Error on minimizing L1 norm

I would like to minimize the objective function |Ax -b|_1 (i.e., L1 norm of an error). The matrix A models the forward projection (sampled Radon transform) of a CT scanner, x is an image, and b is the measured Radon transform. A is not orthogonal. Its size is 46080 x 16384, and it is sparse. The following is the CVX code

variable xk(npix*npix);
minimize(norm(A*xk-b, 1));

CVX has taken about 8 hours to run this, and next I will need to add constraints. I would like to use TFOCS instead, if that’s faster. Please can you suggest how to put this problem in one of the standard forms that TFOCS requires? Thank you.