First of all, you need to find out what finish is on the portrait. There are several kinds of finish. A few professionals usually use a lacquer-based finish. In case you have this type, it is better to take the portrait to a professional.
The lacquer-based finish is not easy to clean and one can easily damage the photo. The lacquer finish must be reapplied after the cleaning – something you cannot do at home.
One can remove the finish by using different items, such as paint thinner or lacquer thinner, but no one can produce a result like a professional does. If your photo does not have a lacquer-based finish, things are pretty easy for you.
To clean a normal picture, you can use a swap. Dampen the swap with distilled water, making sure it is not too wet. You should properly squeeze it in order to get rid of the excess water. Now, it is the time to remove the marks.
There is no need to be an extremist. Don’t rub the surface hard at any stage. Only thing that needs to be done is swirling the area with the wet cotton swab. You may find a few rigid marks, but still you must not rub it hard.
Keep swirling the area gently and the mark will eventually go away. You may ruin the photo by putting any pressure. Too hard rubbing removes the emulsion that actually protects the photo.
If the water trick does not work, you can try rubbing alcohol. If the mark still refuses to go, use the ammonia as a last resort. There is no need to panic, if the surface of the photo slightly rises after getting wet. It will surely go back to its normal shape once it is completely dried.