Caesar statue : Quilted Sagum / Paludamentum ?

[Theodosius the Great]

Avete,

I was looking at a statue of Julius Caesar (from the Louvre) and noticed that the inside of his sagum appears to be quilted.

Julius Caesar statue, click here

See under his left hand where the inside of the sagum is revealed.
Does it really appear to be quilted or is there another explanation ?

Perhaps the statue has been restored based on modern imagination ?

~Theo

[Edited the title of the thread]