The best way is the safest way, although not always the quickest - so that you dont loose too much too quick, that you put it all back on again. You also have to consider injury recovery management whilst doing this.
You can safely use a high protein and low carb diet, When correctly incorporating cardio and exercise this is going to aid recovery. You do not want to risk making the injury you have/are recovering from to worsen. whilst you exercise doing cardio, you also want to build up muscles and surrounding muscle groups with strengthening exercises, which will help support and strengthen the knee joint.
No good going into it like a bull in a china shop, as you will just cause more injury to the knee.
If you need the exercises to incorporate with the diet let me know.
J20