Is it possible to replace the black background with a transparent one without losing quality?

Question

Raster graphics

Magic Erase Tool, Color Range and Hue Saturation do not help, the edges are smoothed out crookedly and a black stroke remains.

Answer 1

There is no Photoshop at hand, but you can do it normally through masks.

Answer 2

chikuyonok.ru/2009/03/photoshop-for-webdevs-3/