By Topic

Accelerating the EMML algorithm and related iterative algorithms by rescaled block-iterative methods

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Byrne, C.L. ; Dept. of Math. Sci., Massachusetts Univ., Lowell, MA, USA

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

Published in:

Image Processing, IEEE Transactions on  (Volume:7 ,  Issue: 1 )