How can I procedurally generate a oval-shaped gradient map?

How can I procedurally generate a oval-shaped gradient map?

I'm using perlin noise to generate a map and want to create an island.
What I'm trying to do is blend two noise maps together, one noise map
representing the terrain and the other representing the outline of the
island:

That would be the island. It's a ovalish/rectangularish shape with little
on the outside. And this would be the terrain:

But how would I go about generating the oval-shaped noise map
procedurally? I'd say basically, my goal is a somewhat-radial gradient
with a little turbulence.