Although high dynamic range (HDR) display has become popular recently, the legacy content such as standard dynamic range (SDR) video is still in service and needs to be properly converted on HDR display devices. Therefore, it is desirable for HDR TV sets to have the capability of automatically converting input SDR video into HDR video, which is called reverse tone mapping (RTM). In this paper, we propose a novel learning-based low-complexity RTM scheme that not only expands the suppressed dynamic ranges (DR) of the SDR videos (or images), but also effectively restores lost detail in the SDR videos. Most existing conventional RTM schemes have focused on how to expand the DR of global contrast, resulting in limitations in recovering lost detail of SDR videos. On the other hand, the recent convolutional neural network-based approaches show promising results, but they are too complex to be applied on the users' devices in practice. In this paper, our learning-based RTM scheme is computationally simple but effective in recovering lost detail. To learn the SDR-to-HDR relation, training "SDR-HDR" images are first separated into their base layer components and detail layer components by applying a guided filter. The detail layer components of the "SDR-HDR" pairs are used to train the SDR-to-HDR mapping. The mapping matrices are computed based on kernel ridge regression. In the meantime, the global contrast of the base layers is expanded by a nonlinear function that suppresses darker regions and amplifies brighter regions to fit the full DR of a target HDR display. To verify the effectiveness of our learning-based RTM scheme, we performed subjective quality assessment for images and videos. The experimental results show that our RTMscheme outperforms the existing RTM scheme with the successful restoration of lost detail in SDR images.