ISSN:
0945-3245
Keywords:
Mathematics Subject Classification (1991):41A15, 41A30, 42C05, 42C15
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary. A nonstationary multiresolution of $L^2(\mathbb{R}^s)$ is generated by a sequence of scaling functions $\phi_k\in L^2(\mathbb{R}^s), k\in \mathbb{Z}.$ We consider $(\phi_k)$ that is the solution of the nonstationary refinement equations $\phi_k = |M|$ $ \sum_{j} h_{k+1}(j)\phi_{k+1}(M \cdot -j), k\in \mathbb{Z},$ where $h_k$ is finitely supported for each k and M is a dilation matrix. We study various forms of convergence in $L^2(\mathbb{R}^s)$ of the corresponding nonstationary cascade algorithm $\phi_{k,n} = |M| \sum_{j} h_{k+1}(j)\phi_{k+1,n-1}(M \cdot -j),$ as k or n tends to $\infty.$ It is assumed that there is a stationary refinement equation at $\infty$ with filter sequence h and that $\sum_k |h_k(j) - h(j)| 〈 \infty.$ The results show that the convergence of the nonstationary cascade algorithm is determined by the spectral properties of the transition operator associated with h.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002110050462
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