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Дата изменения: Fri Jan 10 22:48:37 2003
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XMM-Newton Science Analysis System


asmooth (asmooth-2.10.2) [xmmsas_20030110_1802-5.4.1]

Meta Index / Home Page / Description / Adaptive smoothing

Variance image

If the input image is non-Poissonian, that is if the uncertainties are not equal to the square root of the values for any pixel, the user should prepare an image of the image variance, which is just the square of the uncertainty values. For example, the variance image of a Poissonian image is (approximately, anyhow) just the image itself. If a variance image is not supplied, asmooth assumes that the image to be smoothed is Poissonian.

Examples of cases where one might need to use a variance image:

• If a background map has been subtracted from the image to be smoothed:

  imageB = imageA - bkgMap
  
  variance = imageA + (square of uncertainty image of bkgMap)
  

• If the input image has been divided by an exposure map:

  imageB = imageA / expMap
  
  variance = imageA / expMap / expMap
  

One problem: in XMM useage, it is not unusual to encounter images which have a significant fraction of zero-valued pixels. For pixel values on the order of 0 or 1, estimating the variance by equating it to the pixel value itself is imprecise. This is also a problem for the task when withvarianceset='no', since it computes its own estimate of variance in just this way. It would be far better to calculate an average value over several pixels and use this as an estimate of Poissonian variance. One way to do this would be to iterate: to smooth the image using the present imprecise estimate of variance, then supply this smoothed image as the variance map for the second iteration. Such a procedure might be expected to smooth the low-count background areas much better than a single-pass scheme, at the cost of some extra blurring of sources. The user may wish to experiment. An alternative scheme would use some combination of background map (see subsubsection 3.1.6) and original unsmoothed image - perhaps something like

asmooth inset=<image> withsrclistset=yes srclistset=<source list>
 outset=<bkgMap>

where(image < 2.0)
  varImage = bkgMap
elsewhere
  varImage = image
end where

asmooth inset=<image> withvarianceset=yes varianceset=<varImage>