I wouldnt proceduraly generate the background since its not exactly something youd tend to look at during gameplay but you could make a few star and planet textures and proceduraly place them using simplex noise.
I dont exactly see how randomizing the enemies would require perlin noise but it doesnt sound like a bad idea and it would definetly add more variety.
Maybe this is my personal taste speaking but id make the game a little bit less chaotic becouse after wave 4 its practicly impossible maybe adding upgrades or more weapons could solve this issue.
Anyhow GL.