NDLI: A Primal-Dual Method for Large-Scale Image Reconstruction in Emission Tomography

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Johnson, Calvin A. Sofer, Ariela
Copyright Year	2000
Abstract	In emission tomography, images can be reconstructed from a set of measured projections using a maximum likelihood (ML) criterion. In this paper, we present a primal-dual algorithm for large-scale three-dimensional image reconstruction. The primal-dual method is specialized to the ML reconstruction problem. The reconstruction problem is extremely large; in several of our data sets the Hessian of the objective function is the product of a 1.4 million by 63 million matrix and its scaled transpose. As such, we consider only approaches that are suitable for large-scale parallel computation. We apply a stabilization technique to the system of equations for computing the primal direction and demonstrate the need for stabilization when approximately solving the system using an early-terminated conjugate gradient iteration.We demonstrate that the primal-dual method for this problem converges faster than the logarithmic barrier method and considerably faster than the expectation maximization algorithm. The use of extrapolation in conjunction with the primal-dual method further reduces the overall computation required to achieve convergence.
Starting Page	691
Ending Page	715
Page Count	25
File Format	PDF
ISSN	10526234
DOI	10.1137/S1052623497330148
e-ISSN	10957189
Journal	SIAM Journal on Optimization (SJOPE8)
Issue Number	3
Volume Number	11
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-31
Access Restriction	Subscribed
Subject Keyword	parallel computation Applications of mathematical programming Methods based on necessary conditions Estimation Large-scale problems estimation Biomedical imaging and signal processing large-scale problems applications of nonlinear programming tomography primal-dual methods Parallel computation Nonlinear programming
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Software

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