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   -> Volume 3, Issue 2


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Author Message
Mickey Bhatia (mbhatia@MIT.EDU)
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PostPosted: Mon Dec 02, 2002 11:32 am    
Subject: Preprint available
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Preprint available

The following preprint is available through an anonymous ftp to
"lids.mit.edu" in the directory "pub/ssg/papers" (do "cd
pub/ssg/papers" after logging in). The file name is
"LIDS-P-2182.PS.gz". Read the file "README" in the same directory for
further help.

MIT Technical Report LIDS-P-2182:


A WAVELET-BASED METHOD FOR MULTISCALE TOMOGRAPHIC RECONSTRUCTION

M. Bhatia, W. C. Karl, and A. S. Willsky

Stochastic Systems Group
Laboratory for Information and Decision Systems
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139
Telephone: (617) 253-3816 Telefax: (617) 258-8553
Email: mbhatia@mit.edu

We represent the standard ramp filter operator of the filtered
back-projection (FBP) reconstruction in different bases composed of
Haar and Daubechies compactly supported wavelets. The resulting
multiscale representation of the ramp filter matrix operator is
approximately diagonal. The accuracy of this diagonal approximation
becomes better as wavelets with larger number of vanishing moments
are used. This wavelet-based representation enables us to formulate
a multiscale tomographic reconstruction technique wherein the object
is reconstructed at multiple scales or resolutions. A complete
reconstruction is obtained by combining the reconstructions at
different scales. Our multiscale reconstruction technique has the
same computational complexity as the FBP reconstruction method. It
differs from other multiscale reconstruction techniques in that 1)
the object is defined through a multiscale transformation of the
projection domain, and 2) we explicitly account for noise in the
projection data by calculating maximum aposteriori probability (MAP)
multiscale reconstruction estimates based on a chosen fractal prior
on the multiscale object coefficients. The computational complexity
of this MAP solution is also the same as that of the FBP
reconstruction. This is in contrast to commonly used methods of
statistical regularization which result in computationally intensive
optimization algorithms. The framework for multiscale
reconstruction presented here can find application in object feature
recognition directly from projection data, and regularization of
imaging problems where the projection data are noisy.
Key words: multiresolution reconstruction, wavelets, tomography,
stochastic models.
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