Where we talk about God, we need to be precise and careful.
Christ is the image of God. This is scriptural (cf. Colossians 1:15). I would be cautious about calling him the image of the Father lest we fall into modalism, and I would also be leery of saying “self”-image because Christ is the second Person of the Trinity, so the use of the word “self” with regards to the Father generating the Son is potentially troublesome.
That Christ is the image of God is an idea that is tied closely with the Incarnation, that is, the man Jesus is the image of God. The Second Person of the Trinity is not an image of God but the Word (or, the Idea of God, who must be God since God’s Idea of himself cannot be inadequate, and nothing is perfectly adequate but God himself), and therefore God himself. That is not imagery, but generation.
The Incarnation brought the Person of God into visible form, something we can see with our eyes, so in that, he is the Icon of God. It is from this that the Eastern traditions developed the theology of the icon, and this is why icons are an essential part of Eastern worship, and why Iconoclasm was declared a heresy at the Ecumenical Council level.