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Manuscript Title: A Fixed-Memory Moving, Expanding Window for Obtaining Scatter Corrections in X-Ray CT and Other Stochastic Averages
Authors: Zachary H. Levine, Adam L. Pintar
Program title: mewAvg
Catalogue identifier: AEXA_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 196(2015)455
Programming language: Fortran 95 or C.
Computer: Personal computer or larger.
Operating system: Red Hat Enterprise Linux 6, but probably cross platform.
RAM: kB to GB depending on the application
Keywords: Average, Moving expanding window, Fixed storage, Scatter correction.
Classification: 4.13.

Nature of problem:
Some problems require both a self-consistant solution and Monte Carlo sampling. Monte Carlo samples based on early iterates may not be useful, but discarding all samples and resampling every time solution parameters change can be wasteful.

Solution method:
The solution is to keep a fixed fraction of the samples, such as the most recent half. The trick implemented here involves exponentially expanding windows so that a fixed fraction of the samples can be retained using a fixed amount of physical memory.

Additional comments:
The subprograms are intended to be integrated into a larger program of the user. Small driver programs are provided to illustrate the usage.

Running time:
Microseconds to seconds per iteration

References:
[1] G. T. Herman, Image reconstruction from projections: The fundamentals of computerized tomography (Academic, 1980).
[2] E.-P. Rührnschopf and K. Klingenbeck, Medical Physics 38, 5186 (2011).
[3] M.-H. Chen, Q.-M. Shao, and J. G. Ibrahim, Monte Carlo Methods in Bayesian Computation (Springer-Verlag, 2000).
[4] A. Gelman, J. B. Carlin, H. S. Stern, and D. B. Rubin, Bayesian Data Analysis (Cahpman & Hall/CRC, 2004), 2nd ed.
[5] H. Robbins and S. Monro, The Annals of Mathematical Statistics 22, 400 (1951).
[6] J. C. Spall, Introduction to Stochastic Search and Optimization (John Wiley and Sons, 2003).
[7] H. J. Kushner and J. Yang, SIAM Journal on Control and Optimization 31, 1045 (1993).
[8] A. L. Pintar and Z. H. Levine, mewAvg: A Fixed Memory Moving Expanding Window Average (2014), URL http://cran.r-project.org/web/packages/mewAvg/index.html.