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Scenes with back-light illumination are problematic when captured with a typical LDR camera, as they result in dark regions where details are not perceivable. In this paper, we present a method that, given an LDR backlit image, outputs an image where the information that was not visible in the dark regions is recovered without losing information in the already well-exposed parts of the image. Our method has three main steps: first, a variational model is minimized using gradient descent, and the iterates of the minimization are used to obtain a set of weight maps. Second, we consider the tone-mapping framework [3J that depends on four parameters. Two different sets of parameters are learned by dividing the image in the darker and lighter parts. Then, we interpolate the two sets of parameter values in as many sets as weighting maps, and tone-map the original image with each set of parameters. Finally, we merge the new tone-mapped images depending on the weighting maps. Results show that our method outperforms current backlit image enhancement approaches both quantitatively and qualitatively.