Stuart,

I suspected that the scaling would be a problem with my brute force approach. The number of subsets grows rapidly. I was not sure if you planned on extending this to larger problems. I believe there may be a more intelligent way to get a list of viable subsets of variables. I'll think about that...

Regards

Ok let's use a simplified case as an example.

There are 4 pixels. We can measure them in three ways, bins of 1 (x[1], x[2], x[3], x[4]), bins of 2 (y[1], y[2]) and bins of 4 (z[1]). I want to find all possible way to get y[1]. Here is my code attempting to find the solutions:

Reduce[{y[1] == x[1] + x[2], y[2] == x[3] + x[4], 
  z[1] == x[1] + x[2] + x[3] + x[4]}, {y[1]}]

x[3] == -x[4] + y[2] && x[1] == -x[2] - y[2] + z[1] && 
 y[1] == -y[2] + z[1]

Reduce[{y[1] == x[1] + x[2], y[2] == x[3] + x[4], 
  z[1] == x[1] + x[2] + x[3] + x[4]}, {y[1], y[2]}]

x[1] == -x[2] - x[3] - x[4] + z[1] && y[1] == -x[3] - x[4] + z[1] && 
 y[2] == x[3] + x[4]

So we get these two:

y[1] == -y[2] + z[1]
y[1] == -x[3] - x[4] + z[1]

This seems like a stupid way to do so. Is there anyway to programmatically list all possible ways to get y[1] from other terms? In addition, I would like to extend to the case of higher terms, like 8 pixels having bins of 1,2,4,8, and so on. Can I write a for loop to write those equations?

Thanks in advance!

It would be easier to help if you post what you have done.