A deconvolutionalgorithm (sometimes abbreviated MEM) which functions by minimizing a smoothness function ("entropy") in an image. Maximum entropy is also called
the all-poles model or autoregressive model. For images with more than a million
pixels, maximum entropy is faster than the CLEAN algorithm.
MEM is commonly employed in astronomical synthesis imaging. In this application, the resolution depends on the signal-to-noise ratio, which must be specified. Therefore,
resolution is image dependent and varies across the map. MEM is also biased, since
the ensemble average of the estimated noise is nonzero.
However, this bias is much smaller than the noise for pixels
with a .
It can yield super-resolution, which can usually be trusted to an order of magnitude
in solid angle.
Two definitions of "entropy" normalized to
the flux in the image are
(1)
(2)
where
is a "default image" and is the smoothed image. Several unnormalized entropy measures
(Cornwell 1982, p. 3) are given by
Cornwell, T. J. "Can CLEAN be Improved?" VLA Scientific Memorandum No. 141, March 1982.Cornwell, T. and Braun,
R. "Deconvolution." Ch. 8 in Synthesis
Imaging in Radio Astronomy: Third NRAO Summer School, 1988 (Ed. R. A. Perley,
F. R. Schwab, and A. H. Bridle). San Francisco, CA: Astronomical
Society of the Pacific, pp. 167-183, 1989.Christiansen, W. N.
and Högbom, J. A. Radiotelescopes,
2nd ed. Cambridge, England: Cambridge University Press, pp. 217-218,
1985.Narayan, R. and Nityananda, R. "Maximum Entropy Image Restoration
in Astronomy." Ann. Rev. Astron. Astrophys.24, 127-170, 1986.Press,
W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T.
"Power Spectrum Estimation by the Maximum Entropy (All Poles) Method" and
"Maximum Entropy Image Restoration." §13.7 and 18.7 in Numerical
Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England:
Cambridge University Press, pp. 565-569 and 809-817, 1992.Thompson,
A. R.; Moran, J. M.; and Swenson, G. W. Jr. §3.2 in Interferometry
and Synthesis in Radio Astronomy. New York: Wiley, pp. 349-352, 1986.
.
It can yield super-resolution, which can usually be trusted to an order of magnitude
in solid angle.
is a "default image" and 
is the smoothed image. Several unnormalized entropy measures
(Cornwell 1982, p. 3) are given by
![-sum1/([ln(f_i)]^2)](/images/equations/MaximumEntropyMethod/Inline21.svg)
