  In this paper, a new regularization term is proposed to solve mathematical
image problems. By using difference operators in the four directions;
horizontal, vertical and two diagonal directions, an estimation of derivative
amplitude is found. Based on the new obtained estimation, a new regularization
term will be defined, which can be viewed as a new discretized total variation
(TVprn) model. By improving TVprn, a more effective regularization term is
introduced. By finding conjugate of TVprn and producing vector fields with
special constraints, a new discretized TV for two dimensional discrete
functions is proposed (TVnew). The capability of the new TV model to solve
mathematical image problems is examined in some numerical experiments. It is
shown that the new proposed TV model can reconstruct the edges and corners of
the noisy images better than other TVs. Moreover, two test experiments of
resolution enhancement problem are solved and compared with some other
different TVs.
