However, my understanding is that you can improve things but you can't "truly" correct it, generally speaking, because the optical aberration causes information to be lost. eg. if point A on your mirror focuses to point A' on the resulting image, and point B on your mirror, due to an aberration, also focuses to A', there's no way to determine from the image which point on the mirror a photon came from.
This is why Hubble eventually needed a hardware fix... from the linked paper: "it is clear that many image restoration methods are highly successful at deriving images that 'look good' from HST data. These restored images may be qualitatively faithful to the true (unknown) image. However, for most astronomical purposes qualitative agreement with reality is not sufficient; we want quantitative agreement as well."
However, my understanding is that you can improve things but you can't "truly" correct it, generally speaking, because the optical aberration causes information to be lost. eg. if point A on your mirror focuses to point A' on the resulting image, and point B on your mirror, due to an aberration, also focuses to A', there's no way to determine from the image which point on the mirror a photon came from.
This is why Hubble eventually needed a hardware fix... from the linked paper: "it is clear that many image restoration methods are highly successful at deriving images that 'look good' from HST data. These restored images may be qualitatively faithful to the true (unknown) image. However, for most astronomical purposes qualitative agreement with reality is not sufficient; we want quantitative agreement as well."