One of my wife's favorite spoons got nicked when someone turned on a blender while the spoon was in it. I sanded the nick out but the sanding left scratches that looked like those. The spoon was mirror polished before. I used finer and finer sandpaper, up to like 3000 grit, but the mirror finish eluded me. I bought several buffing wheels and several grits of buffing compound, with them I finally restored the mirror finish. I think that Buck knife blade would look pretty good if you started with 400 sandpaper and worked up to maybe the first (coarsest) buffing compound. Start with 600 grit paper but if it won't remove those scratches drop back to 400, then go 400, 600, 1000, 2000, 3000. If you are not happy buy a buffing wheel and a coarse level compound and keep going from there.
Be careful, buffing wheels can grab a knife. I would put the wheel on a drill and clamp the knife to a bench.