if you search the forum you'll find a post that is exactly as you describe - a list of processes and their applicability to linear and nonlinear images.
deconvolution must be done on linear data because there is a single PSF applied to the whole image. when you stretch an image, you change the PSF in different ways in different parts of the image due to the different SNR, different star sizes, etc. this makes that single PSF no longer applicable to the whole image. this is not to say that you can not run deconvolution on a nonlinear image; it will work, and it will sharpen the image, but it does not have mathematical meaning any more.
rob