Computation

Maximum entropy algorithms tend to be less robust and harder to drive than CLEAN algorithms. The quality of the maximum entropy solution can depend very strongly on the rms and flux parameters - these parameters should be set with some care, or some experimentation may be necessary.

Various parameters to the task maxen are described below:

• map, beam: As with CLEAN, you give task maxen a dirty image and a dirty beam.

• default: You also have the option of supplying a default image. The default image ($M_k$ in the equations above) is some estimate of what the algorithm should tend towards. It could be some a priori model or low-resolution image of the source. The default default (sic) image is a uniform image. The units of the default image are not too important, though it should be positive valued if the Gull and Skilling entropy measure is used.

• model: The model is some initial estimate of the deconvolved image (units of Jy/pixel). In principle, the model image is simply a way to kick start maxen towards the correct solution. In principle it should not affect convergence to the final solution or its quality - it should just speed up the process. In practice, a good initial model can sometimes help.

• region: As with CLEAN, this gives the region in the dirty image which contains all the source emission, and much the same can be restated here about setting the parameter. In particular, you can deconvolve an area no more than a quarter the area of the beam (but see options=pad if you fail to heed this advice).

• measure: This determines the entropy measure used; specify either gull or cornwell (these are the $p\log(p)$ and $\log(\cosh[p])$ forms, respectively). The default is to use the Gull form, but if deconvolving Q, U or V images, the Cornwell form may be useful.

• out: This gives the name of the output image, which has units of Jy/pixel. This is the equivalent image to clean's CLEAN component image. However, unlike CLEAN, maximum entropy techniques tend to be more conservative in their extrapolation of high spatial frequencies, and so this output is more commonly viewed and used as a final image than the CLEAN component image would be. However it is just as valid an operation to pass this output from maxen through restor, and so produce either a restored or a residual image. Those with some courage may choose to look at the residual image. Unlike CLEAN, the residuals tend to be strongly correlated with source structure.

• niters: Task maxen uses an iterative algorithm to arrive at its solution, and terminates when it believes it has converged. The parameter niters gives the maximum number of iterations that maxen will attempt before giving up if it does not converge. For low dynamic-range images, 10 iterations are usually sufficient. Higher dynamic-ranges (greater than 1000) can require 30 iterations to converge. The default maximum number of iterations is 20.

• rms: This is a crucial parameter. It gives the rms noise in Jy/beam. The rms noise value printed by invert should be some guide to setting this parameter, but see the caveats about this value under invert. An alternative way is to measure the rms in a blank portion of the sky. If the beam has few sidelobes you will probably be able to measure this directly from the dirty image. Otherwise you would really need to CLEAN first! If rms is too large, the output image will be too smooth. If it is too small, convergence will be prevented. A useful trick is to underestimate rms and then stop after a few iterations, and then reset rms to the level achieved up to that point. Do not leave rms unset.

• flux: The flux specifies how the zero-spacing flux density is to be estimated. There are three modes of use. First, you specify a known value which must be fitted to within 5%. Second, if you have no idea what the zero-spacing flux density is, then leave flux unset; maxen will attempt to estimate it. Third, if you have a rough idea (within a factor of 2, say) then set flux to the negative of your guess. If at all possible, you should give some estimate of the total flux density.

• q: This gives an estimate of the volume of the main lobe of the dirty beam in units of pixels. Typically it is 10 to 30, and the algorithm does not depend critically on it. The default is determined from the data, and generally will be adequate.

• options, as usual, gives several processing options. Possible values are

  quiet, verbose:

  This controls the verbosity of maxen's messages.

  asym:

  Normally clean assumes that the beam has a 180 degree rotational symmetry, which is the norm in radio interferometry. Making such an assumption allows some optimisations. You should instruct clean if this is not the case, by using the asym switch.

  pad:

  Double the beam size by padding it with zeros. This will give better stability with Clark and Steer modes if you are daring enough to CLEAN an area which is more than a quarter of the beam area.

MAXEN
map=vela.imap	Dirty image
beam=vela.ibem	Dirty beam
model	An initial solution solution - generally unset
default	The image that the solution should tend
	towards - generally unset
out=vela.ivm	Output dataset
niters=20	Maximum number of iterations
region=	Region to be deconvolved
measure	Leaving unset gives you the Gull measure
flux=	Total source flux - give some value
rms=	Rms noise in the dirty image - IMPORTANT!
q=	AN estimate of the value of the beams main lobe.