You're welcome
@feritcik
There are two factors that are going against you.
1) Each of the original dots is pretty much the equivalent of a pixel so the resolution of the image at that scale is quite low and detail information has been lost and is not recoverable.
2) You may not know how sharp the original was to being with
The techniques shown look so good (relatively) is that the human eye is best at seeing edges and they are getting in the way of seeing the underlying image. With the blur and/or FFT, those edges are gone yet the remaining representation will not have higher resoluition
Here is some good news though.
There are some post processing techniques that can fool the eye into seeing a sharper image. Some of that is by adding contrast or local contrast (clarity) and another is to use a AI program/plugin such as Topaz Photo AI or Topaz Gigapixel. For some images they can produce really great improvements yet I have seen real bad results as well. Its a bit hit or miss and really depends on the starting image.
You an always post again as you already indicated to start more discussion which could include the whole image and see how forum members can help.
Here is a newspaper print of my Great Grandmother from ~1940s or so that uses varying dot sizes to represent levels of gray. FFT does not work on that type of iamge yet shown in the animation is the result only using the box blur approach. Not great yet better than just the newspaper print.'
Hope this is helpful
John Wheeler