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We present a new tone mapping method for the display of high dynamic range images in low dynamic range devices. We formulate high dynamic range image tone mapping as an optimisation problem. We introduce a two-term cost function, the first term favours linear scaling mapping, the second term favours histogram equalisation mapping, and jointly optimising the two terms optimally maps a high dynamic range image to a low dynamic range image. We control the mapping results by adjusting the relative weightings of the two terms in the objective function. We also present a fast and simple implementation for solving the optimisation problem. We present results to demonstrate that our method works very effectively.