What procedure will get rid of these deep smile lines (dimples) that are pictured? (photo)

Hi @insecureandcritical. Thank you for sharing your photo. I recommend dermal fillers to help soften the smile smile lines. Restylane Defyne and Refyne work great.

Best of luck,

Dr. Nima

The lines you mentioned here are called smile or accordion lines. They occur for a number of reasons but usually fat loss and increase in muscle activity in the mid face. 
If there is only fat loss I usually address this with a small amount of HA dermal filler to the mid face. The goal of treatment would be to enhance the cheekbone creating a natural appearance and also reduce the accordion lines. 
I cannot quite tell from the photo but if you also have a gummy smile and a thin upper lip when you smile this may suggest increased or hyperactivity of one of the muscles used in smiling. If this is the case I would simultaneously treat that muscle which would also help. The bonus effect of that would be to evert the upper lip and reduce the gummy smile and give you a little more pink lip when you smile.
I hope this helps.

Fillers can be used but generally will only soften the appearance of these lines . The lines are dynamic folds/wrinkles  that occur when in movement or motion . Therefore fillers placed in those areas can help improve but never eliminate the lines . If too much filler is placed this will soften them much more but the downside is there maybe some skin irregularity when you are not smiling  due to too much filler . Newer products from McKesson known as restylane defyne attempts to correct these problems