Spatial Mapping is Not My Friend

I had held out from posting, hoping that at any moment (over the last week), I would have the solution to the problem of the expression needed for the spatial map I am trying to create.  But that moment has not come, though I feel as if I've tried almost everything.  Above is my patch as is.  As you can see, it doesn't work.  The image should look increasingly stretched as you move from the center in either direction, while the center should correspond exactly to the center of the original picture.  I'm quite exhausted at this point and it is getting old spending every free moment I have trying to solve the problem.