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In this paper a Variational Inequality method for multiple in- put, multiple output image restoration is presented using an extended Total Variations (TV) regularizer. This approach calculates an adaptive regularization parameter for each image based on their respective degradations. The proposed ex- tended Total Variations regularizer combines both intra-image and inter-image pixel information for improved restoration performance. Hyperparameters for controlling this new TV measure are calculated using a Bayesian joint maximum a posteriori approach.