Hi,
I need to achieve the bluring as in the original picture (on the bottom), I have tried many blur algorithms but none of them will get close to what I need. I need a sort of blur that will smooth the pixels, kind of un-pixelize blur. Is there something like this available?
I’m not seeing the image in your post.
Yeah, the image link is dead.
Also, when we do get a look at the image, it would help to know exactly what methods you’ve tried (so we don’t waste our time and energy suggesting techniques you’ve already found unsatisfactory), and how/why they didn’t meet your needs.
I fixed the link 
It looks like that’s an 8px X 8px icon. If it is, there is no blur filter that will accomplish your objective. A vector graphic exported to SVG might work, but without some details about what you’re doing, one could only guess.