GENERALIZED ORTHONORMAL PIECEWISE CONSTANT WAVELET BASES WITH 1–4 SPLITTING

摘要

We give the most general expression of orthonormal piecewise constant wavelet bases, innthe case when the refinement process consists in dividing a domain into four subdomainsnhaving the same area. We show that the classical Haar bases are optimal with respectnto the ∞-norm of the reconstruction error, but not with respect to the 1-norm. Thenconstruction applies not only to planar domains, but also to surfaces of revolution, likensphere, cone, paraboloid, or two-sheeted hyperboloid.