Result
Choose a logo to begin.
Source
1 Background
An antialiased edge is part artwork, part background, so removing the background leaves those pixels still holding its colour — a pale rim around everything. Defringe works out how much of each edge pixel was background and takes that colour back out.
Removal spreads inwards from the edges, so background sealed inside a shape is never reached — the white left in the middle of an O. Clear small takes those out afterwards while leaving any large area the design meant to be there.
2 Size
Lanczos resampling — noticeably cleaner than a plain stretch, but it cannot invent detail that was never there. For a logo, tracing it to vector below beats any upscale.
3 Vector
Built for flat marks: solid colours, clean edges. A photograph traces into thousands of shapes and is better left as a raster.