data observed on equispaced grids and taking values in manifolds such as the sphere $S^2$, the special orthogonal group $SO(3)$, the positive definite matrices $SPD(n)$, and the Grassmann manifolds $G(n,k)$. The representations are based on the deployment of Deslauriers--Dubuc and average-interpolating pyramids "in the tangent plane" of such manifolds, using the $Exp$ and $Log$ maps of those manifolds. The representations provide "wavelet coefficients… 

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