All depends on how brave you are, toothpaste can be used as an alternative to cutting compound and does deliver results, cutting compound will be better and with enough effort they will look almost like new.
However eventually it will come back, what happens is over time the UV coating deteriorates and the sun eventually breaks down and yellows the plastic, the only way to get rid of this is to sand it back with some fine grit wet and dry paper, the buff with a cutting compound and finally wax. This was my approach as I have some experience with sanding paint and using a DA polisher.
This will last you years as opposed to several months. Alternatively buy a new set from the stealers, circa £350 for the pair I think. But try the toothpaste or cutting compound route first and see how satisfied with it you are.