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We discuss multiscale representations of discrete manifold-valued data. As itturns out that we cannot expect general manifold-analogues of biorthogonalwavelets to possess perfect reconstruction, we focus our attention on thoseconstructions which are based on upscaling operators which are eitherinterpolating or midpoint-interpolating. For definable multiscaledecompositions we obtain a stability result.

Definability and stability of multiscale decompositions for manifold-valued data