# I will greatly rejoice in Yahweh

"I" refers to the people of God speaking as one person whom Yahweh has restored.

# clothed me with the garments of salvation; he has clothed me with the robe of righteousness

The people of God speaking as one person that has salvation and righteousness as the appearance visible to all. 

# as a bridegroom adorns himself with a turban, and as a bride adorns herself with her jewels

This comparison emphasizes that the speaker is extremely happy, joyful, celebrating.