So, filtering bottom shelf vodka definitely cleans it up a bit, but it wont make it a bottle of Stoli or Kettle One. Instead, it would need to be diluted and re-distilled. Typically top shelf vodkas run through a number of distillations before being proofed and bottled.
With that said, during parties and classes I will buy a bottle of bottom shelf vodka, filter it with my ghetto 2-liter bottle filter design and flavor it with essences or with herbs and spices. It comes out nice as the "crappiness" of the vodka is covered up with sugar and flavor. There would be no way in hell that I would sip on $2.50 vodka straight!!! Talk about a headache in the morning!!!