permanently removed (psalm 51:9)

Psalm 51:9
Hide your face from my sins, and blot out all my iniquities.

In the previous verse, David is asking God to restore joy and gladness to him. How is that going to be possible with David's guilt and shame over his sin? It can happen if God blots out his iniquities and hides his face from his sins.
The image of God hiding his face is usually seen as a bad thing throughout the bible - God hiding his face from people who have rebelled against him (eg Deuteronomy 31:17-18, Jeremiah 33:5, Micah 3:4). In other psalms the writer cries out that God has hidden his face because He seems absent (Psalm 13:1, 27:9, 69:17). So why would David ask God to hide his face from him now? How can God hide his face from our sin, without hiding his face from us as well. The reason is Jesus who became like one from whom people hide their faces (Isaiah 53:3) and who did not hide his face from mocking and spitting (Isaiah 50:6).

The idea of blotting out is permanent removal. When we consider our sin and are convicted, how can that possibly result in joy and gladness? Because of Jesus' life, death and resurrection, which means that our sin is permanently removed, God has hidden His face from it, but not from us.