Acceleration of Landweber-type algorithms by suppression of projection on the maximum singular vector
- 1 January 1992
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Medical Imaging
- Vol. 11 (4) , 479-487
- https://doi.org/10.1109/42.192683
Abstract
A procedure that speeds up convergence during the initial stage (the first 100 forward and backward projections) of Landweber-type algorithms, for iterative image reconstruction for positron emission tomography (PET), which include the Landweber, generalized Landweber, and steepest descent algorithms, is discussed. The procedure first identifies the singular vector associated with the maximum singular value of the PET system matrix, and then suppresses projection of the data on this singular vector after a single Landweber iteration. It is shown that typical PET system matrices have a significant gap between their two largest singular values; hence, this suppression allows larger gains in subsequent iterations, speeding up convergence by roughly a factor of three.Keywords
This publication has 23 references indexed in Scilit:
- Image reconstruction and restoration: overview of common estimation structures and problemsIEEE Transactions on Acoustics, Speech, and Signal Processing, 1989
- Object-dependent performance comparison of two iterative reconstruction algorithmsIEEE Transactions on Nuclear Science, 1988
- Constrained Iterative Reconstruction by the Conjugate Gradient MethodIEEE Transactions on Medical Imaging, 1985
- Finite series-expansion reconstruction methodsProceedings of the IEEE, 1983
- Convergence criteria for iterative restoration methodsIEEE Transactions on Acoustics, Speech, and Signal Processing, 1983
- Maximum Likelihood Reconstruction for Emission TomographyIEEE Transactions on Medical Imaging, 1982
- Emission computed tomographyPublished by Springer Nature ,1979
- Theory and Methods Related to the Singular-Function Expansion and Landweber’s Iteration for Integral Equations of the First KindSIAM Journal on Numerical Analysis, 1974
- Projection method for solving a singular system of linear equations and its applicationsNumerische Mathematik, 1971
- An Iteration Formula for Fredholm Integral Equations of the First KindAmerican Journal of Mathematics, 1951