Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction
- 1 April 1997
- journal article
- research article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Medical Imaging
- Vol. 16 (2) , 166-175
- https://doi.org/10.1109/42.563662
Abstract
This paper presents a new class of algorithms for penalized-likelihood reconstruction of attenuation maps from low-count transmission scans. We derive the algorithms by applying to the transmission log-likelihood a version of the convexity technique developed by De Pierro for emission tomography. The new class includes the single-coordinate ascent (SCA) algorithm and Lange's convex algorithm for transmission tomography as special cases. The new grouped-coordinate ascent (GCA) algorithms in the class overcome several limitations associated with previous algorithms. 1) Fewer exponentiations are required than in the transmission maximum likelihood-expectation maximization (ML-EM) algorithm or in the SCA algorithm. 2) The algorithms intrinsically accommodate nonnegativity constraints, unlike many gradient-based methods. 3) The algorithms are easily parallelizable, unlike the SCA algorithm and perhaps line-search algorithms. We show that the GCA algorithms converge faster than the SCA algorithm, even on conventional workstations. An example from a low-count positron emission tomography (PET) transmission scan illustrates the method.Keywords
This publication has 33 references indexed in Scilit:
- Parallel computation of sequential pixel updates in statistical tomographic reconstructionPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Fast parallelizable algorithms for transmission image reconstructionPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1995
- Penalized weighted least-squares image reconstruction for positron emission tomographyIEEE Transactions on Medical Imaging, 1994
- High sensitivity, total body PET scanning using 3D data acquisition and reconstructionIEEE Transactions on Nuclear Science, 1992
- Globally Convergent Algorithms for Maximizing Likelihood FunctionBiometrika, 1991
- Signal processing via least squares error modelingIEEE ASSP Magazine, 1990
- Maximum likelihood localization of multiple sources by alternating projectionIEEE Transactions on Acoustics, Speech, and Signal Processing, 1988
- Parameter estimation of superimposed signals using the EM algorithmIEEE Transactions on Acoustics, Speech, and Signal Processing, 1988
- Maximum likelihood array processing for the estimation of superimposed signalsProceedings of the IEEE, 1988
- Quantitation in Positron Emission Computed TomographyJournal of Computer Assisted Tomography, 1986