The way to avoid this when drawing your sprites is to make sure that the alpha edges (where alpha goes from >0 to 0) are not coloured white but coloured the same as the pixels next to them.
Normally you wouldn't see these white/grey pixels but because of bi-linear filtering they bleed very slightly into the edges of the sprites.
Normally you wouldn't see these white/grey pixels but because of bi-linear filtering they bleed very slightly into the edges of the sprites.