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Improving the convergence of iterative filtered backprojection algorithms
Author(s) -
Lalush David S.,
Tsui Benjamin M. W.
Publication year - 1994
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.597210
Subject(s) - conjugate gradient method , algorithm , gradient descent , convergence (economics) , minification , rate of convergence , iterative method , mathematics , computer science , mathematical optimization , method of steepest descent , artificial neural network , artificial intelligence , key (lock) , computer security , economics , economic growth
Several authors have proposed variations of the iterative filtered backprojection (IFBP) reconstruction algorithms claiming fast initial convergence rates. We have found that these algorithms are trying to minimize an unusual squared‐error criterion in a suboptimal way. As a result, existing IFBP algorithms are inefficient in the minimization of the criterion, and may become unstable at higher iteration numbers. We show that existing IFBP algorithms can be modified to use the steepest descent technique by simply optimizing the step size at each iteration. Further gains in convergence rates can be achieved with conjugate gradient IFBP algorithms derived from the same criterion. The steepest descent and conjugate gradient IFBP algorithms are guaranteed to converge, unlike some IFBP algorithms, and will do so in fewer iterations than existing IFBP algorithms.