This discussion was lifted from Tim Cornwell's article in the NRAO imaging workshop (1988).
CLEAN approaches the deconvolution problem by using a procedure which selects a plausible image from the set of feasible images. This makes a noise analysis of CLEAN very difficult. The Maxiumum Entropy Method (MEM) is not procedural. The image selected is that which fits the data, to within the noise level, and also has maximum entropy. This has nothing to do with physical entropy, it's just something that when maximized, produces a positive image with a compressed range of pixel values. The latter aspect forces the MEM image to be smooth, and the positivity forces super-resolution on bright, isolated objects. One general-purpose definition of entropy is
where 
is the brightness of the kth pixel, and 
is some
default image. An example might be a low-resolution image of the object.
This allows a priori information to be incorporated into the problem.
The requirement that each visibility be fitted exactly by the model
usually invalidates the positivity constraint. Therefore, data are incorporated
with the constraint that the fit, 
, of the predicted visibility
to that observed, be close to the expected value:
Maximizing H subject to the constraint that 
be equal to
its expected value leads to an image which fits the long spacings too well,
and the zero and short spacings poorly.