Discrete tomography by convex conconve regularization and d.c. programming

1 The paper introduce a regularization term for discrete tomography.

2 The paper use d.c. programing (difference of convex function) to solve the optimization problem. Here the cost function is a convex function minus a convex function, in other words a convex-concave function.

Two things confused me.

1 prime-dual method

The paper did not describe how to derive the iterations.

A referenced paper has to be read

[a d.c. optimization algorithm for solving the trust region subproblem]

2 the gradient for an indicate function

say the indicate function is

The paper only present that if (xi) = 1

is 1 , if (xi) = 0

is -1.

what about other case?

so from (31) to (32) is not clear.