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Many conventional DCT based Just Noticeable Distortion (JND) models incorporate luminance adaptation (LA) effect of the human visual system (HVS). The conventional LA-JND models exploit only background luminance to estimate JND values. In this letter, we reveal that the LA effect of HVS depends not only on background luminance but also on frequency in DCT domain. In addition, we first propose a novel DCT-based LA-JND model that takes into account its frequency characteristics. From our psychophysical experiment results, we found that the LA-JND threshold exhibits quasi-parabolic shapes with lower and higher curvatures in lower and higher frequency ranges, respectively. Our subjective evaluation shows that the proposed LA-JND model yields almost invisible distortions for test images with average PSNR of 29.11 dB, which is 2.63 dB lower than the other models for comparison, showing higher consistency with real visual perception for the LA in DCT domain.