GENERALIZED ORTHONORMAL PIECEWISE CONSTANT WAVELET BASES WITH 1-4 SPLITTING
We give the most general expression of orthonormal piecewise constant wavelet bases, in the case when the refinement process consists in dividing a domain into four subdomains having the same area. We show that the classical Haar bases are optimal with respect to the infinity-norm of the reconstruction error, but not with respect to the 1-norm. The construction applies not only to planar domains, but also to surfaces of revolution, like sphere, cone, paraboloid, or two-sheeted hyperboloid.
multivariate approximation piecewise constant wavelets on manifolds uniform grids