Wavelet bases, approximation theory and subdivision schemes. (English) Zbl 0766.41034
Approximation theory VII, Proc. 7th Int. Symp., Austin/TX (USA) 1992, 63-85 (1993).
Summary: [For the entire collection see Zbl 0755.00008.]
Almost all wavelet bases are constructed from multiresolution analysis, a concept which is well-known in approximation theory. We review the relations between wavelet bases, subband coding schemes and subdivision (or cascade) algorithms. We present several strategies that can be used to evaluate the regularity of the wavelet as well as the convergence of the associated subdivision scheme.
Almost all wavelet bases are constructed from multiresolution analysis, a concept which is well-known in approximation theory. We review the relations between wavelet bases, subband coding schemes and subdivision (or cascade) algorithms. We present several strategies that can be used to evaluate the regularity of the wavelet as well as the convergence of the associated subdivision scheme.
MSC:
| 41A65 | Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) |
