Nonnegative matrix factorization with quadratic programming
Neurocomputing
MEDITOMO: a high performance software package for 3D SPECT imaging
International Journal of Computer Mathematics
A multiresolution approach to iterative reconstruction algorithms in x-ray computed tomography
IEEE Transactions on Image Processing
Emission image reconstruction based on incremental optimisation transfer algorithm
International Journal of Computational Science and Engineering
Transmission tomography reconstruction using compound gauss-markov random fields and ordered subsets
ICIAR'06 Proceedings of the Third international conference on Image Analysis and Recognition - Volume Part II
Csiszár’s divergences for non-negative matrix factorization: family of new algorithms
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Extended SMART algorithms for non-negative matrix factorization
ICAISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Soft Computing
Non-negative matrix factorization with quasi-newton optimization
ICAISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Soft Computing
Hi-index | 0.01 |
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