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A technique for film grain noise extraction, modeling and synthesis is studied and applied to high-definition video coding in this paper. Film grain noise enhances the natural appearance of pictures in high-definition video and should be preserved in coded video. However, the coding of video contents with film grain noise is expensive. In previous art, it was proposed to enhance the coding performance by extracting film grain noise from the input video at the encoder as a preprocessing step, and by resynthesizing and adding it back to the decoded video at the decoder as a postprocessing step. In a novel implementation of this approach, we first remove film grain noise from image/video with a variational denoising approach without distorting its original content. Then, we present a parametric model (consisting of a small set of parameters) to generate film grain noise that is close to the actual one in terms of a couple of observed statistical properties, such as the power spectral density and the crosschannel spectral correlation. Under this framework, the coding gain of denoised video is higher while the visual quality of the final reconstructed video is well preserved. Experimental results are provided to demonstrate the superior performance of the proposed approach.