While ART converges in the consistent case to a minimal norm solution of (4.1), MART is designed to converge to a solution of (4.1) which minimizes the entropy
For this to make sense we assume that (4.1) has a positive solution, and we seek the minimizer of (4.7) among those f which have only positive components. This is reasonable in many tomographic problems.
The step 
of the MART algorithm for (4.1) is as follows:
MART is an example of a multiplicative algorithm, see Pierro (1990); another example is the EM algorithm.
