Is there a python implementation of a basis pursuit solver?

Question

Originally, I wanted to use the YALL1 package for L1 minimization, however, it's written in matlab. After some research I couldn't find a basis pursuit solver in Python but is there one out there? Alternatively, which existing libraries can I use to solve this minimization problem?

Here's the original problem (BP+):

Answer 1

I think you can do basis pursuit using quadratic cone programming (quick reference).

In python you can use cvxopt to solve quadratic cone programs

Edit: it is even one of their examples.