Multigrid Tomographic Inversion with Variable Resolution Data and Image Spaces
 
Seungseok Oh (1), Charles A. Bouman (2), and Kevin J. Webb (2) 
 
Abstract 

A multigrid inversion approach that uses variable resolutions of both data
space and image space is proposed.  Since computational complexity of inverse
problems typically increases with a larger number of unknown image pixels and
a larger number of measurements, the proposed algorithm further reduces the
computation relative to conventional multigrid approaches, which change only
the image space resolution at coarse scales.  The advantage is particularly
important for data-rich applications, where data resolutions may differ for
different scales.  Applications of the approach to Bayesian reconstruction
algorithms in transmission and emission tomography with a generalized Gaussian
Markov random field image prior are presented, both with a Poisson noise model
and with a quadratic data term.  Simulation results indicate that the proposed
multigrid approach results in significant improvement in convergence speed
compared to the fixed-grid iterative coordinate descent (ICD) method and a
multigrid method with fixed data resolution.
 
Index Terms 
Multigrid algorithms, multiresolution, inverse problems, image reconstruction,
computed tomography, emission tomography, transmission tomography
 
(1) Fujifilm Software (California), Inc., San Jose, CA, USA,
soh@fujifilmsoft.com

(2) School of Electrical and Computer Engineering, Purdue University, West
Lafayette, IN, USA, {bouman,webb}@ecn.purdue.edu