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Advanced programs (a la Magical Fractials) that claim to do a loss-less scale only work on very high-res pictures, and at that, expect a plausible result only when you downscale..
The fact remains: you cannot scale without losing information (which results in compensation, thus noise, etc), and no special algorithm or filter applied by "professional program" will help you in most cases...
Considering your souce image is incredibly low-res (and a gif to boot), unfortunatelly you are kinda out of luck ;(
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