From an interview about “Imagine”:

Yoko: ‘Cloud Piece’: ‘Imagine the clouds dripping, dig a hole in your garden to put them in.’ This is not a piece of poetry. Poetry to me is nouns or adjectives. This is verbs. And you have to do them. These are all instructions and when you just do it, then you start to understand it.

John: ‘Imagine’ was inspired by Yoko’s Grapefruit. There’s a lot of pieces in it saying like ‘Imagine this’ or ‘Imagine that’. If you get a copy of Grapefruit and look through, you’ll see where I was influenced by her. ‘Imagine’ could never have been written without her. And I know she helped on a lot of the lyrics but I wasn’t man enough to let her have credit for it. So that song was actually written by John & Yoko, but I was still selfish enough and unaware enough to take her contribution without acknowledging it. The song itself expresses what I’d learned through being with Yoko and my own feelings on it. It should really have said ‘Lennon/Ono’ on that song, because she contributed a lot of that song.

 (mehr below the youtube video)