M.E Thesis, Submitted in April 1999 at the Dept. of ECE, IISc, Bangalore
In the first section, we propose to extend the conventional
multi-resolution axioms to what we call as the Generalized Multi-Resolution Axioms (GMRA).
We look at scaling functions that satisfy a multi-scale relation. This class of functions are
richer than the conventional scaling functions. (The asymptotically optimal scaling functions
MOMS are in this general class). This class of
functions was later studied in much detail by Dekel et al [1].
In the second section, we deal with the development of multiwavelets optimized for the representation
of collage error in fractal image coder. The fractal block coder generate collage error that are discontinous at
the block boundaries. Conventional wavelet transforms propagate this discontinuity to finer scales. Hence, the
truncation of the fine scale coefficients for compression will result in blocky artifacts in the reconstructed image. We propose
a multi-wavelet transform that can accomodate discontinuties at the block boundaries while having a specified approximation order.
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References
[1] S. Dekel and N. Dyn, "Poly-scale refinability and subdivision" preprint.