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   -> Volume 3, Issue 6

Preprint: A Multiscale Relaxation Algorithm for $SNR$ Maximization...
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Author Message (Pierre Moulin)

PostPosted: Mon Dec 02, 2002 12:59 pm    
Subject: Preprint: A Multiscale Relaxation Algorithm for $SNR$ Maximization...
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Preprint: A Multiscale Relaxation Algorithm for $SNR$ Maximization...

The following preprint is available by anonymous ftp from
as pub/moulin/ (execute UNIX's "uncompress" command before
printing postscript file).

A Multiscale Relaxation Algorithm for $SNR$ Maximization
in 2-D Nonorthogonal Subband Coding

P. Moulin

In this paper, we develop a technique for improving the applicability
of complete, nonorthogonal, multiresolution transforms to image coding.
As is well known, the $L^2$ norm of the quantization errors is not preserved
by nonorthogonal transforms, so the $L^2$ reconstruction error may be
unacceptably large. However, given the quantizers and synthesis filters,
we show that this artifact can be eliminated by formulating the coding problem
as that of minimizing the $L^2$ reconstruction error over the set of possible
encoded images. With this new formulation, the coding problem becomes
a high-dimensional, discrete optimization problem and features a coupling
between the redundancy-removing and quantization operations.
A practical solution to the optimization problem is presented in the form
of a multiscale relaxation algorithm, using inter- and intra-scale quantization
noise feedback filters. Bounds on the coding gain over the standard coding
technique are derived. A simple extension of the algorithm allows for the use
of non-MMSE quantizers of a type frequently encountered in image coding.
Experiments using biorthogonal spline filters demonstrate appreciable SNR
gains over the standard coding technique, and comparable visual improvements.
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