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   -> Volume 7, Issue 5


Preprint: Stochastic Atomic Decompositions in a Wavelet Dictionary
 
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mafs (t.sapatinas@bristol.ac.uk)
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PostPosted: Mon Apr 20, 1998 11:29 am    
Subject: Preprint: Stochastic Atomic Decompositions in a Wavelet Dictionary
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#3 Preprint: Stochastic Atomic Decompositions in a Wavelet Dictionary

Authors: Felix Abramovich (University of Tel Aviv, Israel)
Theofanis Sapatinas (University of Kent, United Kingdom)
Bernard Silverman (University of Bristol, United Kingdom)

Title: Stochastic Atomic Decompositions in a Wavelet Dictionary

Abstract:

We consider random functions defined by atomic decompositions in a
wavelet dictionary. The scale and dilation of the wavelet atoms are
not dyadic constraints, but the function is modelled as a sum of
wavelet functions at arbitrary positions and scales. The locations of
the wavelet atoms and the magnitudes of their coefficients are chosen
with respect to a certain marked Poisson process model, allowing
intuitive notions about the functions genuinely to be modelled. We
explore the properties of realizations from the proposed models by
investigating the relationships between the parameters of the models
and the Besov spaces within which realizations fall. Such relations
may be seen as giving insight into the meaning of the Besov space
parameters themselves. Moreover, although we do not elaborate on
this, the established relations make it possible in principle to
incorporate prior knowledge about the function's regularity into
statistical applications of the proposed models.

Keywords: Atomic Decompositions; Besov Spaces;
Poisson Processes; Wavelet Dictionaries.

The preprint is available at:

http://www.stats.bris.ac.uk/~mafs/atomic4.ps.gz
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