By Topic

New fast smoothers for multiscale systems

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
E. Fabre ; INRIA, IRISA, Rennes, France

We consider the smoothing problem for multiscale stochastic systems based on the wavelet transform. These models involve processes indexed by the nodes of a dyadic tree. Each level of the dyadic tree represents one scale or resolution of the process; therefore, moving upward on the tree divides the resolution by 2, whereas moving downward multiplies it by 2. The processes are built according to a recursion in scale from coarse to fine to which random details are added. To operate the change in scale, one must perform an interpolation. This is achieved using the QMF pair of operators attached to a wavelet transform. These models have proved to be of great value to capture textures or fractal-like processes as well as to perform multiresolution sensor fusion (an example of which is given here). Up to now however, only subclasses of multiscale systems were amenable to fast algorithms and through different formalisms: those relying on Haar's wavelet and those involving only one of the two wavelet interpolators. We provide here a unifying framework that handles any system based on orthogonal wavelets. A smoothing theory is presented to define the field of fast algorithms for Markov random fields and give intuition on how to design them. This theory reveals the difficulties arising with general multiscale systems. We then prove that orthogonality properties of wavelets are the gate to fastness

Published in:

IEEE Transactions on Signal Processing  (Volume:44 ,  Issue: 8 )