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Low light images suffer from a low dynamic range and severe noise due to low signal-to-noise ratio (SNR). In this paper, we propose joint contrast enhancement and noise reduction of low light images via just-noticeable-difference (JND) transform. We adopt the JND transform to achieve both contrast enhancement and noise reduction based on human visual perception. First, we generate a JND map based on an the human visual system (HVS) response model from foreground and background luminance, called JND transform. Second, for base image, we perform perceptual contrast enhancement based on luminance adaptation to effectively allocate a dynamic range to each gray level while preventing under enhancement (tone distortion) and over-enhancement. Third, we refine the JND map using Weber's law, luminance adaptation and visual masking. Weber's law enhances the JND map based on the luminance variation after contrast enhancement. Luminance adaptation suppresses noise for smooth regions, while visual masking enforces detail enhancement for textural regions. Fourth, we perform inverse JND transform to generate the enhanced luma channel from the JND map and base image. Finally, we conduct chroma denoising by transferring texture information of the enhanced luma channel to the chroma channels with guided filtering. Experimental results show that the proposed method achieves both contrast enhancement and noise reduction for low light images as well as outperforms state-of-the-art methods in terms of quantitative measurements.