How CLEAN Works

• Deconvolves a Point Spread Function (PSF) from a "dirty map" (the back-projection map)
• The basic CLEAN method was developed by Högbom (1974) for radio astronomy.
• CLEAN constructs discrete approximations to the CLEAN Map from the convolution equation

  P ⊗ Isource = D
  	where Isource is the source distribution,
  	D is the "dirty map",
  	and ⊗ denotes a convolution

  (Note: For RHESSI, this is NOT strictly a convolution!)

• The algorithm goes as follows:
  1. Start with an initial approximation I₀
  2. Copy it to a new image, called the residual map.
  3. Search for the largest value in the residual map, saving the position in a ``CLEAN component'' table.
  4. Center a PSF at the location of the largest residual flux and scale it by a "gain" μ times the peak value.
  5. Subtract the scaled PSF from I_n-1 to yield I_n.
  6. Continue this iteratively until a specified iteration limit is reached, or until the peak residual is negative.

The main disadvantage of CLEAN is that it does not, at least in the Högbom version, compare the observed modulation profile with a model modulation profile, to assess the "goodness of fit" during the iteration.