Abstract In this paper, a new discretization of total variation model is proposed to solve mathematical image problems. By using difference operators in the four directions (i.e. 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 ( T V p r n ) model. By improving T V p r n , a more effective discrete total variation is introduced. By finding conjugate of T V p r n and producing vector fields with special constraints, a new discretized TV for two dimensional discrete functions is proposed ( T V n e w ). The capability of the new TV model to solve mathematical image problems is examined in some numerical experiments. For some denoising and upscaling problems, the new model is compared with three famous total variation models. Generally, the proposed model has the best performance in comparison with all the other models in the experiments in sense of reconstructing the edges, smoothing, denoising and accuracy.