It sounds batty but we remove our carpet, hoover it well on the drive, sprinkle it with carpet shampoo, and then power wash it, and keep going until there are no more bubbles. It's been done every year for twelve years, and it still looks as good as new! However, ours is one of those 'woven' type ones, very solid, with a good backing, not the tufty, fluffy sort so I'm not sure how you'd manage with one of those.
It might be worth a try, and if it all goes wrong, then buy a remnant of carpet, cut it to the same size and shape as your existing carpet, and have it 'whipped' (oversewn around the edges with matching yarn). Most carpet warehouses around here have a contact who will do it for them.