Options to enhance a poor image
There is no way to regain any lost data at all. However, there are many phenomena that might distort the image in a recoverable way, not actually losing any data. You seem to try to undo a "point spread function", that is eg. some consistent blur. This would be not the only way an image can be distorted, however it is by far the most common.

In that case you would assume that the original image is convolved or filtered by an (initially unknown) point spread function. There may be the inverse operation to that. You could call this "equalization" of the frequency space of the image, then.

Not every inverse operation would be represented by an "edge sharpening" operation that is known a priori. You could maybe try to look at the image a virtually point-shaped light source gives, preferrably in front of a dark background. A laser pointer or a bright LED might serve as an example.