Hi to everyone!

I want to solve the BPDN

But instead of using a sparsity inducing l1-norm …

… i want to use this approximation function (please replace the **x** from above by **s**, sorry):

where

and

m denotes the number of elements in **s**.

I assumed this problem to be convex, and therefore tried to implement it directly using this expression:

**minimize(-sum(sigma * inv_pos(pow_abs(s,2) + 2 * power(sigma,2))))**

But this does not work (“*Disciplined convex programming error*”). What needs to be changed in this formulation? I cant see what’s wrong since the problem must be convex?

Thanks in advance!

Best,

Jul