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We investigate an optimal transport problem augmented with a total variation regularization term that penalizes deviations of a transport plan from the inde- pendent product of the marginals. This approach yields a convex but non-smooth optimization problem and provides an alternative to entropy-based regularization. We establish existence of minimizers and prove that for any positive regularization parameter, the resulting functional defines a metric on the space of probability mea- sures. Detailed analysis of the triangle inequality and other metric properties is provided. We study limiting regimes as the regularization parameter tends to zero (recovering the Wasserstein distance) and to infinity (yielding a multiple of the total variation distance). A discrete formulation leading to a linear programming problem is presented, along with qualitative examples illustrating the sparsity-promoting na- ture of the model. Comparisons with entropic regularization highlight the trade-offs between computational efficiency and structural properties of optimal couplings.