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We apply the joint entropy prior to limited view transmission tomography and demonstrate its sensitivity to local optima. We propose to increase robustness by modelling the joint histogram as the sum of a limited number of bivariate clusters. The method is illustrated for the case of Gaussian distributions. This approximation increases robustness by reducing the possible number of local optima in the cost function. The resulting reconstruction prior mimicks the behaviour of the joint entropy prior in that it narrows clusters in the joint histogram, and yields promisingly accurate reconstruction results despite the null space problem.