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The observation has been made by Aujol and Gilboa that the cartoon and texture components of the decomposition of an image should not be correlated, as they are generated from independent processes. They use this observation in order to choose an optimal fidelity parameter lambda for the decomposition process. However, this determination can be quite inefficient since a wide range of parameters lambda must be searched through before an estimated optimal parameter can be found. In the present paper, we take a different approach, in which the cartoon and texture components are explicitly decorrelated by adding a decorrelation term to the energy functional of the decomposition model of Osher, Sole, and Vese (the OSV model). Decomposition results of improved quality over those from the OSV model are obtained, as quantified by a series of new decomposition quality measures, with cartoon and texture information better separated into their respective components. A new derivation of the OSV model is developed which maintains the texture subcomponents g1 and g2 so that discrimination results similar to those from other decomposition models (e.g., from the model of Vese and Osher and Improved Edge Segregation) may be obtained. This derivation is extended to the proposed model, for which discrimination results are obtained in a substantially smaller number of iterations.