Questions about convolving/deconvolving with a PSF A point spread function (PSF) has many different uses. Consider for instance the following quote:


  To  extract  the  maximum  information  out  of  an  observation, even the smallest details of the PSF are important. Some examples include: deconvolving the PSF from an observed image to remove the blurring caused by diffraction and reveal fine structure; convolving a model image by the PSF to compare to an observed one;


My question about this is the following:
If we know the PSF of a system, and use this to deconvolve the raw image (purpose 1 from the quote above), why would we convolve a model with the PSF to compare it to an image (purpose 2 from the quote)? That is, can't we just compare the original, unconvolved model, with the deconvolved image? In terms of maximizing the information that seems like the way to go.
Convolution is not a uniquely invertible process in the presence of random noise in your image. Deconvolving a noisy image can give misleading results, even if you have perfect knowledge of the PSF.

In general, when you are fitting models to data, it is far better to compare the models and data in the observational space of the data, where the uncertainties are reasonably well understood.