DocumentCode :
1253162
Title :
Accelerating the EMML algorithm and related iterative algorithms by rescaled block-iterative methods
Author :
Byrne, Charles L.
Author_Institution :
Dept. of Math. Sci., Massachusetts Univ., Lowell, MA, USA
Volume :
7
Issue :
1
fYear :
1998
fDate :
1/1/1998 12:00:00 AM
Firstpage :
100
Lastpage :
109
Abstract :
Analysis of convergence of the algebraic reconstruction technique (ART) shows it to be predisposed to converge to a solution faster than simultaneous methods, such as those of the Cimmino-Landweber (1992) type, the expectation maximization maximum likelihood method for the Poisson model (EMML), and the simultaneous multiplicative ART (SMART), which use all the data at each step. Although the choice of ordering of the data and of relaxation parameters are important, as Herman and Meyer (1993) have shown, they are not the full story. The analogous multiplicative ART (MART), which applies only to systems y=Px in which y>0, P⩾0 and a nonnegative solution is sought, is also sequential (or “row-action”), rather than simultaneous, but does not generally exhibit the same accelerated convergence relative to its simultaneous version, SMART. By dividing each equation by the maximum of the corresponding row of P, we find that this rescaled MART (RMART) does converge faster, when solutions exist, significantly so in cases in which the row maxima are substantially less than one. Such cases arise frequently in tomography and when the columns of P have been normalized to have sum one. Between simultaneous methods, which use all the data at each step, and sequential (or row-action) methods, which use only a single data value at each step, there are the block-iterative (or ordered subset) methods, in which a single block or subset of the data is processed at each step. The ordered subset EM (OSEM) of Hudson et al. (see IEEE Trans. Med. Imag., vol.13, p.601-9, 1994) is significantly faster than the EMML, but often fails to converge. The “rescaled block-iterative” EMML (RBI-EMML) is an accelerated block-iterative version of EMML that converges, in the consistent case, to a solution, for any choice of subsets; it reduces to OSEM when the restrictive “subset balanced” condition holds. Rescaled block-iterative versions of SMART and MART also exhibit accelerated convergence
Keywords :
convergence of numerical methods; image reconstruction; iterative methods; maximum likelihood estimation; medical image processing; positron emission tomography; EMML algorithm acceleration; Poisson model; accelerated convergence; algebraic reconstruction technique; block-iterative methods; expectation maximization maximum likelihood method; image reconstruction; iterative algorithms; multiplicative ART; nonnegative solution; ordered subset EM; ordered subset methods; positron emission tomography; relaxation parameters; rescaled MART; rescaled block-iterative EMML; rescaled block-iterative methods; row-action methods; sequential methods; simultaneous methods; simultaneous multiplicative ART; tomography; Acceleration; Algorithm design and analysis; Cancer; Convergence; Equations; Image converters; Image reconstruction; Iterative algorithms; Positron emission tomography; Subspace constraints;
fLanguage :
English
Journal_Title :
Image Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1057-7149
Type :
jour
DOI :
10.1109/83.650854
Filename :
650854
Link To Document :
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